%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN473-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:15 AM UTC 2025
% Result : Unsatisfiable 1.47s 1.63s
% Output : Proof 1.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN473-1 : TPTP v9.0.0. Released v2.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 12:40:50 EDT 2025
% 0.13/0.33 % CPUTime :
% 1.47/1.63 % SZS status Unsatisfiable
% 1.47/1.63 % SZS output start Proof
% 1.47/1.63 tff(c3_1_type, type, (
% 1.47/1.63 c3_1: $i > $o)).
% 1.47/1.63 tff(a802_type, type, (
% 1.47/1.63 a802: $i)).
% 1.47/1.63 tff(c2_1_type, type, (
% 1.47/1.63 c2_1: $i > $o)).
% 1.47/1.63 tff(a806_type, type, (
% 1.47/1.63 a806: $i)).
% 1.47/1.63 tff(c0_1_type, type, (
% 1.47/1.63 c0_1: $i > $o)).
% 1.47/1.63 tff(hskp9_type, type, (
% 1.47/1.63 hskp9: $o)).
% 1.47/1.63 tff(c1_1_type, type, (
% 1.47/1.63 c1_1: $i > $o)).
% 1.47/1.63 tff(ndr1_0_type, type, (
% 1.47/1.63 ndr1_0: $o)).
% 1.47/1.63 tff(hskp19_type, type, (
% 1.47/1.63 hskp19: $o)).
% 1.47/1.63 tff(a803_type, type, (
% 1.47/1.63 a803: $i)).
% 1.47/1.63 tff(hskp7_type, type, (
% 1.47/1.63 hskp7: $o)).
% 1.47/1.63 tff(a808_type, type, (
% 1.47/1.63 a808: $i)).
% 1.47/1.63 tff(hskp20_type, type, (
% 1.47/1.63 hskp20: $o)).
% 1.47/1.63 tff(hskp11_type, type, (
% 1.47/1.63 hskp11: $o)).
% 1.47/1.63 tff(a796_type, type, (
% 1.47/1.63 a796: $i)).
% 1.47/1.63 tff(hskp27_type, type, (
% 1.47/1.63 hskp27: $o)).
% 1.47/1.63 tff(a832_type, type, (
% 1.47/1.63 a832: $i)).
% 1.47/1.63 tff(hskp21_type, type, (
% 1.47/1.63 hskp21: $o)).
% 1.47/1.63 tff(hskp30_type, type, (
% 1.47/1.63 hskp30: $o)).
% 1.47/1.63 tff(a867_type, type, (
% 1.47/1.63 a867: $i)).
% 1.47/1.63 tff(a800_type, type, (
% 1.47/1.63 a800: $i)).
% 1.47/1.63 tff(a809_type, type, (
% 1.47/1.63 a809: $i)).
% 1.47/1.63 tff(hskp12_type, type, (
% 1.47/1.63 hskp12: $o)).
% 1.47/1.63 tff(hskp28_type, type, (
% 1.47/1.63 hskp28: $o)).
% 1.47/1.63 tff(hskp5_type, type, (
% 1.47/1.63 hskp5: $o)).
% 1.47/1.63 tff(a807_type, type, (
% 1.47/1.63 a807: $i)).
% 1.47/1.63 tff(hskp10_type, type, (
% 1.47/1.63 hskp10: $o)).
% 1.47/1.63 tff(hskp1_type, type, (
% 1.47/1.63 hskp1: $o)).
% 1.47/1.63 tff(a794_type, type, (
% 1.47/1.63 a794: $i)).
% 1.47/1.63 tff(a833_type, type, (
% 1.47/1.63 a833: $i)).
% 1.47/1.63 tff(hskp6_type, type, (
% 1.47/1.63 hskp6: $o)).
% 1.47/1.63 tff(a793_type, type, (
% 1.47/1.63 a793: $i)).
% 1.47/1.63 tff(hskp0_type, type, (
% 1.47/1.63 hskp0: $o)).
% 1.47/1.63 tff(a814_type, type, (
% 1.47/1.63 a814: $i)).
% 1.47/1.63 tff(a798_type, type, (
% 1.47/1.63 a798: $i)).
% 1.47/1.63 tff(hskp3_type, type, (
% 1.47/1.63 hskp3: $o)).
% 1.47/1.63 tff(a797_type, type, (
% 1.47/1.63 a797: $i)).
% 1.47/1.63 tff(a838_type, type, (
% 1.47/1.63 a838: $i)).
% 1.47/1.63 tff(hskp8_type, type, (
% 1.47/1.63 hskp8: $o)).
% 1.47/1.63 tff(a805_type, type, (
% 1.47/1.63 a805: $i)).
% 1.47/1.63 tff(a869_type, type, (
% 1.47/1.63 a869: $i)).
% 1.47/1.63 tff(hskp26_type, type, (
% 1.47/1.63 hskp26: $o)).
% 1.47/1.63 tff(a825_type, type, (
% 1.47/1.63 a825: $i)).
% 1.47/1.63 tff(hskp17_type, type, (
% 1.47/1.63 hskp17: $o)).
% 1.47/1.63 tff(a828_type, type, (
% 1.47/1.63 a828: $i)).
% 1.47/1.63 tff(hskp18_type, type, (
% 1.47/1.63 hskp18: $o)).
% 1.47/1.63 tff(a795_type, type, (
% 1.47/1.63 a795: $i)).
% 1.47/1.63 tff(hskp2_type, type, (
% 1.47/1.63 hskp2: $o)).
% 1.47/1.63 tff(a821_type, type, (
% 1.47/1.63 a821: $i)).
% 1.47/1.63 tff(hskp15_type, type, (
% 1.47/1.63 hskp15: $o)).
% 1.47/1.63 tff(a817_type, type, (
% 1.47/1.63 a817: $i)).
% 1.47/1.63 tff(a840_type, type, (
% 1.47/1.63 a840: $i)).
% 1.47/1.63 tff(hskp22_type, type, (
% 1.47/1.63 hskp22: $o)).
% 1.47/1.63 tff(hskp4_type, type, (
% 1.47/1.63 hskp4: $o)).
% 1.47/1.63 tff(a799_type, type, (
% 1.47/1.63 a799: $i)).
% 1.47/1.63 tff(hskp16_type, type, (
% 1.47/1.63 hskp16: $o)).
% 1.47/1.63 tff(a865_type, type, (
% 1.47/1.63 a865: $i)).
% 1.47/1.63 tff(hskp25_type, type, (
% 1.47/1.63 hskp25: $o)).
% 1.47/1.63 tff(a829_type, type, (
% 1.47/1.63 a829: $i)).
% 1.47/1.63 tff(hskp29_type, type, (
% 1.47/1.63 hskp29: $o)).
% 1.47/1.63 tff(a816_type, type, (
% 1.47/1.63 a816: $i)).
% 1.47/1.63 tff(hskp14_type, type, (
% 1.47/1.63 hskp14: $o)).
% 1.47/1.63 tff(hskp13_type, type, (
% 1.47/1.63 hskp13: $o)).
% 1.47/1.63 tff(1,plain,
% 1.47/1.63 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 1.47/1.63 inference(bind,[status(th)],[])).
% 1.47/1.63 tff(2,plain,
% 1.47/1.63 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.47/1.63 inference(quant_intro,[status(thm)],[1])).
% 1.47/1.63 tff(3,plain,
% 1.47/1.63 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(4,plain,
% 1.47/1.63 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 1.47/1.63 inference(bind,[status(th)],[])).
% 1.47/1.63 tff(5,plain,
% 1.47/1.63 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.47/1.63 inference(quant_intro,[status(thm)],[4])).
% 1.47/1.63 tff(6,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 1.47/1.63 tff(7,plain,
% 1.47/1.63 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.47/1.63 tff(8,plain,
% 1.47/1.63 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.47/1.63 tff(9,plain,(
% 1.47/1.63 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.47/1.63 inference(skolemize,[status(sab)],[8])).
% 1.47/1.63 tff(10,plain,
% 1.47/1.63 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.47/1.63 tff(11,assumption,(~hskp9), introduced(assumption)).
% 1.47/1.63 tff(12,plain,
% 1.47/1.63 (^[U: $i] : refl((hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.47/1.63 inference(bind,[status(th)],[])).
% 1.47/1.63 tff(13,plain,
% 1.47/1.63 (![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(quant_intro,[status(thm)],[12])).
% 1.47/1.63 tff(14,plain,
% 1.47/1.63 (![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(15,plain,
% 1.47/1.63 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp20) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp20) <=> (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.47/1.63 inference(bind,[status(th)],[])).
% 1.47/1.63 tff(16,plain,
% 1.47/1.63 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp20) <=> ![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(quant_intro,[status(thm)],[15])).
% 1.47/1.63 tff(17,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp9) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 1.47/1.63 tff(18,plain,
% 1.47/1.63 (![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.47/1.63 tff(19,plain,
% 1.47/1.63 (![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.47/1.63 tff(20,plain,(
% 1.47/1.63 ![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(skolemize,[status(sab)],[19])).
% 1.47/1.63 tff(21,plain,
% 1.47/1.63 (![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.47/1.63 tff(22,assumption,(~c3_1(a832)), introduced(assumption)).
% 1.47/1.63 tff(23,assumption,(hskp30), introduced(assumption)).
% 1.47/1.63 tff(24,plain,
% 1.47/1.63 (((~hskp30) | c3_1(a867)) <=> ((~hskp30) | c3_1(a867))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(25,axiom,((~hskp30) | c3_1(a867)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.47/1.63 tff(26,plain,
% 1.47/1.63 ((~hskp30) | c3_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.47/1.63 tff(27,plain,
% 1.47/1.63 ((~hskp30) | c3_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[26, 24])).
% 1.47/1.63 tff(28,plain,
% 1.47/1.63 ((~hskp30) | c3_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[27, 24])).
% 1.47/1.63 tff(29,plain,
% 1.47/1.63 ((~hskp30) | c3_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.47/1.63 tff(30,plain,
% 1.47/1.63 ((~hskp30) | c3_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[29, 24])).
% 1.47/1.63 tff(31,plain,
% 1.47/1.63 (c3_1(a867)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[30, 23])).
% 1.47/1.63 tff(32,plain,
% 1.47/1.63 (((~hskp30) | c1_1(a867)) <=> ((~hskp30) | c1_1(a867))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(33,axiom,((~hskp30) | c1_1(a867)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.47/1.63 tff(34,plain,
% 1.47/1.63 ((~hskp30) | c1_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.47/1.63 tff(35,plain,
% 1.47/1.63 ((~hskp30) | c1_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[34, 32])).
% 1.47/1.63 tff(36,plain,
% 1.47/1.63 ((~hskp30) | c1_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[35, 32])).
% 1.47/1.63 tff(37,plain,
% 1.47/1.63 ((~hskp30) | c1_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[36, 32])).
% 1.47/1.63 tff(38,plain,
% 1.47/1.63 ((~hskp30) | c1_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[37, 32])).
% 1.47/1.63 tff(39,plain,
% 1.47/1.63 (c1_1(a867)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[38, 23])).
% 1.47/1.63 tff(40,plain,
% 1.47/1.63 (((~hskp30) | c0_1(a867)) <=> ((~hskp30) | c0_1(a867))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(41,axiom,((~hskp30) | c0_1(a867)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 1.47/1.63 tff(42,plain,
% 1.47/1.63 ((~hskp30) | c0_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.47/1.63 tff(43,plain,
% 1.47/1.63 ((~hskp30) | c0_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[42, 40])).
% 1.47/1.63 tff(44,plain,
% 1.47/1.63 ((~hskp30) | c0_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[43, 40])).
% 1.47/1.63 tff(45,plain,
% 1.47/1.63 ((~hskp30) | c0_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.47/1.63 tff(46,plain,
% 1.47/1.63 ((~hskp30) | c0_1(a867)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[45, 40])).
% 1.47/1.63 tff(47,plain,
% 1.47/1.63 (c0_1(a867)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[46, 23])).
% 1.47/1.63 tff(48,assumption,(hskp9), introduced(assumption)).
% 1.47/1.63 tff(49,plain,
% 1.47/1.63 (((~hskp9) | c0_1(a806)) <=> ((~hskp9) | c0_1(a806))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(50,axiom,((~hskp9) | c0_1(a806)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.47/1.63 tff(51,plain,
% 1.47/1.63 ((~hskp9) | c0_1(a806)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.47/1.63 tff(52,plain,
% 1.47/1.63 ((~hskp9) | c0_1(a806)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[51, 49])).
% 1.47/1.63 tff(53,plain,
% 1.47/1.63 ((~hskp9) | c0_1(a806)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[52, 49])).
% 1.47/1.63 tff(54,plain,
% 1.47/1.63 ((~hskp9) | c0_1(a806)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.47/1.63 tff(55,plain,
% 1.47/1.63 ((~hskp9) | c0_1(a806)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[54, 49])).
% 1.47/1.63 tff(56,plain,
% 1.47/1.63 (c0_1(a806)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[55, 48])).
% 1.47/1.63 tff(57,assumption,(c1_1(a867)), introduced(assumption)).
% 1.47/1.63 tff(58,assumption,(c0_1(a867)), introduced(assumption)).
% 1.47/1.63 tff(59,plain,
% 1.47/1.63 (((~hskp9) | (~c3_1(a806))) <=> ((~hskp9) | (~c3_1(a806)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(60,plain,
% 1.47/1.63 (((~c3_1(a806)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a806)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(61,axiom,((~c3_1(a806)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.47/1.63 tff(62,plain,
% 1.47/1.63 ((~hskp9) | (~c3_1(a806))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.47/1.63 tff(63,plain,
% 1.47/1.63 ((~hskp9) | (~c3_1(a806))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[62, 59])).
% 1.47/1.63 tff(64,plain,
% 1.47/1.63 (~c3_1(a806)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[63, 48])).
% 1.47/1.63 tff(65,assumption,(c3_1(a867)), introduced(assumption)).
% 1.47/1.63 tff(66,plain,
% 1.47/1.63 (((~hskp9) | c1_1(a806)) <=> ((~hskp9) | c1_1(a806))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(67,axiom,((~hskp9) | c1_1(a806)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.47/1.63 tff(68,plain,
% 1.47/1.63 ((~hskp9) | c1_1(a806)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.47/1.63 tff(69,plain,
% 1.47/1.63 ((~hskp9) | c1_1(a806)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[68, 66])).
% 1.47/1.63 tff(70,plain,
% 1.47/1.63 ((~hskp9) | c1_1(a806)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[69, 66])).
% 1.47/1.63 tff(71,plain,
% 1.47/1.63 ((~hskp9) | c1_1(a806)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[70, 66])).
% 1.47/1.63 tff(72,plain,
% 1.47/1.63 ((~hskp9) | c1_1(a806)),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[71, 66])).
% 1.47/1.63 tff(73,plain,
% 1.47/1.63 (c1_1(a806)),
% 1.47/1.63 inference(unit_resolution,[status(thm)],[72, 48])).
% 1.47/1.63 tff(74,assumption,(~c2_1(a806)), introduced(assumption)).
% 1.47/1.63 tff(75,plain,
% 1.47/1.63 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 1.47/1.63 inference(bind,[status(th)],[])).
% 1.47/1.63 tff(76,plain,
% 1.47/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.63 inference(quant_intro,[status(thm)],[75])).
% 1.47/1.63 tff(77,plain,
% 1.47/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(78,plain,
% 1.47/1.63 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 1.47/1.63 inference(bind,[status(th)],[])).
% 1.47/1.63 tff(79,plain,
% 1.47/1.63 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.63 inference(quant_intro,[status(thm)],[78])).
% 1.47/1.63 tff(80,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.47/1.63 tff(81,plain,
% 1.47/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.47/1.63 tff(82,plain,
% 1.47/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[81, 77])).
% 1.47/1.63 tff(83,plain,(
% 1.47/1.63 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.63 inference(skolemize,[status(sab)],[82])).
% 1.47/1.63 tff(84,plain,
% 1.47/1.63 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 1.47/1.63 inference(modus_ponens,[status(thm)],[83, 76])).
% 1.47/1.63 tff(85,assumption,(~c3_1(a806)), introduced(assumption)).
% 1.47/1.63 tff(86,plain,
% 1.47/1.63 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 1.47/1.63 inference(bind,[status(th)],[])).
% 1.47/1.63 tff(87,plain,
% 1.47/1.63 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.47/1.63 inference(quant_intro,[status(thm)],[86])).
% 1.47/1.63 tff(88,plain,
% 1.47/1.63 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.47/1.63 inference(rewrite,[status(thm)],[])).
% 1.47/1.63 tff(89,plain,
% 1.47/1.63 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 1.47/1.64 inference(bind,[status(th)],[])).
% 1.47/1.64 tff(90,plain,
% 1.47/1.64 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.47/1.64 inference(quant_intro,[status(thm)],[89])).
% 1.47/1.64 tff(91,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.47/1.64 tff(92,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.47/1.64 tff(93,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[92, 88])).
% 1.47/1.64 tff(94,plain,(
% 1.47/1.64 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.47/1.64 inference(skolemize,[status(sab)],[93])).
% 1.47/1.64 tff(95,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[94, 87])).
% 1.47/1.64 tff(96,assumption,(c1_1(a806)), introduced(assumption)).
% 1.47/1.64 tff(97,assumption,(~ndr1_0), introduced(assumption)).
% 1.47/1.64 tff(98,plain,
% 1.47/1.64 ((ndr1_0 | (~hskp19)) <=> (ndr1_0 | (~hskp19))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(99,plain,
% 1.47/1.64 (((~hskp19) | ndr1_0) <=> (ndr1_0 | (~hskp19))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(100,axiom,((~hskp19) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause12')).
% 1.47/1.64 tff(101,plain,
% 1.47/1.64 (ndr1_0 | (~hskp19)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[100, 99])).
% 1.47/1.64 tff(102,plain,
% 1.47/1.64 (ndr1_0 | (~hskp19)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[101, 98])).
% 1.47/1.64 tff(103,plain,
% 1.47/1.64 (~hskp19),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[102, 97])).
% 1.47/1.64 tff(104,plain,
% 1.47/1.64 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(105,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 1.47/1.64 tff(106,plain,
% 1.47/1.64 ((~hskp30) | ndr1_0),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.47/1.64 tff(107,plain,
% 1.47/1.64 ((~hskp30) | ndr1_0),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[106, 104])).
% 1.47/1.64 tff(108,plain,
% 1.47/1.64 ((~hskp30) | ndr1_0),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[107, 104])).
% 1.47/1.64 tff(109,plain,
% 1.47/1.64 ((~hskp30) | ndr1_0),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[108, 104])).
% 1.47/1.64 tff(110,plain,
% 1.47/1.64 ((~hskp30) | ndr1_0),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[109, 104])).
% 1.47/1.64 tff(111,plain,
% 1.47/1.64 (~hskp30),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[110, 97])).
% 1.47/1.64 tff(112,plain,
% 1.47/1.64 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(113,plain,
% 1.47/1.64 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(114,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 1.47/1.64 tff(115,plain,
% 1.47/1.64 (ndr1_0 | (~hskp28)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.47/1.64 tff(116,plain,
% 1.47/1.64 (ndr1_0 | (~hskp28)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[115, 112])).
% 1.47/1.64 tff(117,plain,
% 1.47/1.64 (~hskp28),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[116, 97])).
% 1.47/1.64 tff(118,plain,
% 1.47/1.64 ((hskp30 | hskp28 | hskp19) <=> (hskp30 | hskp28 | hskp19)),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(119,plain,
% 1.47/1.64 (((hskp30 | hskp28) | hskp19) <=> (hskp30 | hskp28 | hskp19)),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(120,plain,
% 1.47/1.64 ((hskp30 | hskp28) <=> (hskp30 | hskp28)),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(121,plain,
% 1.47/1.64 (((hskp30 | hskp28) | hskp19) <=> ((hskp30 | hskp28) | hskp19)),
% 1.47/1.64 inference(monotonicity,[status(thm)],[120])).
% 1.47/1.64 tff(122,plain,
% 1.47/1.64 (((hskp30 | hskp28) | hskp19) <=> (hskp30 | hskp28 | hskp19)),
% 1.47/1.64 inference(transitivity,[status(thm)],[121, 119])).
% 1.47/1.64 tff(123,axiom,((hskp30 | hskp28) | hskp19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 1.47/1.64 tff(124,plain,
% 1.47/1.64 (hskp30 | hskp28 | hskp19),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.47/1.64 tff(125,plain,
% 1.47/1.64 (hskp30 | hskp28 | hskp19),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[124, 118])).
% 1.47/1.64 tff(126,plain,
% 1.47/1.64 (hskp30 | hskp28 | hskp19),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[125, 118])).
% 1.47/1.64 tff(127,plain,
% 1.47/1.64 (hskp30 | hskp28 | hskp19),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[126, 118])).
% 1.47/1.64 tff(128,plain,
% 1.47/1.64 (hskp30 | hskp28 | hskp19),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[127, 118])).
% 1.47/1.64 tff(129,plain,
% 1.47/1.64 ($false),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[128, 117, 111, 103])).
% 1.47/1.64 tff(130,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.47/1.64 tff(131,plain,
% 1.47/1.64 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c2_1(a806) | (~c1_1(a806)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(132,plain,
% 1.47/1.64 ((hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806))) <=> (hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c2_1(a806) | (~c1_1(a806)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(133,plain,
% 1.47/1.64 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c2_1(a806) | (~c1_1(a806))))),
% 1.47/1.64 inference(monotonicity,[status(thm)],[132])).
% 1.47/1.64 tff(134,plain,
% 1.47/1.64 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c2_1(a806) | (~c1_1(a806)))),
% 1.47/1.64 inference(transitivity,[status(thm)],[133, 131])).
% 1.47/1.64 tff(135,plain,
% 1.47/1.64 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))),
% 1.47/1.64 inference(quant_inst,[status(thm)],[])).
% 1.47/1.64 tff(136,plain,
% 1.47/1.64 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c2_1(a806) | (~c1_1(a806))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.47/1.64 tff(137,plain,
% 1.47/1.64 (hskp12 | c2_1(a806)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[136, 130, 58, 57, 65, 96, 85, 95])).
% 1.47/1.64 tff(138,plain,
% 1.47/1.64 (hskp12),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[137, 74])).
% 1.47/1.64 tff(139,plain,
% 1.47/1.64 (((~hskp12) | (~c0_1(a809))) <=> ((~hskp12) | (~c0_1(a809)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(140,plain,
% 1.47/1.64 (((~c0_1(a809)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a809)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(141,axiom,((~c0_1(a809)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.47/1.64 tff(142,plain,
% 1.47/1.64 ((~hskp12) | (~c0_1(a809))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[141, 140])).
% 1.47/1.64 tff(143,plain,
% 1.47/1.64 ((~hskp12) | (~c0_1(a809))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[142, 139])).
% 1.47/1.64 tff(144,plain,
% 1.47/1.64 (~c0_1(a809)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[143, 138])).
% 1.47/1.64 tff(145,assumption,(c0_1(a806)), introduced(assumption)).
% 1.47/1.64 tff(146,plain,
% 1.47/1.64 (((~hskp12) | c2_1(a809)) <=> ((~hskp12) | c2_1(a809))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(147,axiom,((~hskp12) | c2_1(a809)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.47/1.64 tff(148,plain,
% 1.47/1.64 ((~hskp12) | c2_1(a809)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.47/1.64 tff(149,plain,
% 1.47/1.64 ((~hskp12) | c2_1(a809)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[148, 146])).
% 1.47/1.64 tff(150,plain,
% 1.47/1.64 ((~hskp12) | c2_1(a809)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[149, 146])).
% 1.47/1.64 tff(151,plain,
% 1.47/1.64 ((~hskp12) | c2_1(a809)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[150, 146])).
% 1.47/1.64 tff(152,plain,
% 1.47/1.64 ((~hskp12) | c2_1(a809)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[151, 146])).
% 1.47/1.64 tff(153,plain,
% 1.47/1.64 (c2_1(a809)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[152, 138])).
% 1.47/1.64 tff(154,plain,
% 1.47/1.64 (((~hskp12) | c1_1(a809)) <=> ((~hskp12) | c1_1(a809))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(155,axiom,((~hskp12) | c1_1(a809)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.47/1.64 tff(156,plain,
% 1.47/1.64 ((~hskp12) | c1_1(a809)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.47/1.64 tff(157,plain,
% 1.47/1.64 ((~hskp12) | c1_1(a809)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[156, 154])).
% 1.47/1.64 tff(158,plain,
% 1.47/1.64 ((~hskp12) | c1_1(a809)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[157, 154])).
% 1.47/1.64 tff(159,plain,
% 1.47/1.64 ((~hskp12) | c1_1(a809)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[158, 154])).
% 1.47/1.64 tff(160,plain,
% 1.47/1.64 ((~hskp12) | c1_1(a809)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[159, 154])).
% 1.47/1.64 tff(161,plain,
% 1.47/1.64 (c1_1(a809)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[160, 138])).
% 1.47/1.64 tff(162,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a809) | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a809) | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(163,plain,
% 1.47/1.64 (((~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809))) <=> (c0_1(a809) | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(164,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a809) | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a809)) | (~c1_1(a809))))),
% 1.47/1.64 inference(monotonicity,[status(thm)],[163])).
% 1.47/1.64 tff(165,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a809) | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.47/1.64 inference(transitivity,[status(thm)],[164, 162])).
% 1.47/1.64 tff(166,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.47/1.64 inference(quant_inst,[status(thm)],[])).
% 1.47/1.64 tff(167,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a809) | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a809)) | (~c1_1(a809))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.47/1.64 tff(168,plain,
% 1.47/1.64 ($false),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[167, 130, 161, 153, 145, 96, 144, 85, 84, 74])).
% 1.47/1.64 tff(169,plain,(c2_1(a806) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a806) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a867))), inference(lemma,lemma(discharge,[]))).
% 1.47/1.64 tff(170,plain,
% 1.47/1.64 (c2_1(a806)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[169, 73, 65, 64, 58, 57, 56])).
% 1.47/1.64 tff(171,plain,
% 1.47/1.64 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.47/1.64 inference(bind,[status(th)],[])).
% 1.47/1.64 tff(172,plain,
% 1.47/1.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.47/1.64 inference(quant_intro,[status(thm)],[171])).
% 1.47/1.64 tff(173,plain,
% 1.47/1.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(174,plain,
% 1.47/1.64 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.47/1.64 inference(bind,[status(th)],[])).
% 1.47/1.64 tff(175,plain,
% 1.47/1.64 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.47/1.64 inference(quant_intro,[status(thm)],[174])).
% 1.47/1.64 tff(176,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 1.47/1.64 tff(177,plain,
% 1.47/1.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.47/1.64 tff(178,plain,
% 1.47/1.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[177, 173])).
% 1.47/1.64 tff(179,plain,(
% 1.47/1.64 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.47/1.64 inference(skolemize,[status(sab)],[178])).
% 1.47/1.64 tff(180,plain,
% 1.47/1.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[179, 172])).
% 1.47/1.64 tff(181,plain,
% 1.47/1.64 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 1.47/1.64 inference(bind,[status(th)],[])).
% 1.47/1.64 tff(182,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.47/1.64 inference(quant_intro,[status(thm)],[181])).
% 1.47/1.64 tff(183,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(184,plain,
% 1.47/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.47/1.64 inference(bind,[status(th)],[])).
% 1.47/1.64 tff(185,plain,
% 1.47/1.64 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.47/1.64 inference(quant_intro,[status(thm)],[184])).
% 1.47/1.64 tff(186,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.47/1.64 tff(187,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[186, 185])).
% 1.47/1.64 tff(188,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[187, 183])).
% 1.47/1.64 tff(189,plain,(
% 1.47/1.64 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.47/1.64 inference(skolemize,[status(sab)],[188])).
% 1.47/1.64 tff(190,plain,
% 1.47/1.64 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[189, 182])).
% 1.47/1.64 tff(191,plain,
% 1.47/1.64 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(192,plain,
% 1.47/1.64 ((hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806))) <=> (hskp5 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(193,plain,
% 1.47/1.64 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806))))),
% 1.47/1.64 inference(monotonicity,[status(thm)],[192])).
% 1.47/1.64 tff(194,plain,
% 1.47/1.64 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.47/1.64 inference(transitivity,[status(thm)],[193, 191])).
% 1.47/1.64 tff(195,plain,
% 1.47/1.64 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806)))),
% 1.47/1.64 inference(quant_inst,[status(thm)],[])).
% 1.47/1.64 tff(196,plain,
% 1.47/1.64 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a806) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[195, 194])).
% 1.47/1.64 tff(197,plain,
% 1.47/1.64 (hskp5),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[196, 130, 58, 57, 65, 56, 64, 190, 170])).
% 1.47/1.64 tff(198,plain,
% 1.47/1.64 (((~hskp5) | (~c0_1(a800))) <=> ((~hskp5) | (~c0_1(a800)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(199,plain,
% 1.47/1.64 (((~c0_1(a800)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a800)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(200,axiom,((~c0_1(a800)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.47/1.64 tff(201,plain,
% 1.47/1.64 ((~hskp5) | (~c0_1(a800))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.47/1.64 tff(202,plain,
% 1.47/1.64 ((~hskp5) | (~c0_1(a800))),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[201, 198])).
% 1.47/1.64 tff(203,plain,
% 1.47/1.64 (~c0_1(a800)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[202, 197])).
% 1.47/1.64 tff(204,plain,
% 1.47/1.64 (((~hskp5) | c3_1(a800)) <=> ((~hskp5) | c3_1(a800))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(205,axiom,((~hskp5) | c3_1(a800)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.47/1.64 tff(206,plain,
% 1.47/1.64 ((~hskp5) | c3_1(a800)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[205, 204])).
% 1.47/1.64 tff(207,plain,
% 1.47/1.64 ((~hskp5) | c3_1(a800)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[206, 204])).
% 1.47/1.64 tff(208,plain,
% 1.47/1.64 ((~hskp5) | c3_1(a800)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[207, 204])).
% 1.47/1.64 tff(209,plain,
% 1.47/1.64 ((~hskp5) | c3_1(a800)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.47/1.64 tff(210,plain,
% 1.47/1.64 ((~hskp5) | c3_1(a800)),
% 1.47/1.64 inference(modus_ponens,[status(thm)],[209, 204])).
% 1.47/1.64 tff(211,plain,
% 1.47/1.64 (c3_1(a800)),
% 1.47/1.64 inference(unit_resolution,[status(thm)],[210, 197])).
% 1.47/1.64 tff(212,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)) | (~c2_1(a800)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)) | (~c2_1(a800)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(213,plain,
% 1.47/1.64 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a800) | (~c3_1(a800)) | (~c2_1(a800))) <=> (c0_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)) | (~c2_1(a800)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 1.47/1.64 inference(rewrite,[status(thm)],[])).
% 1.47/1.64 tff(214,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a800) | (~c3_1(a800)) | (~c2_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)) | (~c2_1(a800)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806))))),
% 1.47/1.64 inference(monotonicity,[status(thm)],[213])).
% 1.47/1.64 tff(215,plain,
% 1.47/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a800) | (~c3_1(a800)) | (~c2_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)) | (~c2_1(a800)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 1.47/1.64 inference(transitivity,[status(thm)],[214, 212])).
% 1.47/1.64 tff(216,plain,
% 1.47/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a800) | (~c3_1(a800)) | (~c2_1(a800)))),
% 1.47/1.65 inference(quant_inst,[status(thm)],[])).
% 1.47/1.65 tff(217,plain,
% 1.47/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)) | (~c2_1(a800)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[216, 215])).
% 1.47/1.65 tff(218,plain,
% 1.47/1.65 (~c2_1(a800)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[217, 130, 58, 57, 65, 56, 73, 211, 203, 180, 170])).
% 1.47/1.65 tff(219,plain,
% 1.47/1.65 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(220,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[219])).
% 1.47/1.65 tff(221,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(222,plain,
% 1.47/1.65 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(223,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[222])).
% 1.47/1.65 tff(224,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 1.47/1.65 tff(225,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.47/1.65 tff(226,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[225, 221])).
% 1.47/1.65 tff(227,plain,(
% 1.47/1.65 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.65 inference(skolemize,[status(sab)],[226])).
% 1.47/1.65 tff(228,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[227, 220])).
% 1.47/1.65 tff(229,plain,
% 1.47/1.65 (((~hskp5) | (~c1_1(a800))) <=> ((~hskp5) | (~c1_1(a800)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(230,plain,
% 1.47/1.65 (((~c1_1(a800)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a800)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(231,axiom,((~c1_1(a800)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.47/1.65 tff(232,plain,
% 1.47/1.65 ((~hskp5) | (~c1_1(a800))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[231, 230])).
% 1.47/1.65 tff(233,plain,
% 1.47/1.65 ((~hskp5) | (~c1_1(a800))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[232, 229])).
% 1.47/1.65 tff(234,plain,
% 1.47/1.65 (~c1_1(a800)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[233, 197])).
% 1.47/1.65 tff(235,plain,
% 1.47/1.65 (^[U: $i] : refl((hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(236,plain,
% 1.47/1.65 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[235])).
% 1.47/1.65 tff(237,plain,
% 1.47/1.65 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(238,plain,
% 1.47/1.65 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp10) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp10))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp10) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp10) <=> (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(239,plain,
% 1.47/1.65 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp10) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[238])).
% 1.47/1.65 tff(240,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.47/1.65 tff(241,plain,
% 1.47/1.65 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[240, 239])).
% 1.47/1.65 tff(242,plain,
% 1.47/1.65 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[241, 237])).
% 1.47/1.65 tff(243,plain,(
% 1.47/1.65 ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.47/1.65 inference(skolemize,[status(sab)],[242])).
% 1.47/1.65 tff(244,plain,
% 1.47/1.65 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[243, 236])).
% 1.47/1.65 tff(245,assumption,(hskp1), introduced(assumption)).
% 1.47/1.65 tff(246,plain,
% 1.47/1.65 (((~hskp1) | (~c2_1(a794))) <=> ((~hskp1) | (~c2_1(a794)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(247,plain,
% 1.47/1.65 (((~c2_1(a794)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a794)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(248,axiom,((~c2_1(a794)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.47/1.65 tff(249,plain,
% 1.47/1.65 ((~hskp1) | (~c2_1(a794))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[248, 247])).
% 1.47/1.65 tff(250,plain,
% 1.47/1.65 ((~hskp1) | (~c2_1(a794))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[249, 246])).
% 1.47/1.65 tff(251,plain,
% 1.47/1.65 (~c2_1(a794)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[250, 245])).
% 1.47/1.65 tff(252,plain,
% 1.47/1.65 (((~hskp1) | c3_1(a794)) <=> ((~hskp1) | c3_1(a794))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(253,axiom,((~hskp1) | c3_1(a794)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.47/1.65 tff(254,plain,
% 1.47/1.65 ((~hskp1) | c3_1(a794)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[253, 252])).
% 1.47/1.65 tff(255,plain,
% 1.47/1.65 ((~hskp1) | c3_1(a794)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[254, 252])).
% 1.47/1.65 tff(256,plain,
% 1.47/1.65 ((~hskp1) | c3_1(a794)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[255, 252])).
% 1.47/1.65 tff(257,plain,
% 1.47/1.65 ((~hskp1) | c3_1(a794)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[256, 252])).
% 1.47/1.65 tff(258,plain,
% 1.47/1.65 ((~hskp1) | c3_1(a794)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[257, 252])).
% 1.47/1.65 tff(259,plain,
% 1.47/1.65 (c3_1(a794)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[258, 245])).
% 1.47/1.65 tff(260,plain,
% 1.47/1.65 (((~hskp1) | (~c0_1(a794))) <=> ((~hskp1) | (~c0_1(a794)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(261,plain,
% 1.47/1.65 (((~c0_1(a794)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a794)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(262,axiom,((~c0_1(a794)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.47/1.65 tff(263,plain,
% 1.47/1.65 ((~hskp1) | (~c0_1(a794))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[262, 261])).
% 1.47/1.65 tff(264,plain,
% 1.47/1.65 ((~hskp1) | (~c0_1(a794))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[263, 260])).
% 1.47/1.65 tff(265,plain,
% 1.47/1.65 (~c0_1(a794)),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[264, 245])).
% 1.47/1.65 tff(266,plain,
% 1.47/1.65 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(267,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[266])).
% 1.47/1.65 tff(268,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(269,plain,
% 1.47/1.65 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(270,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[269])).
% 1.47/1.65 tff(271,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 1.47/1.65 tff(272,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[271, 270])).
% 1.47/1.65 tff(273,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[272, 268])).
% 1.47/1.65 tff(274,plain,(
% 1.47/1.65 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.47/1.65 inference(skolemize,[status(sab)],[273])).
% 1.47/1.65 tff(275,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[274, 267])).
% 1.47/1.65 tff(276,assumption,(~c2_1(a833)), introduced(assumption)).
% 1.47/1.65 tff(277,assumption,(~c3_1(a833)), introduced(assumption)).
% 1.47/1.65 tff(278,plain,
% 1.47/1.65 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(279,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[278])).
% 1.47/1.65 tff(280,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(281,plain,
% 1.47/1.65 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(282,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[281])).
% 1.47/1.65 tff(283,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.47/1.65 tff(284,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[283, 282])).
% 1.47/1.65 tff(285,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[284, 280])).
% 1.47/1.65 tff(286,plain,(
% 1.47/1.65 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.47/1.65 inference(skolemize,[status(sab)],[285])).
% 1.47/1.65 tff(287,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[286, 279])).
% 1.47/1.65 tff(288,assumption,(~c0_1(a833)), introduced(assumption)).
% 1.47/1.65 tff(289,assumption,(~c1_1(a832)), introduced(assumption)).
% 1.47/1.65 tff(290,plain,
% 1.47/1.65 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(291,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[290])).
% 1.47/1.65 tff(292,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(293,plain,
% 1.47/1.65 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(294,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[293])).
% 1.47/1.65 tff(295,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.47/1.65 tff(296,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[295, 294])).
% 1.47/1.65 tff(297,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[296, 292])).
% 1.47/1.65 tff(298,plain,(
% 1.47/1.65 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.65 inference(skolemize,[status(sab)],[297])).
% 1.47/1.65 tff(299,plain,
% 1.47/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[298, 291])).
% 1.47/1.65 tff(300,assumption,(~c1_1(a833)), introduced(assumption)).
% 1.47/1.65 tff(301,plain,
% 1.47/1.65 (((~hskp20) | c1_1(a833)) <=> ((~hskp20) | c1_1(a833))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(302,axiom,((~hskp20) | c1_1(a833)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.47/1.65 tff(303,plain,
% 1.47/1.65 ((~hskp20) | c1_1(a833)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[302, 301])).
% 1.47/1.65 tff(304,plain,
% 1.47/1.65 ((~hskp20) | c1_1(a833)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[303, 301])).
% 1.47/1.65 tff(305,plain,
% 1.47/1.65 ((~hskp20) | c1_1(a833)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[304, 301])).
% 1.47/1.65 tff(306,plain,
% 1.47/1.65 ((~hskp20) | c1_1(a833)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[305, 301])).
% 1.47/1.65 tff(307,plain,
% 1.47/1.65 ((~hskp20) | c1_1(a833)),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[306, 301])).
% 1.47/1.65 tff(308,plain,
% 1.47/1.65 (~hskp20),
% 1.47/1.65 inference(unit_resolution,[status(thm)],[307, 300])).
% 1.47/1.65 tff(309,assumption,(~hskp30), introduced(assumption)).
% 1.47/1.65 tff(310,assumption,(~hskp20), introduced(assumption)).
% 1.47/1.65 tff(311,plain,
% 1.47/1.65 (^[U: $i] : refl((hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(312,plain,
% 1.47/1.65 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[311])).
% 1.47/1.65 tff(313,plain,
% 1.47/1.65 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.65 inference(rewrite,[status(thm)],[])).
% 1.47/1.65 tff(314,plain,
% 1.47/1.65 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) <=> (hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20) <=> ((hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp30 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(315,plain,
% 1.47/1.65 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20) <=> ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[314])).
% 1.47/1.65 tff(316,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp30) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.47/1.65 tff(317,plain,
% 1.47/1.65 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[316, 315])).
% 1.47/1.65 tff(318,plain,
% 1.47/1.65 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[317, 313])).
% 1.47/1.65 tff(319,plain,(
% 1.47/1.65 ![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.65 inference(skolemize,[status(sab)],[318])).
% 1.47/1.65 tff(320,plain,
% 1.47/1.65 (![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.65 inference(modus_ponens,[status(thm)],[319, 312])).
% 1.47/1.65 tff(321,assumption,(~hskp28), introduced(assumption)).
% 1.47/1.65 tff(322,assumption,(~c2_1(a867)), introduced(assumption)).
% 1.47/1.65 tff(323,plain,
% 1.47/1.65 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.47/1.65 inference(bind,[status(th)],[])).
% 1.47/1.65 tff(324,plain,
% 1.47/1.65 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.65 inference(quant_intro,[status(thm)],[323])).
% 1.47/1.65 tff(325,plain,
% 1.47/1.65 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(326,plain,
% 1.47/1.66 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.47/1.66 inference(bind,[status(th)],[])).
% 1.47/1.66 tff(327,plain,
% 1.47/1.66 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.66 inference(quant_intro,[status(thm)],[326])).
% 1.47/1.66 tff(328,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.47/1.66 tff(329,plain,
% 1.47/1.66 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[328, 327])).
% 1.47/1.66 tff(330,plain,
% 1.47/1.66 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[329, 325])).
% 1.47/1.66 tff(331,plain,(
% 1.47/1.66 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.66 inference(skolemize,[status(sab)],[330])).
% 1.47/1.66 tff(332,plain,
% 1.47/1.66 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[331, 324])).
% 1.47/1.66 tff(333,plain,
% 1.47/1.66 (hskp19),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[128, 309, 321])).
% 1.47/1.66 tff(334,plain,
% 1.47/1.66 (((~hskp19) | c2_1(a832)) <=> ((~hskp19) | c2_1(a832))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(335,axiom,((~hskp19) | c2_1(a832)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.47/1.66 tff(336,plain,
% 1.47/1.66 ((~hskp19) | c2_1(a832)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[335, 334])).
% 1.47/1.66 tff(337,plain,
% 1.47/1.66 ((~hskp19) | c2_1(a832)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[336, 334])).
% 1.47/1.66 tff(338,plain,
% 1.47/1.66 ((~hskp19) | c2_1(a832)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[337, 334])).
% 1.47/1.66 tff(339,plain,
% 1.47/1.66 ((~hskp19) | c2_1(a832)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[338, 334])).
% 1.47/1.66 tff(340,plain,
% 1.47/1.66 ((~hskp19) | c2_1(a832)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[339, 334])).
% 1.47/1.66 tff(341,plain,
% 1.47/1.66 (c2_1(a832)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[340, 333])).
% 1.47/1.66 tff(342,plain,
% 1.47/1.66 (((~hskp19) | (~c3_1(a832))) <=> ((~hskp19) | (~c3_1(a832)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(343,plain,
% 1.47/1.66 (((~c3_1(a832)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a832)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(344,axiom,((~c3_1(a832)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.47/1.66 tff(345,plain,
% 1.47/1.66 ((~hskp19) | (~c3_1(a832))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[344, 343])).
% 1.47/1.66 tff(346,plain,
% 1.47/1.66 ((~hskp19) | (~c3_1(a832))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[345, 342])).
% 1.47/1.66 tff(347,plain,
% 1.47/1.66 (~c3_1(a832)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[346, 333])).
% 1.47/1.66 tff(348,plain,
% 1.47/1.66 (((~hskp19) | (~c1_1(a832))) <=> ((~hskp19) | (~c1_1(a832)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(349,plain,
% 1.47/1.66 (((~c1_1(a832)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a832)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(350,axiom,((~c1_1(a832)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.47/1.66 tff(351,plain,
% 1.47/1.66 ((~hskp19) | (~c1_1(a832))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[350, 349])).
% 1.47/1.66 tff(352,plain,
% 1.47/1.66 ((~hskp19) | (~c1_1(a832))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[351, 348])).
% 1.47/1.66 tff(353,plain,
% 1.47/1.66 (~c1_1(a832)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[352, 333])).
% 1.47/1.66 tff(354,plain,
% 1.47/1.66 (^[U: $i] : refl((hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))),
% 1.47/1.66 inference(bind,[status(th)],[])).
% 1.47/1.66 tff(355,plain,
% 1.47/1.66 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.47/1.66 inference(quant_intro,[status(thm)],[354])).
% 1.47/1.66 tff(356,plain,
% 1.47/1.66 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(357,plain,
% 1.47/1.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp27))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp28) <=> ((hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp28))), rewrite(((hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp28) <=> (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp28) <=> (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))))),
% 1.47/1.66 inference(bind,[status(th)],[])).
% 1.47/1.66 tff(358,plain,
% 1.47/1.66 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp28) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.47/1.66 inference(quant_intro,[status(thm)],[357])).
% 1.47/1.66 tff(359,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.47/1.66 tff(360,plain,
% 1.47/1.66 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.47/1.66 tff(361,plain,
% 1.47/1.66 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[360, 356])).
% 1.47/1.66 tff(362,plain,(
% 1.47/1.66 ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.47/1.66 inference(skolemize,[status(sab)],[361])).
% 1.47/1.66 tff(363,plain,
% 1.47/1.66 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[362, 355])).
% 1.47/1.66 tff(364,assumption,(~hskp27), introduced(assumption)).
% 1.47/1.66 tff(365,plain,
% 1.47/1.66 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp27 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(366,plain,
% 1.47/1.66 ((hskp28 | hskp27 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832)) <=> (hskp28 | hskp27 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(367,plain,
% 1.47/1.66 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832)))),
% 1.47/1.66 inference(monotonicity,[status(thm)],[366])).
% 1.47/1.66 tff(368,plain,
% 1.47/1.66 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp27 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 1.47/1.66 inference(transitivity,[status(thm)],[367, 365])).
% 1.47/1.66 tff(369,plain,
% 1.47/1.66 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832))),
% 1.47/1.66 inference(quant_inst,[status(thm)],[])).
% 1.47/1.66 tff(370,plain,
% 1.47/1.66 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp27 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[369, 368])).
% 1.47/1.66 tff(371,plain,
% 1.47/1.66 (hskp27 | c0_1(a832)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[370, 130, 321, 289, 22, 363])).
% 1.47/1.66 tff(372,plain,
% 1.47/1.66 (c0_1(a832)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[371, 364])).
% 1.47/1.66 tff(373,plain,
% 1.47/1.66 ((hskp28 | hskp27 | hskp21) <=> (hskp28 | hskp27 | hskp21)),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(374,plain,
% 1.47/1.66 (((hskp27 | hskp21) | hskp28) <=> (hskp28 | hskp27 | hskp21)),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(375,plain,
% 1.47/1.66 ((hskp27 | hskp21) <=> (hskp27 | hskp21)),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(376,plain,
% 1.47/1.66 (((hskp27 | hskp21) | hskp28) <=> ((hskp27 | hskp21) | hskp28)),
% 1.47/1.66 inference(monotonicity,[status(thm)],[375])).
% 1.47/1.66 tff(377,plain,
% 1.47/1.66 (((hskp27 | hskp21) | hskp28) <=> (hskp28 | hskp27 | hskp21)),
% 1.47/1.66 inference(transitivity,[status(thm)],[376, 374])).
% 1.47/1.66 tff(378,axiom,((hskp27 | hskp21) | hskp28), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.47/1.66 tff(379,plain,
% 1.47/1.66 (hskp28 | hskp27 | hskp21),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[378, 377])).
% 1.47/1.66 tff(380,plain,
% 1.47/1.66 (hskp28 | hskp27 | hskp21),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[379, 373])).
% 1.47/1.66 tff(381,plain,
% 1.47/1.66 (hskp28 | hskp27 | hskp21),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[380, 373])).
% 1.47/1.66 tff(382,plain,
% 1.47/1.66 (hskp28 | hskp27 | hskp21),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[381, 373])).
% 1.47/1.66 tff(383,plain,
% 1.47/1.66 (hskp28 | hskp27 | hskp21),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[382, 373])).
% 1.47/1.66 tff(384,plain,
% 1.47/1.66 (hskp21),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[383, 364, 321])).
% 1.47/1.66 tff(385,plain,
% 1.47/1.66 (((~hskp21) | (~c2_1(a838))) <=> ((~hskp21) | (~c2_1(a838)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(386,plain,
% 1.47/1.66 (((~c2_1(a838)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a838)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(387,axiom,((~c2_1(a838)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.47/1.66 tff(388,plain,
% 1.47/1.66 ((~hskp21) | (~c2_1(a838))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[387, 386])).
% 1.47/1.66 tff(389,plain,
% 1.47/1.66 ((~hskp21) | (~c2_1(a838))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[388, 385])).
% 1.47/1.66 tff(390,plain,
% 1.47/1.66 (~c2_1(a838)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[389, 384])).
% 1.47/1.66 tff(391,assumption,(c2_1(a832)), introduced(assumption)).
% 1.47/1.66 tff(392,plain,
% 1.47/1.66 (((~hskp21) | c3_1(a838)) <=> ((~hskp21) | c3_1(a838))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(393,axiom,((~hskp21) | c3_1(a838)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.47/1.66 tff(394,plain,
% 1.47/1.66 ((~hskp21) | c3_1(a838)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[393, 392])).
% 1.47/1.66 tff(395,plain,
% 1.47/1.66 ((~hskp21) | c3_1(a838)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[394, 392])).
% 1.47/1.66 tff(396,plain,
% 1.47/1.66 ((~hskp21) | c3_1(a838)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[395, 392])).
% 1.47/1.66 tff(397,plain,
% 1.47/1.66 ((~hskp21) | c3_1(a838)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[396, 392])).
% 1.47/1.66 tff(398,plain,
% 1.47/1.66 ((~hskp21) | c3_1(a838)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[397, 392])).
% 1.47/1.66 tff(399,plain,
% 1.47/1.66 (c3_1(a838)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[398, 384])).
% 1.47/1.66 tff(400,plain,
% 1.47/1.66 (((~hskp21) | c0_1(a838)) <=> ((~hskp21) | c0_1(a838))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(401,axiom,((~hskp21) | c0_1(a838)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.47/1.66 tff(402,plain,
% 1.47/1.66 ((~hskp21) | c0_1(a838)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[401, 400])).
% 1.47/1.66 tff(403,plain,
% 1.47/1.66 ((~hskp21) | c0_1(a838)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[402, 400])).
% 1.47/1.66 tff(404,plain,
% 1.47/1.66 ((~hskp21) | c0_1(a838)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[403, 400])).
% 1.47/1.66 tff(405,plain,
% 1.47/1.66 ((~hskp21) | c0_1(a838)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[404, 400])).
% 1.47/1.66 tff(406,plain,
% 1.47/1.66 ((~hskp21) | c0_1(a838)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[405, 400])).
% 1.47/1.66 tff(407,plain,
% 1.47/1.66 (c0_1(a838)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[406, 384])).
% 1.47/1.66 tff(408,assumption,(c0_1(a832)), introduced(assumption)).
% 1.47/1.66 tff(409,assumption,(hskp8), introduced(assumption)).
% 1.47/1.66 tff(410,plain,
% 1.47/1.66 (((~hskp8) | (~c3_1(a805))) <=> ((~hskp8) | (~c3_1(a805)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(411,plain,
% 1.47/1.66 (((~c3_1(a805)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a805)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(412,axiom,((~c3_1(a805)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.47/1.66 tff(413,plain,
% 1.47/1.66 ((~hskp8) | (~c3_1(a805))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[412, 411])).
% 1.47/1.66 tff(414,plain,
% 1.47/1.66 ((~hskp8) | (~c3_1(a805))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[413, 410])).
% 1.47/1.66 tff(415,plain,
% 1.47/1.66 (~c3_1(a805)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[414, 409])).
% 1.47/1.66 tff(416,plain,
% 1.47/1.66 (((~hskp8) | (~c2_1(a805))) <=> ((~hskp8) | (~c2_1(a805)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(417,plain,
% 1.47/1.66 (((~c2_1(a805)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a805)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(418,axiom,((~c2_1(a805)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.47/1.66 tff(419,plain,
% 1.47/1.66 ((~hskp8) | (~c2_1(a805))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.47/1.66 tff(420,plain,
% 1.47/1.66 ((~hskp8) | (~c2_1(a805))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[419, 416])).
% 1.47/1.66 tff(421,plain,
% 1.47/1.66 (~c2_1(a805)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[420, 409])).
% 1.47/1.66 tff(422,assumption,(~c2_1(a838)), introduced(assumption)).
% 1.47/1.66 tff(423,plain,
% 1.47/1.66 (((~hskp8) | c1_1(a805)) <=> ((~hskp8) | c1_1(a805))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(424,axiom,((~hskp8) | c1_1(a805)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.47/1.66 tff(425,plain,
% 1.47/1.66 ((~hskp8) | c1_1(a805)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[424, 423])).
% 1.47/1.66 tff(426,plain,
% 1.47/1.66 ((~hskp8) | c1_1(a805)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[425, 423])).
% 1.47/1.66 tff(427,plain,
% 1.47/1.66 ((~hskp8) | c1_1(a805)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[426, 423])).
% 1.47/1.66 tff(428,plain,
% 1.47/1.66 ((~hskp8) | c1_1(a805)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[427, 423])).
% 1.47/1.66 tff(429,plain,
% 1.47/1.66 ((~hskp8) | c1_1(a805)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[428, 423])).
% 1.47/1.66 tff(430,plain,
% 1.47/1.66 (c1_1(a805)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[429, 409])).
% 1.47/1.66 tff(431,assumption,(c3_1(a838)), introduced(assumption)).
% 1.47/1.66 tff(432,assumption,(c0_1(a838)), introduced(assumption)).
% 1.47/1.66 tff(433,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c3_1(a832) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c3_1(a832) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(434,plain,
% 1.47/1.66 (((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c2_1(a838) | c3_1(a832) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(435,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c3_1(a832) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 1.47/1.66 inference(monotonicity,[status(thm)],[434])).
% 1.47/1.66 tff(436,plain,
% 1.47/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c3_1(a832) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.47/1.66 inference(transitivity,[status(thm)],[435, 433])).
% 1.47/1.66 tff(437,plain,
% 1.47/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 1.47/1.66 inference(quant_inst,[status(thm)],[])).
% 1.47/1.66 tff(438,plain,
% 1.47/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c3_1(a832) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a838)) | (~c0_1(a838))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[437, 436])).
% 1.47/1.66 tff(439,plain,
% 1.47/1.66 ($false),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[438, 130, 432, 431, 391, 430, 422, 22, 421, 415, 299, 408])).
% 1.47/1.66 tff(440,plain,((~hskp8) | (~c0_1(a838)) | (~c3_1(a838)) | (~c2_1(a832)) | c2_1(a838) | c3_1(a832) | (~c0_1(a832))), inference(lemma,lemma(discharge,[]))).
% 1.47/1.66 tff(441,plain,
% 1.47/1.66 (~hskp8),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[440, 407, 399, 391, 390, 22, 372])).
% 1.47/1.66 tff(442,plain,
% 1.47/1.66 ((hskp28 | hskp10 | hskp8) <=> (hskp28 | hskp10 | hskp8)),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(443,plain,
% 1.47/1.66 (((hskp28 | hskp8) | hskp10) <=> (hskp28 | hskp10 | hskp8)),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(444,axiom,((hskp28 | hskp8) | hskp10), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 1.47/1.66 tff(445,plain,
% 1.47/1.66 (hskp28 | hskp10 | hskp8),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[444, 443])).
% 1.47/1.66 tff(446,plain,
% 1.47/1.66 (hskp28 | hskp10 | hskp8),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[445, 442])).
% 1.47/1.66 tff(447,plain,
% 1.47/1.66 (hskp28 | hskp10 | hskp8),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[446, 442])).
% 1.47/1.66 tff(448,plain,
% 1.47/1.66 (hskp28 | hskp10 | hskp8),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[447, 442])).
% 1.47/1.66 tff(449,plain,
% 1.47/1.66 (hskp28 | hskp10 | hskp8),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[448, 442])).
% 1.47/1.66 tff(450,plain,
% 1.47/1.66 (hskp10),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[449, 441, 321])).
% 1.47/1.66 tff(451,plain,
% 1.47/1.66 (((~hskp10) | (~c3_1(a807))) <=> ((~hskp10) | (~c3_1(a807)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(452,plain,
% 1.47/1.66 (((~c3_1(a807)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a807)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(453,axiom,((~c3_1(a807)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.47/1.66 tff(454,plain,
% 1.47/1.66 ((~hskp10) | (~c3_1(a807))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.47/1.66 tff(455,plain,
% 1.47/1.66 ((~hskp10) | (~c3_1(a807))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[454, 451])).
% 1.47/1.66 tff(456,plain,
% 1.47/1.66 (~c3_1(a807)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[455, 450])).
% 1.47/1.66 tff(457,plain,
% 1.47/1.66 (((~hskp10) | (~c0_1(a807))) <=> ((~hskp10) | (~c0_1(a807)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(458,plain,
% 1.47/1.66 (((~c0_1(a807)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a807)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(459,axiom,((~c0_1(a807)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.47/1.66 tff(460,plain,
% 1.47/1.66 ((~hskp10) | (~c0_1(a807))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[459, 458])).
% 1.47/1.66 tff(461,plain,
% 1.47/1.66 ((~hskp10) | (~c0_1(a807))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[460, 457])).
% 1.47/1.66 tff(462,plain,
% 1.47/1.66 (~c0_1(a807)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[461, 450])).
% 1.47/1.66 tff(463,plain,
% 1.47/1.66 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | c0_1(a807) | c3_1(a807) | (~ndr1_0) | c1_1(a807))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp27 | c0_1(a807) | c3_1(a807) | (~ndr1_0) | c1_1(a807))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(464,plain,
% 1.47/1.66 ((hskp28 | hskp27 | (~ndr1_0) | c1_1(a807) | c0_1(a807) | c3_1(a807)) <=> (hskp28 | hskp27 | c0_1(a807) | c3_1(a807) | (~ndr1_0) | c1_1(a807))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(465,plain,
% 1.47/1.66 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | (~ndr1_0) | c1_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | c0_1(a807) | c3_1(a807) | (~ndr1_0) | c1_1(a807)))),
% 1.47/1.66 inference(monotonicity,[status(thm)],[464])).
% 1.47/1.66 tff(466,plain,
% 1.47/1.66 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | (~ndr1_0) | c1_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp27 | c0_1(a807) | c3_1(a807) | (~ndr1_0) | c1_1(a807))),
% 1.47/1.66 inference(transitivity,[status(thm)],[465, 463])).
% 1.47/1.66 tff(467,plain,
% 1.47/1.66 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp27 | (~ndr1_0) | c1_1(a807) | c0_1(a807) | c3_1(a807))),
% 1.47/1.66 inference(quant_inst,[status(thm)],[])).
% 1.47/1.66 tff(468,plain,
% 1.47/1.66 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp27 | c0_1(a807) | c3_1(a807) | (~ndr1_0) | c1_1(a807)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[467, 466])).
% 1.47/1.66 tff(469,plain,
% 1.47/1.66 (c1_1(a807)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[468, 130, 321, 364, 462, 456, 363])).
% 1.47/1.66 tff(470,plain,
% 1.47/1.66 (^[U: $i] : refl((hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.47/1.66 inference(bind,[status(th)],[])).
% 1.47/1.66 tff(471,plain,
% 1.47/1.66 (![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(quant_intro,[status(thm)],[470])).
% 1.47/1.66 tff(472,plain,
% 1.47/1.66 (![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(473,plain,
% 1.47/1.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp3) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp3))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp3) <=> (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.47/1.66 inference(bind,[status(th)],[])).
% 1.47/1.66 tff(474,plain,
% 1.47/1.66 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp3) <=> ![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(quant_intro,[status(thm)],[473])).
% 1.47/1.66 tff(475,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.47/1.66 tff(476,plain,
% 1.47/1.66 (![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[475, 474])).
% 1.47/1.66 tff(477,plain,
% 1.47/1.66 (![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[476, 472])).
% 1.47/1.66 tff(478,plain,(
% 1.47/1.66 ![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(skolemize,[status(sab)],[477])).
% 1.47/1.66 tff(479,plain,
% 1.47/1.66 (![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[478, 471])).
% 1.47/1.66 tff(480,plain,
% 1.47/1.66 (((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp3 | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp3 | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(481,plain,
% 1.47/1.66 ((hskp27 | hskp3 | (~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832))) <=> (hskp27 | hskp3 | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(482,plain,
% 1.47/1.66 (((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp3 | (~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp3 | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832))))),
% 1.47/1.66 inference(monotonicity,[status(thm)],[481])).
% 1.47/1.66 tff(483,plain,
% 1.47/1.66 (((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp3 | (~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp3 | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.47/1.66 inference(transitivity,[status(thm)],[482, 480])).
% 1.47/1.66 tff(484,plain,
% 1.47/1.66 ((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp27 | hskp3 | (~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.47/1.66 inference(quant_inst,[status(thm)],[])).
% 1.47/1.66 tff(485,plain,
% 1.47/1.66 ((~![U: $i] : (hskp27 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp27 | hskp3 | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[484, 483])).
% 1.47/1.66 tff(486,plain,
% 1.47/1.66 (hskp27 | hskp3 | (~c0_1(a832))),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[485, 130, 391, 22, 479])).
% 1.47/1.66 tff(487,plain,
% 1.47/1.66 (hskp3),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[486, 372, 364])).
% 1.47/1.66 tff(488,plain,
% 1.47/1.66 (((~hskp3) | (~c3_1(a798))) <=> ((~hskp3) | (~c3_1(a798)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(489,plain,
% 1.47/1.66 (((~c3_1(a798)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a798)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(490,axiom,((~c3_1(a798)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.47/1.66 tff(491,plain,
% 1.47/1.66 ((~hskp3) | (~c3_1(a798))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.47/1.66 tff(492,plain,
% 1.47/1.66 ((~hskp3) | (~c3_1(a798))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[491, 488])).
% 1.47/1.66 tff(493,plain,
% 1.47/1.66 (~c3_1(a798)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[492, 487])).
% 1.47/1.66 tff(494,plain,
% 1.47/1.66 (((~hskp10) | (~c2_1(a807))) <=> ((~hskp10) | (~c2_1(a807)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(495,plain,
% 1.47/1.66 (((~c2_1(a807)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a807)))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(496,axiom,((~c2_1(a807)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.47/1.66 tff(497,plain,
% 1.47/1.66 ((~hskp10) | (~c2_1(a807))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[496, 495])).
% 1.47/1.66 tff(498,plain,
% 1.47/1.66 ((~hskp10) | (~c2_1(a807))),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[497, 494])).
% 1.47/1.66 tff(499,plain,
% 1.47/1.66 (~c2_1(a807)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[498, 450])).
% 1.47/1.66 tff(500,plain,
% 1.47/1.66 (((~hskp3) | c2_1(a798)) <=> ((~hskp3) | c2_1(a798))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(501,axiom,((~hskp3) | c2_1(a798)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.47/1.66 tff(502,plain,
% 1.47/1.66 ((~hskp3) | c2_1(a798)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[501, 500])).
% 1.47/1.66 tff(503,plain,
% 1.47/1.66 ((~hskp3) | c2_1(a798)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[502, 500])).
% 1.47/1.66 tff(504,plain,
% 1.47/1.66 ((~hskp3) | c2_1(a798)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[503, 500])).
% 1.47/1.66 tff(505,plain,
% 1.47/1.66 ((~hskp3) | c2_1(a798)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[504, 500])).
% 1.47/1.66 tff(506,plain,
% 1.47/1.66 ((~hskp3) | c2_1(a798)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[505, 500])).
% 1.47/1.66 tff(507,plain,
% 1.47/1.66 (c2_1(a798)),
% 1.47/1.66 inference(unit_resolution,[status(thm)],[506, 487])).
% 1.47/1.66 tff(508,plain,
% 1.47/1.66 (((~hskp3) | c0_1(a798)) <=> ((~hskp3) | c0_1(a798))),
% 1.47/1.66 inference(rewrite,[status(thm)],[])).
% 1.47/1.66 tff(509,axiom,((~hskp3) | c0_1(a798)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.47/1.66 tff(510,plain,
% 1.47/1.66 ((~hskp3) | c0_1(a798)),
% 1.47/1.66 inference(modus_ponens,[status(thm)],[509, 508])).
% 1.47/1.66 tff(511,plain,
% 1.47/1.66 ((~hskp3) | c0_1(a798)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[510, 508])).
% 1.47/1.67 tff(512,plain,
% 1.47/1.67 ((~hskp3) | c0_1(a798)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[511, 508])).
% 1.47/1.67 tff(513,plain,
% 1.47/1.67 ((~hskp3) | c0_1(a798)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[512, 508])).
% 1.47/1.67 tff(514,plain,
% 1.47/1.67 ((~hskp3) | c0_1(a798)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[513, 508])).
% 1.47/1.67 tff(515,plain,
% 1.47/1.67 (c0_1(a798)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[514, 487])).
% 1.47/1.67 tff(516,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c2_1(a807) | c3_1(a807) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a807)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a807) | c3_1(a807) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a807)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(517,plain,
% 1.47/1.67 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a807) | c3_1(a807) | (~c1_1(a807))) <=> (c2_1(a838) | c2_1(a807) | c3_1(a807) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a807)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(518,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a807) | c3_1(a807) | (~c1_1(a807)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c2_1(a807) | c3_1(a807) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a807)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 1.47/1.67 inference(monotonicity,[status(thm)],[517])).
% 1.47/1.67 tff(519,plain,
% 1.47/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a807) | c3_1(a807) | (~c1_1(a807)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a807) | c3_1(a807) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a807)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.47/1.67 inference(transitivity,[status(thm)],[518, 516])).
% 1.47/1.67 tff(520,plain,
% 1.47/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a807) | c3_1(a807) | (~c1_1(a807)))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(521,plain,
% 1.47/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a807) | c3_1(a807) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a807)) | (~c3_1(a838)) | (~c0_1(a838))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[520, 519])).
% 1.47/1.67 tff(522,plain,
% 1.47/1.67 ($false),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[521, 130, 407, 399, 515, 507, 390, 499, 456, 493, 299, 469])).
% 1.47/1.67 tff(523,plain,(hskp27 | hskp28 | (~c2_1(a832)) | c3_1(a832) | c1_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.67 tff(524,plain,
% 1.47/1.67 (hskp27),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[523, 341, 321, 347, 353])).
% 1.47/1.67 tff(525,plain,
% 1.47/1.67 (((~hskp27) | c3_1(a796)) <=> ((~hskp27) | c3_1(a796))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(526,axiom,((~hskp27) | c3_1(a796)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.47/1.67 tff(527,plain,
% 1.47/1.67 ((~hskp27) | c3_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[526, 525])).
% 1.47/1.67 tff(528,plain,
% 1.47/1.67 ((~hskp27) | c3_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[527, 525])).
% 1.47/1.67 tff(529,plain,
% 1.47/1.67 ((~hskp27) | c3_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[528, 525])).
% 1.47/1.67 tff(530,plain,
% 1.47/1.67 ((~hskp27) | c3_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[529, 525])).
% 1.47/1.67 tff(531,plain,
% 1.47/1.67 ((~hskp27) | c3_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[530, 525])).
% 1.47/1.67 tff(532,plain,
% 1.47/1.67 (c3_1(a796)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[531, 524])).
% 1.47/1.67 tff(533,plain,
% 1.47/1.67 (((~hskp27) | c2_1(a796)) <=> ((~hskp27) | c2_1(a796))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(534,axiom,((~hskp27) | c2_1(a796)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.47/1.67 tff(535,plain,
% 1.47/1.67 ((~hskp27) | c2_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[534, 533])).
% 1.47/1.67 tff(536,plain,
% 1.47/1.67 ((~hskp27) | c2_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[535, 533])).
% 1.47/1.67 tff(537,plain,
% 1.47/1.67 ((~hskp27) | c2_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[536, 533])).
% 1.47/1.67 tff(538,plain,
% 1.47/1.67 ((~hskp27) | c2_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[537, 533])).
% 1.47/1.67 tff(539,plain,
% 1.47/1.67 ((~hskp27) | c2_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[538, 533])).
% 1.47/1.67 tff(540,plain,
% 1.47/1.67 (c2_1(a796)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[539, 524])).
% 1.47/1.67 tff(541,plain,
% 1.47/1.67 (((~hskp27) | c0_1(a796)) <=> ((~hskp27) | c0_1(a796))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(542,axiom,((~hskp27) | c0_1(a796)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.47/1.67 tff(543,plain,
% 1.47/1.67 ((~hskp27) | c0_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[542, 541])).
% 1.47/1.67 tff(544,plain,
% 1.47/1.67 ((~hskp27) | c0_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[543, 541])).
% 1.47/1.67 tff(545,plain,
% 1.47/1.67 ((~hskp27) | c0_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[544, 541])).
% 1.47/1.67 tff(546,plain,
% 1.47/1.67 ((~hskp27) | c0_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[545, 541])).
% 1.47/1.67 tff(547,plain,
% 1.47/1.67 ((~hskp27) | c0_1(a796)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[546, 541])).
% 1.47/1.67 tff(548,plain,
% 1.47/1.67 (c0_1(a796)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[547, 524])).
% 1.47/1.67 tff(549,plain,
% 1.47/1.67 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(550,plain,
% 1.47/1.67 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(551,plain,
% 1.47/1.67 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[550, 549])).
% 1.47/1.67 tff(552,plain,
% 1.47/1.67 (hskp20),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[551, 309, 130, 548, 540, 532, 320])).
% 1.47/1.67 tff(553,plain,
% 1.47/1.67 (((~hskp20) | (~c2_1(a833))) <=> ((~hskp20) | (~c2_1(a833)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(554,plain,
% 1.47/1.67 (((~c2_1(a833)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a833)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(555,axiom,((~c2_1(a833)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.47/1.67 tff(556,plain,
% 1.47/1.67 ((~hskp20) | (~c2_1(a833))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[555, 554])).
% 1.47/1.67 tff(557,plain,
% 1.47/1.67 ((~hskp20) | (~c2_1(a833))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[556, 553])).
% 1.47/1.67 tff(558,plain,
% 1.47/1.67 (~c2_1(a833)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[557, 552])).
% 1.47/1.67 tff(559,plain,
% 1.47/1.67 (((~hskp20) | (~c0_1(a833))) <=> ((~hskp20) | (~c0_1(a833)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(560,plain,
% 1.47/1.67 (((~c0_1(a833)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a833)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(561,axiom,((~c0_1(a833)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.47/1.67 tff(562,plain,
% 1.47/1.67 ((~hskp20) | (~c0_1(a833))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[561, 560])).
% 1.47/1.67 tff(563,plain,
% 1.47/1.67 ((~hskp20) | (~c0_1(a833))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[562, 559])).
% 1.47/1.67 tff(564,plain,
% 1.47/1.67 (~c0_1(a833)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[563, 552])).
% 1.47/1.67 tff(565,plain,
% 1.47/1.67 (c1_1(a833)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[307, 552])).
% 1.47/1.67 tff(566,plain,
% 1.47/1.67 (hskp27),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[523, 391, 321, 22, 289])).
% 1.47/1.67 tff(567,plain,
% 1.47/1.67 (c0_1(a796)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[547, 566])).
% 1.47/1.67 tff(568,plain,
% 1.47/1.67 (c3_1(a796)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[531, 566])).
% 1.47/1.67 tff(569,plain,
% 1.47/1.67 (c2_1(a796)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[539, 566])).
% 1.47/1.67 tff(570,assumption,(c1_1(a833)), introduced(assumption)).
% 1.47/1.67 tff(571,assumption,(~c0_1(a838)), introduced(assumption)).
% 1.47/1.67 tff(572,plain,
% 1.47/1.67 (~hskp21),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[406, 571])).
% 1.47/1.67 tff(573,plain,
% 1.47/1.67 (^[U: $i] : refl((hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.47/1.67 inference(bind,[status(th)],[])).
% 1.47/1.67 tff(574,plain,
% 1.47/1.67 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.67 inference(quant_intro,[status(thm)],[573])).
% 1.47/1.67 tff(575,plain,
% 1.47/1.67 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(576,plain,
% 1.47/1.67 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp21) <=> ((hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21))), rewrite(((hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp21) <=> (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp21) <=> (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.47/1.67 inference(bind,[status(th)],[])).
% 1.47/1.67 tff(577,plain,
% 1.47/1.67 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp21) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.67 inference(quant_intro,[status(thm)],[576])).
% 1.47/1.67 tff(578,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 1.47/1.67 tff(579,plain,
% 1.47/1.67 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[578, 577])).
% 1.47/1.67 tff(580,plain,
% 1.47/1.67 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[579, 575])).
% 1.47/1.67 tff(581,plain,(
% 1.47/1.67 ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.67 inference(skolemize,[status(sab)],[580])).
% 1.47/1.67 tff(582,plain,
% 1.47/1.67 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[581, 574])).
% 1.47/1.67 tff(583,plain,
% 1.47/1.67 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(584,plain,
% 1.47/1.67 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832))) <=> (hskp21 | hskp0 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(585,plain,
% 1.47/1.67 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832))))),
% 1.47/1.67 inference(monotonicity,[status(thm)],[584])).
% 1.47/1.67 tff(586,plain,
% 1.47/1.67 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)))),
% 1.47/1.67 inference(transitivity,[status(thm)],[585, 583])).
% 1.47/1.67 tff(587,plain,
% 1.47/1.67 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(588,plain,
% 1.47/1.67 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[587, 586])).
% 1.47/1.67 tff(589,plain,
% 1.47/1.67 (hskp21 | hskp0),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[588, 130, 391, 289, 22, 582])).
% 1.47/1.67 tff(590,plain,
% 1.47/1.67 (hskp0),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[589, 572])).
% 1.47/1.67 tff(591,plain,
% 1.47/1.67 (((~hskp0) | c2_1(a793)) <=> ((~hskp0) | c2_1(a793))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(592,axiom,((~hskp0) | c2_1(a793)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.47/1.67 tff(593,plain,
% 1.47/1.67 ((~hskp0) | c2_1(a793)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[592, 591])).
% 1.47/1.67 tff(594,plain,
% 1.47/1.67 ((~hskp0) | c2_1(a793)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[593, 591])).
% 1.47/1.67 tff(595,plain,
% 1.47/1.67 ((~hskp0) | c2_1(a793)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[594, 591])).
% 1.47/1.67 tff(596,plain,
% 1.47/1.67 ((~hskp0) | c2_1(a793)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[595, 591])).
% 1.47/1.67 tff(597,plain,
% 1.47/1.67 ((~hskp0) | c2_1(a793)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[596, 591])).
% 1.47/1.67 tff(598,plain,
% 1.47/1.67 (c2_1(a793)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[597, 590])).
% 1.47/1.67 tff(599,plain,
% 1.47/1.67 (((~hskp0) | (~c1_1(a793))) <=> ((~hskp0) | (~c1_1(a793)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(600,plain,
% 1.47/1.67 (((~c1_1(a793)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a793)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(601,axiom,((~c1_1(a793)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.47/1.67 tff(602,plain,
% 1.47/1.67 ((~hskp0) | (~c1_1(a793))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[601, 600])).
% 1.47/1.67 tff(603,plain,
% 1.47/1.67 ((~hskp0) | (~c1_1(a793))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[602, 599])).
% 1.47/1.67 tff(604,plain,
% 1.47/1.67 (~c1_1(a793)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[603, 590])).
% 1.47/1.67 tff(605,plain,
% 1.47/1.67 (((~hskp0) | c0_1(a793)) <=> ((~hskp0) | c0_1(a793))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(606,axiom,((~hskp0) | c0_1(a793)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.47/1.67 tff(607,plain,
% 1.47/1.67 ((~hskp0) | c0_1(a793)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[606, 605])).
% 1.47/1.67 tff(608,plain,
% 1.47/1.67 ((~hskp0) | c0_1(a793)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[607, 605])).
% 1.47/1.67 tff(609,plain,
% 1.47/1.67 ((~hskp0) | c0_1(a793)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[608, 605])).
% 1.47/1.67 tff(610,plain,
% 1.47/1.67 ((~hskp0) | c0_1(a793)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[609, 605])).
% 1.47/1.67 tff(611,plain,
% 1.47/1.67 ((~hskp0) | c0_1(a793)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[610, 605])).
% 1.47/1.67 tff(612,plain,
% 1.47/1.67 (c0_1(a793)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[611, 590])).
% 1.47/1.67 tff(613,assumption,(c2_1(a796)), introduced(assumption)).
% 1.47/1.67 tff(614,assumption,(c2_1(a793)), introduced(assumption)).
% 1.47/1.67 tff(615,assumption,(c0_1(a796)), introduced(assumption)).
% 1.47/1.67 tff(616,assumption,(~c1_1(a793)), introduced(assumption)).
% 1.47/1.67 tff(617,assumption,(c0_1(a793)), introduced(assumption)).
% 1.47/1.67 tff(618,assumption,(c3_1(a796)), introduced(assumption)).
% 1.47/1.67 tff(619,plain,
% 1.47/1.67 (^[U: $i] : refl((hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))),
% 1.47/1.67 inference(bind,[status(th)],[])).
% 1.47/1.67 tff(620,plain,
% 1.47/1.67 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.47/1.67 inference(quant_intro,[status(thm)],[619])).
% 1.47/1.67 tff(621,plain,
% 1.47/1.67 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(622,plain,
% 1.47/1.67 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp21))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) | hskp11) <=> ((hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp11))), rewrite(((hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp11) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) | hskp11) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.47/1.67 inference(bind,[status(th)],[])).
% 1.47/1.67 tff(623,plain,
% 1.47/1.67 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) | hskp11) <=> ![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.47/1.67 inference(quant_intro,[status(thm)],[622])).
% 1.47/1.67 tff(624,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp21) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 1.47/1.67 tff(625,plain,
% 1.47/1.67 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[624, 623])).
% 1.47/1.67 tff(626,plain,
% 1.47/1.67 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[625, 621])).
% 1.47/1.67 tff(627,plain,(
% 1.47/1.67 ![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.47/1.67 inference(skolemize,[status(sab)],[626])).
% 1.47/1.67 tff(628,plain,
% 1.47/1.67 (![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[627, 620])).
% 1.47/1.67 tff(629,assumption,(~hskp21), introduced(assumption)).
% 1.47/1.67 tff(630,assumption,(~hskp11), introduced(assumption)).
% 1.47/1.67 tff(631,plain,
% 1.47/1.67 (^[U: $i] : refl((hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 1.47/1.67 inference(bind,[status(th)],[])).
% 1.47/1.67 tff(632,plain,
% 1.47/1.67 (![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.67 inference(quant_intro,[status(thm)],[631])).
% 1.47/1.67 tff(633,plain,
% 1.47/1.67 (![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(634,plain,
% 1.47/1.67 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp11) <=> ((hskp26 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp26 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp11) <=> (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.47/1.67 inference(bind,[status(th)],[])).
% 1.47/1.67 tff(635,plain,
% 1.47/1.67 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp11) <=> ![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.67 inference(quant_intro,[status(thm)],[634])).
% 1.47/1.67 tff(636,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp26) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 1.47/1.67 tff(637,plain,
% 1.47/1.67 (![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[636, 635])).
% 1.47/1.67 tff(638,plain,
% 1.47/1.67 (![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[637, 633])).
% 1.47/1.67 tff(639,plain,(
% 1.47/1.67 ![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.67 inference(skolemize,[status(sab)],[638])).
% 1.47/1.67 tff(640,plain,
% 1.47/1.67 (![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[639, 632])).
% 1.47/1.67 tff(641,plain,
% 1.47/1.67 (((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)))) <=> ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(642,plain,
% 1.47/1.67 ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(643,plain,
% 1.47/1.67 ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[642, 641])).
% 1.47/1.67 tff(644,plain,
% 1.47/1.67 (hskp26 | hskp11),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[643, 130, 615, 613, 618, 640])).
% 1.47/1.67 tff(645,plain,
% 1.47/1.67 (hskp26),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[644, 630])).
% 1.47/1.67 tff(646,plain,
% 1.47/1.67 (((~hskp26) | c3_1(a869)) <=> ((~hskp26) | c3_1(a869))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(647,axiom,((~hskp26) | c3_1(a869)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 1.47/1.67 tff(648,plain,
% 1.47/1.67 ((~hskp26) | c3_1(a869)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[647, 646])).
% 1.47/1.67 tff(649,plain,
% 1.47/1.67 ((~hskp26) | c3_1(a869)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[648, 646])).
% 1.47/1.67 tff(650,plain,
% 1.47/1.67 ((~hskp26) | c3_1(a869)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[649, 646])).
% 1.47/1.67 tff(651,plain,
% 1.47/1.67 ((~hskp26) | c3_1(a869)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[650, 646])).
% 1.47/1.67 tff(652,plain,
% 1.47/1.67 ((~hskp26) | c3_1(a869)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[651, 646])).
% 1.47/1.67 tff(653,plain,
% 1.47/1.67 (c3_1(a869)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[652, 645])).
% 1.47/1.67 tff(654,plain,
% 1.47/1.67 (((~hskp26) | c2_1(a869)) <=> ((~hskp26) | c2_1(a869))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(655,axiom,((~hskp26) | c2_1(a869)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.47/1.67 tff(656,plain,
% 1.47/1.67 ((~hskp26) | c2_1(a869)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[655, 654])).
% 1.47/1.67 tff(657,plain,
% 1.47/1.67 ((~hskp26) | c2_1(a869)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[656, 654])).
% 1.47/1.67 tff(658,plain,
% 1.47/1.67 ((~hskp26) | c2_1(a869)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[657, 654])).
% 1.47/1.67 tff(659,plain,
% 1.47/1.67 ((~hskp26) | c2_1(a869)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[658, 654])).
% 1.47/1.67 tff(660,plain,
% 1.47/1.67 ((~hskp26) | c2_1(a869)),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[659, 654])).
% 1.47/1.67 tff(661,plain,
% 1.47/1.67 (c2_1(a869)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[660, 645])).
% 1.47/1.67 tff(662,plain,
% 1.47/1.67 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a869)) | (~c1_1(a869)) | (~c3_1(a869)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a869)) | (~c1_1(a869)) | (~c3_1(a869)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(663,plain,
% 1.47/1.67 ((hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a869)) | (~c1_1(a869)) | (~c2_1(a869))) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a869)) | (~c1_1(a869)) | (~c3_1(a869)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(664,plain,
% 1.47/1.67 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a869)) | (~c1_1(a869)) | (~c2_1(a869)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a869)) | (~c1_1(a869)) | (~c3_1(a869))))),
% 1.47/1.67 inference(monotonicity,[status(thm)],[663])).
% 1.47/1.67 tff(665,plain,
% 1.47/1.67 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a869)) | (~c1_1(a869)) | (~c2_1(a869)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a869)) | (~c1_1(a869)) | (~c3_1(a869)))),
% 1.47/1.67 inference(transitivity,[status(thm)],[664, 662])).
% 1.47/1.67 tff(666,plain,
% 1.47/1.67 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a869)) | (~c1_1(a869)) | (~c2_1(a869)))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(667,plain,
% 1.47/1.67 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a869)) | (~c1_1(a869)) | (~c3_1(a869))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[666, 665])).
% 1.47/1.67 tff(668,plain,
% 1.47/1.67 (~c1_1(a869)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[667, 130, 629, 630, 661, 653, 628])).
% 1.47/1.67 tff(669,assumption,(c3_1(a833)), introduced(assumption)).
% 1.47/1.67 tff(670,plain,
% 1.47/1.67 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c1_1(a796)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c1_1(a796)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(671,plain,
% 1.47/1.67 ((hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c2_1(a796))) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c1_1(a796)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(672,plain,
% 1.47/1.67 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c2_1(a796)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c1_1(a796))))),
% 1.47/1.67 inference(monotonicity,[status(thm)],[671])).
% 1.47/1.67 tff(673,plain,
% 1.47/1.67 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c2_1(a796)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c1_1(a796)))),
% 1.47/1.67 inference(transitivity,[status(thm)],[672, 670])).
% 1.47/1.67 tff(674,plain,
% 1.47/1.67 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c2_1(a796)))),
% 1.47/1.67 inference(quant_inst,[status(thm)],[])).
% 1.47/1.67 tff(675,plain,
% 1.47/1.67 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c1_1(a796))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[674, 673])).
% 1.47/1.67 tff(676,plain,
% 1.47/1.67 (hskp21 | hskp11 | (~c1_1(a796))),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[675, 130, 613, 618, 628])).
% 1.47/1.67 tff(677,plain,
% 1.47/1.67 (~c1_1(a796)),
% 1.47/1.67 inference(unit_resolution,[status(thm)],[676, 630, 629])).
% 1.47/1.67 tff(678,plain,
% 1.47/1.67 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.47/1.67 inference(bind,[status(th)],[])).
% 1.47/1.67 tff(679,plain,
% 1.47/1.67 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.47/1.67 inference(quant_intro,[status(thm)],[678])).
% 1.47/1.67 tff(680,plain,
% 1.47/1.67 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.47/1.67 inference(rewrite,[status(thm)],[])).
% 1.47/1.67 tff(681,plain,
% 1.47/1.67 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.47/1.67 inference(bind,[status(th)],[])).
% 1.47/1.67 tff(682,plain,
% 1.47/1.67 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.47/1.67 inference(quant_intro,[status(thm)],[681])).
% 1.47/1.67 tff(683,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 1.47/1.67 tff(684,plain,
% 1.47/1.67 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.47/1.67 inference(modus_ponens,[status(thm)],[683, 682])).
% 1.47/1.67 tff(685,plain,
% 1.47/1.67 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[684, 680])).
% 1.47/1.68 tff(686,plain,(
% 1.47/1.68 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.47/1.68 inference(skolemize,[status(sab)],[685])).
% 1.47/1.68 tff(687,plain,
% 1.47/1.68 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[686, 679])).
% 1.47/1.68 tff(688,plain,
% 1.47/1.68 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(689,plain,
% 1.47/1.68 ((hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833))) <=> (hskp8 | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(690,plain,
% 1.47/1.68 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.47/1.68 inference(monotonicity,[status(thm)],[689])).
% 1.47/1.68 tff(691,plain,
% 1.47/1.68 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.47/1.68 inference(transitivity,[status(thm)],[690, 688])).
% 1.47/1.68 tff(692,plain,
% 1.47/1.68 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(693,plain,
% 1.47/1.68 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[692, 691])).
% 1.47/1.68 tff(694,plain,
% 1.47/1.68 (hskp8),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[693, 130, 613, 618, 570, 288, 687, 677, 669])).
% 1.47/1.68 tff(695,plain,
% 1.47/1.68 (~c2_1(a805)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[420, 694])).
% 1.47/1.68 tff(696,plain,
% 1.47/1.68 (((~hskp26) | (~c0_1(a869))) <=> ((~hskp26) | (~c0_1(a869)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(697,plain,
% 1.47/1.68 (((~c0_1(a869)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a869)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(698,axiom,((~c0_1(a869)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.47/1.68 tff(699,plain,
% 1.47/1.68 ((~hskp26) | (~c0_1(a869))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[698, 697])).
% 1.47/1.68 tff(700,plain,
% 1.47/1.68 ((~hskp26) | (~c0_1(a869))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[699, 696])).
% 1.47/1.68 tff(701,plain,
% 1.47/1.68 (~c0_1(a869)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[700, 645])).
% 1.47/1.68 tff(702,plain,
% 1.47/1.68 (c1_1(a805)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[429, 694])).
% 1.47/1.68 tff(703,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a869) | c2_1(a805) | c1_1(a793) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a869) | (~c3_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a869) | c2_1(a805) | c1_1(a793) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a869) | (~c3_1(a869)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(704,plain,
% 1.47/1.68 (((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a869) | c0_1(a869) | (~c3_1(a869))) <=> (c0_1(a869) | c2_1(a805) | c1_1(a793) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a869) | (~c3_1(a869)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(705,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a869) | c0_1(a869) | (~c3_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a869) | c2_1(a805) | c1_1(a793) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a869) | (~c3_1(a869))))),
% 1.47/1.68 inference(monotonicity,[status(thm)],[704])).
% 1.47/1.68 tff(706,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a869) | c0_1(a869) | (~c3_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a869) | c2_1(a805) | c1_1(a793) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a869) | (~c3_1(a869)))),
% 1.47/1.68 inference(transitivity,[status(thm)],[705, 703])).
% 1.47/1.68 tff(707,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a869) | c0_1(a869) | (~c3_1(a869)))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(708,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a869) | c2_1(a805) | c1_1(a793) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a869) | (~c3_1(a869))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[707, 706])).
% 1.47/1.68 tff(709,plain,
% 1.47/1.68 (~c0_1(a805)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[708, 130, 653, 702, 617, 614, 701, 695, 616, 287, 668])).
% 1.47/1.68 tff(710,plain,
% 1.47/1.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 1.47/1.68 inference(bind,[status(th)],[])).
% 1.47/1.68 tff(711,plain,
% 1.47/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.68 inference(quant_intro,[status(thm)],[710])).
% 1.47/1.68 tff(712,plain,
% 1.47/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(713,plain,
% 1.47/1.68 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 1.47/1.68 inference(bind,[status(th)],[])).
% 1.47/1.68 tff(714,plain,
% 1.47/1.68 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.68 inference(quant_intro,[status(thm)],[713])).
% 1.47/1.68 tff(715,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 1.47/1.68 tff(716,plain,
% 1.47/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[715, 714])).
% 1.47/1.68 tff(717,plain,
% 1.47/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[716, 712])).
% 1.47/1.68 tff(718,plain,(
% 1.47/1.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.68 inference(skolemize,[status(sab)],[717])).
% 1.47/1.68 tff(719,plain,
% 1.47/1.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[718, 711])).
% 1.47/1.68 tff(720,plain,
% 1.47/1.68 (~c3_1(a805)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[414, 694])).
% 1.47/1.68 tff(721,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a805) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c0_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c0_1(a805) | (~c1_1(a805)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(722,plain,
% 1.47/1.68 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c3_1(a805) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c0_1(a805) | (~c1_1(a805)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(723,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a805) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c0_1(a805) | (~c1_1(a805))))),
% 1.47/1.68 inference(monotonicity,[status(thm)],[722])).
% 1.47/1.68 tff(724,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c0_1(a805) | (~c1_1(a805)))),
% 1.47/1.68 inference(transitivity,[status(thm)],[723, 721])).
% 1.47/1.68 tff(725,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(726,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c0_1(a805) | (~c1_1(a805))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[725, 724])).
% 1.47/1.68 tff(727,plain,
% 1.47/1.68 ($false),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[726, 130, 615, 613, 618, 702, 720, 719, 677, 709])).
% 1.47/1.68 tff(728,plain,(hskp11 | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796)) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a793) | (~c1_1(a833)) | c0_1(a833) | (~c3_1(a833)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.47/1.68 tff(729,plain,
% 1.47/1.68 (~c3_1(a833)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[728, 630, 613, 618, 629, 614, 616, 570, 288, 617, 615])).
% 1.47/1.68 tff(730,assumption,(~hskp12), introduced(assumption)).
% 1.47/1.68 tff(731,plain,
% 1.47/1.68 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c0_1(a796)) | (~c1_1(a796)) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c0_1(a796)) | (~c1_1(a796)) | c3_1(a833) | (~c1_1(a833)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(732,plain,
% 1.47/1.68 ((hskp12 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c0_1(a796)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833))) <=> (hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c0_1(a796)) | (~c1_1(a796)) | c3_1(a833) | (~c1_1(a833)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(733,plain,
% 1.47/1.68 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c0_1(a796)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c0_1(a796)) | (~c1_1(a796)) | c3_1(a833) | (~c1_1(a833))))),
% 1.47/1.68 inference(monotonicity,[status(thm)],[732])).
% 1.47/1.68 tff(734,plain,
% 1.47/1.68 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c0_1(a796)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c0_1(a796)) | (~c1_1(a796)) | c3_1(a833) | (~c1_1(a833)))),
% 1.47/1.68 inference(transitivity,[status(thm)],[733, 731])).
% 1.47/1.68 tff(735,plain,
% 1.47/1.68 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a796)) | (~c1_1(a796)) | (~c0_1(a796)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(736,plain,
% 1.47/1.68 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c0_1(a796)) | (~c1_1(a796)) | c3_1(a833) | (~c1_1(a833))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[735, 734])).
% 1.47/1.68 tff(737,plain,
% 1.47/1.68 (~c1_1(a796)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[736, 130, 730, 615, 618, 570, 276, 95, 277])).
% 1.47/1.68 tff(738,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c3_1(a833) | (~c1_1(a833)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(739,plain,
% 1.47/1.68 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c3_1(a833) | (~c1_1(a833)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(740,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c3_1(a833) | (~c1_1(a833))))),
% 1.47/1.68 inference(monotonicity,[status(thm)],[739])).
% 1.47/1.68 tff(741,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c3_1(a833) | (~c1_1(a833)))),
% 1.47/1.68 inference(transitivity,[status(thm)],[740, 738])).
% 1.47/1.68 tff(742,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(743,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | c3_1(a833) | (~c1_1(a833))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[742, 741])).
% 1.47/1.68 tff(744,plain,
% 1.47/1.68 ($false),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[743, 130, 615, 613, 618, 570, 288, 719, 737, 277])).
% 1.47/1.68 tff(745,plain,(c3_1(a833) | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796)) | (~c1_1(a833)) | c0_1(a833) | hskp12 | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.47/1.68 tff(746,plain,
% 1.47/1.68 (hskp12),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[745, 729, 613, 618, 570, 288, 276, 615])).
% 1.47/1.68 tff(747,plain,
% 1.47/1.68 (c2_1(a809)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[152, 746])).
% 1.47/1.68 tff(748,plain,
% 1.47/1.68 (c1_1(a809)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[160, 746])).
% 1.47/1.68 tff(749,plain,
% 1.47/1.68 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a809)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a809)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(750,plain,
% 1.47/1.68 ((hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a809)) | (~c1_1(a809)) | (~c2_1(a809))) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a809)))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(751,plain,
% 1.47/1.68 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a809)) | (~c1_1(a809)) | (~c2_1(a809)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a809))))),
% 1.47/1.68 inference(monotonicity,[status(thm)],[750])).
% 1.47/1.68 tff(752,plain,
% 1.47/1.68 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a809)) | (~c1_1(a809)) | (~c2_1(a809)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a809)))),
% 1.47/1.68 inference(transitivity,[status(thm)],[751, 749])).
% 1.47/1.68 tff(753,plain,
% 1.47/1.68 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a809)) | (~c1_1(a809)) | (~c2_1(a809)))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(754,plain,
% 1.47/1.68 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a809))),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[753, 752])).
% 1.47/1.68 tff(755,plain,
% 1.47/1.68 (~c3_1(a809)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[754, 130, 629, 630, 748, 747, 628])).
% 1.47/1.68 tff(756,plain,
% 1.47/1.68 (~c0_1(a809)),
% 1.47/1.68 inference(unit_resolution,[status(thm)],[143, 746])).
% 1.47/1.68 tff(757,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c1_1(a809)) | c3_1(a809))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c1_1(a809)) | c3_1(a809))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(758,plain,
% 1.47/1.68 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809))) <=> (c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c1_1(a809)) | c3_1(a809))),
% 1.47/1.68 inference(rewrite,[status(thm)],[])).
% 1.47/1.68 tff(759,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c1_1(a809)) | c3_1(a809)))),
% 1.47/1.68 inference(monotonicity,[status(thm)],[758])).
% 1.47/1.68 tff(760,plain,
% 1.47/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c1_1(a809)) | c3_1(a809))),
% 1.47/1.68 inference(transitivity,[status(thm)],[759, 757])).
% 1.47/1.68 tff(761,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809)))),
% 1.47/1.68 inference(quant_inst,[status(thm)],[])).
% 1.47/1.68 tff(762,plain,
% 1.47/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a796) | (~c1_1(a809)) | c3_1(a809)),
% 1.47/1.68 inference(modus_ponens,[status(thm)],[761, 760])).
% 1.53/1.69 tff(763,plain,
% 1.53/1.69 ($false),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[762, 130, 615, 613, 618, 748, 756, 719, 677, 755])).
% 1.53/1.69 tff(764,plain,(hskp11 | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796)) | hskp21 | (~c1_1(a833)) | c0_1(a833) | c2_1(a833) | (~c2_1(a793)) | c1_1(a793) | (~c0_1(a793))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.69 tff(765,plain,
% 1.53/1.69 (hskp11),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[764, 572, 613, 618, 615, 570, 288, 276, 614, 616, 617])).
% 1.53/1.69 tff(766,plain,
% 1.53/1.69 (((~hskp11) | (~c1_1(a808))) <=> ((~hskp11) | (~c1_1(a808)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(767,plain,
% 1.53/1.69 (((~c1_1(a808)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a808)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(768,axiom,((~c1_1(a808)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.53/1.69 tff(769,plain,
% 1.53/1.69 ((~hskp11) | (~c1_1(a808))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[768, 767])).
% 1.53/1.69 tff(770,plain,
% 1.53/1.69 ((~hskp11) | (~c1_1(a808))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[769, 766])).
% 1.53/1.69 tff(771,plain,
% 1.53/1.69 (~c1_1(a808)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[770, 765])).
% 1.53/1.69 tff(772,plain,
% 1.53/1.69 (((~hskp11) | (~c2_1(a808))) <=> ((~hskp11) | (~c2_1(a808)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(773,plain,
% 1.53/1.69 (((~c2_1(a808)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a808)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(774,axiom,((~c2_1(a808)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.53/1.69 tff(775,plain,
% 1.53/1.69 ((~hskp11) | (~c2_1(a808))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[774, 773])).
% 1.53/1.69 tff(776,plain,
% 1.53/1.69 ((~hskp11) | (~c2_1(a808))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[775, 772])).
% 1.53/1.69 tff(777,plain,
% 1.53/1.69 (~c2_1(a808)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[776, 765])).
% 1.53/1.69 tff(778,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(779,plain,
% 1.53/1.69 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(780,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793))))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[779])).
% 1.53/1.69 tff(781,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 1.53/1.69 inference(transitivity,[status(thm)],[780, 778])).
% 1.53/1.69 tff(782,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(783,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[782, 781])).
% 1.53/1.69 tff(784,plain,
% 1.53/1.69 (c3_1(a833) | (~c3_1(a793))),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[783, 130, 615, 613, 618, 570, 614, 288, 616, 719])).
% 1.53/1.69 tff(785,plain,
% 1.53/1.69 (~c3_1(a793)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[784, 277])).
% 1.53/1.69 tff(786,plain,
% 1.53/1.69 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(787,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[786])).
% 1.53/1.69 tff(788,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(789,plain,
% 1.53/1.69 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(790,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[789])).
% 1.53/1.69 tff(791,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 1.53/1.69 tff(792,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[791, 790])).
% 1.53/1.69 tff(793,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[792, 788])).
% 1.53/1.69 tff(794,plain,(
% 1.53/1.69 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.69 inference(skolemize,[status(sab)],[793])).
% 1.53/1.69 tff(795,plain,
% 1.53/1.69 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[794, 787])).
% 1.53/1.69 tff(796,assumption,(~c2_1(a808)), introduced(assumption)).
% 1.53/1.69 tff(797,assumption,(~c1_1(a808)), introduced(assumption)).
% 1.53/1.69 tff(798,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a833) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(799,plain,
% 1.53/1.69 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833)) <=> (c0_1(a833) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(800,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a833) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793)))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[799])).
% 1.53/1.69 tff(801,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793))),
% 1.53/1.69 inference(transitivity,[status(thm)],[800, 798])).
% 1.53/1.69 tff(802,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(803,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[802, 801])).
% 1.53/1.69 tff(804,plain,
% 1.53/1.69 ((~c3_1(a808)) | c3_1(a833) | c3_1(a793)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[803, 130, 617, 288, 276, 797, 796, 616, 795])).
% 1.53/1.69 tff(805,plain,
% 1.53/1.69 (~c3_1(a808)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[804, 277, 785])).
% 1.53/1.69 tff(806,plain,
% 1.53/1.69 (((~hskp11) | c3_1(a808)) <=> ((~hskp11) | c3_1(a808))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(807,axiom,((~hskp11) | c3_1(a808)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.53/1.69 tff(808,plain,
% 1.53/1.69 ((~hskp11) | c3_1(a808)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[807, 806])).
% 1.53/1.69 tff(809,plain,
% 1.53/1.69 ((~hskp11) | c3_1(a808)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[808, 806])).
% 1.53/1.69 tff(810,plain,
% 1.53/1.69 ((~hskp11) | c3_1(a808)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[809, 806])).
% 1.53/1.69 tff(811,plain,
% 1.53/1.69 ((~hskp11) | c3_1(a808)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[810, 806])).
% 1.53/1.69 tff(812,plain,
% 1.53/1.69 ((~hskp11) | c3_1(a808)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[811, 806])).
% 1.53/1.69 tff(813,plain,
% 1.53/1.69 (~hskp11),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[812, 805])).
% 1.53/1.69 tff(814,plain,
% 1.53/1.69 (~c1_1(a796)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[676, 813, 629])).
% 1.53/1.69 tff(815,plain,
% 1.53/1.69 ($false),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[743, 130, 615, 613, 618, 570, 288, 719, 814, 277])).
% 1.53/1.69 tff(816,plain,(c3_1(a833) | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796)) | (~c1_1(a833)) | c0_1(a833) | hskp21 | (~c0_1(a793)) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~c2_1(a793))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.69 tff(817,plain,
% 1.53/1.69 (c3_1(a833)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[816, 777, 613, 618, 570, 288, 572, 617, 276, 614, 771, 616, 615])).
% 1.53/1.69 tff(818,assumption,(~hskp8), introduced(assumption)).
% 1.53/1.69 tff(819,plain,
% 1.53/1.69 (hskp10),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[449, 818, 321])).
% 1.53/1.69 tff(820,plain,
% 1.53/1.69 (~c3_1(a807)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[455, 819])).
% 1.53/1.69 tff(821,plain,
% 1.53/1.69 (~c2_1(a807)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[498, 819])).
% 1.53/1.69 tff(822,plain,
% 1.53/1.69 (hskp12),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[745, 277, 613, 618, 570, 288, 276, 615])).
% 1.53/1.69 tff(823,plain,
% 1.53/1.69 (~c0_1(a809)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[143, 822])).
% 1.53/1.69 tff(824,plain,
% 1.53/1.69 (^[U: $i] : refl((hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(825,plain,
% 1.53/1.69 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[824])).
% 1.53/1.69 tff(826,plain,
% 1.53/1.69 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(827,plain,
% 1.53/1.69 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp17) | hskp8) <=> ((hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp8))), rewrite(((hskp17 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp8) <=> (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp17) | hskp8) <=> (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.53/1.69 inference(bind,[status(th)],[])).
% 1.53/1.69 tff(828,plain,
% 1.53/1.69 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp17) | hskp8) <=> ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.69 inference(quant_intro,[status(thm)],[827])).
% 1.53/1.69 tff(829,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp17) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 1.53/1.69 tff(830,plain,
% 1.53/1.69 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[829, 828])).
% 1.53/1.69 tff(831,plain,
% 1.53/1.69 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[830, 826])).
% 1.53/1.69 tff(832,plain,(
% 1.53/1.69 ![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.69 inference(skolemize,[status(sab)],[831])).
% 1.53/1.69 tff(833,plain,
% 1.53/1.69 (![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[832, 825])).
% 1.53/1.69 tff(834,plain,
% 1.53/1.69 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp8 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(835,plain,
% 1.53/1.69 ((hskp17 | hskp8 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (hskp17 | hskp8 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(836,plain,
% 1.53/1.69 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[835])).
% 1.53/1.69 tff(837,plain,
% 1.53/1.69 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp8 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 1.53/1.69 inference(transitivity,[status(thm)],[836, 834])).
% 1.53/1.69 tff(838,plain,
% 1.53/1.69 ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(839,plain,
% 1.53/1.69 ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp8 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[838, 837])).
% 1.53/1.69 tff(840,plain,
% 1.53/1.69 (hskp17 | hskp8 | c3_1(a833)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[839, 130, 570, 276, 833])).
% 1.53/1.69 tff(841,plain,
% 1.53/1.69 (hskp17),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[840, 277, 818])).
% 1.53/1.69 tff(842,plain,
% 1.53/1.69 (((~hskp17) | (~c2_1(a825))) <=> ((~hskp17) | (~c2_1(a825)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(843,plain,
% 1.53/1.69 (((~c2_1(a825)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a825)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(844,axiom,((~c2_1(a825)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.53/1.69 tff(845,plain,
% 1.53/1.69 ((~hskp17) | (~c2_1(a825))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[844, 843])).
% 1.53/1.69 tff(846,plain,
% 1.53/1.69 ((~hskp17) | (~c2_1(a825))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[845, 842])).
% 1.53/1.69 tff(847,plain,
% 1.53/1.69 (~c2_1(a825)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[846, 841])).
% 1.53/1.69 tff(848,plain,
% 1.53/1.69 (c2_1(a809)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[152, 822])).
% 1.53/1.69 tff(849,plain,
% 1.53/1.69 (c1_1(a809)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[160, 822])).
% 1.53/1.69 tff(850,plain,
% 1.53/1.69 (((~hskp17) | c1_1(a825)) <=> ((~hskp17) | c1_1(a825))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(851,axiom,((~hskp17) | c1_1(a825)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.53/1.69 tff(852,plain,
% 1.53/1.69 ((~hskp17) | c1_1(a825)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[851, 850])).
% 1.53/1.69 tff(853,plain,
% 1.53/1.69 ((~hskp17) | c1_1(a825)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[852, 850])).
% 1.53/1.69 tff(854,plain,
% 1.53/1.69 ((~hskp17) | c1_1(a825)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[853, 850])).
% 1.53/1.69 tff(855,plain,
% 1.53/1.69 ((~hskp17) | c1_1(a825)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[854, 850])).
% 1.53/1.69 tff(856,plain,
% 1.53/1.69 ((~hskp17) | c1_1(a825)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[855, 850])).
% 1.53/1.69 tff(857,plain,
% 1.53/1.69 (c1_1(a825)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[856, 841])).
% 1.53/1.69 tff(858,plain,
% 1.53/1.69 (((~hskp17) | c0_1(a825)) <=> ((~hskp17) | c0_1(a825))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(859,axiom,((~hskp17) | c0_1(a825)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.53/1.69 tff(860,plain,
% 1.53/1.69 ((~hskp17) | c0_1(a825)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[859, 858])).
% 1.53/1.69 tff(861,plain,
% 1.53/1.69 ((~hskp17) | c0_1(a825)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[860, 858])).
% 1.53/1.69 tff(862,plain,
% 1.53/1.69 ((~hskp17) | c0_1(a825)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[861, 858])).
% 1.53/1.69 tff(863,plain,
% 1.53/1.69 ((~hskp17) | c0_1(a825)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[862, 858])).
% 1.53/1.69 tff(864,plain,
% 1.53/1.69 ((~hskp17) | c0_1(a825)),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[863, 858])).
% 1.53/1.69 tff(865,plain,
% 1.53/1.69 (c0_1(a825)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[864, 841])).
% 1.53/1.69 tff(866,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a833) | c2_1(a825) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a825)) | (~c1_1(a825)) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a833) | c2_1(a825) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a825)) | (~c1_1(a825)) | c3_1(a833) | (~c1_1(a833)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(867,plain,
% 1.53/1.69 (((~ndr1_0) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809))) <=> (c2_1(a833) | c2_1(a825) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a825)) | (~c1_1(a825)) | c3_1(a833) | (~c1_1(a833)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.69 tff(868,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a833) | c2_1(a825) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a825)) | (~c1_1(a825)) | c3_1(a833) | (~c1_1(a833))))),
% 1.53/1.69 inference(monotonicity,[status(thm)],[867])).
% 1.53/1.69 tff(869,plain,
% 1.53/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a833) | c2_1(a825) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a825)) | (~c1_1(a825)) | c3_1(a833) | (~c1_1(a833)))),
% 1.53/1.69 inference(transitivity,[status(thm)],[868, 866])).
% 1.53/1.69 tff(870,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.53/1.69 inference(quant_inst,[status(thm)],[])).
% 1.53/1.69 tff(871,plain,
% 1.53/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a833) | c2_1(a825) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a825)) | (~c1_1(a825)) | c3_1(a833) | (~c1_1(a833))),
% 1.53/1.69 inference(modus_ponens,[status(thm)],[870, 869])).
% 1.53/1.69 tff(872,plain,
% 1.53/1.69 ($false),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[871, 130, 570, 865, 857, 849, 848, 276, 847, 823, 84, 277])).
% 1.53/1.69 tff(873,plain,(c3_1(a833) | (~c1_1(a833)) | c2_1(a833) | hskp8 | (~c2_1(a796)) | (~c3_1(a796)) | c0_1(a833) | (~c0_1(a796))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.69 tff(874,plain,
% 1.53/1.69 (c3_1(a833)),
% 1.53/1.69 inference(unit_resolution,[status(thm)],[873, 818, 276, 570, 613, 618, 288, 615])).
% 1.53/1.69 tff(875,plain,
% 1.53/1.69 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 1.53/1.69 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(876,plain,
% 1.53/1.70 ((hskp8 | (~ndr1_0) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833))) <=> (hskp8 | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(877,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[876])).
% 1.53/1.70 tff(878,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[877, 875])).
% 1.53/1.70 tff(879,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(880,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a793) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | (~c3_1(a793))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[879, 878])).
% 1.53/1.70 tff(881,plain,
% 1.53/1.70 (hskp8 | (~c3_1(a833)) | (~c3_1(a793))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[880, 130, 570, 614, 288, 616, 687])).
% 1.53/1.70 tff(882,plain,
% 1.53/1.70 (~c3_1(a793)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[881, 874, 818])).
% 1.53/1.70 tff(883,plain,
% 1.53/1.70 (hskp11),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[728, 874, 613, 618, 572, 614, 616, 570, 288, 617, 615])).
% 1.53/1.70 tff(884,plain,
% 1.53/1.70 (~c2_1(a808)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[776, 883])).
% 1.53/1.70 tff(885,plain,
% 1.53/1.70 (~c1_1(a808)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[770, 883])).
% 1.53/1.70 tff(886,plain,
% 1.53/1.70 (c3_1(a808)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[812, 883])).
% 1.53/1.70 tff(887,assumption,(~c3_1(a838)), introduced(assumption)).
% 1.53/1.70 tff(888,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a838) | c3_1(a838) | c2_1(a838) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a838) | c3_1(a838) | c2_1(a838) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(889,plain,
% 1.53/1.70 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a838) | c0_1(a838) | c3_1(a838)) <=> (c0_1(a838) | c3_1(a838) | c2_1(a838) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(890,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a838) | c0_1(a838) | c3_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a838) | c3_1(a838) | c2_1(a838) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[889])).
% 1.53/1.70 tff(891,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a838) | c0_1(a838) | c3_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a838) | c3_1(a838) | c2_1(a838) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))),
% 1.53/1.70 inference(transitivity,[status(thm)],[890, 888])).
% 1.53/1.70 tff(892,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a838) | c0_1(a838) | c3_1(a838))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(893,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a838) | c3_1(a838) | c2_1(a838) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[892, 891])).
% 1.53/1.70 tff(894,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[893, 130, 571, 887, 886, 617, 422, 885, 884, 616, 795, 882])).
% 1.53/1.70 tff(895,plain,(hskp8 | c0_1(a838) | c3_1(a838) | (~c0_1(a793)) | c2_1(a838) | c1_1(a793) | (~c1_1(a833)) | (~c2_1(a793)) | c0_1(a833) | (~c2_1(a796)) | (~c3_1(a796)) | (~c0_1(a796)) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(896,plain,
% 1.53/1.70 (c3_1(a838)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[895, 818, 571, 617, 422, 616, 570, 614, 288, 613, 618, 615, 276])).
% 1.53/1.70 tff(897,plain,
% 1.53/1.70 (~c0_1(a807)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[461, 819])).
% 1.53/1.70 tff(898,plain,
% 1.53/1.70 (~c3_1(a793)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[881, 818, 669])).
% 1.53/1.70 tff(899,assumption,(~c3_1(a807)), introduced(assumption)).
% 1.53/1.70 tff(900,assumption,(~c2_1(a807)), introduced(assumption)).
% 1.53/1.70 tff(901,assumption,(~c0_1(a807)), introduced(assumption)).
% 1.53/1.70 tff(902,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(903,plain,
% 1.53/1.70 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a807) | c0_1(a807) | c3_1(a807)) <=> (c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(904,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[903])).
% 1.53/1.70 tff(905,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 1.53/1.70 inference(transitivity,[status(thm)],[904, 902])).
% 1.53/1.70 tff(906,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a807) | c0_1(a807) | c3_1(a807))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(907,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[906, 905])).
% 1.53/1.70 tff(908,plain,
% 1.53/1.70 (c3_1(a793) | (~c3_1(a838)) | c1_1(a838)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[907, 130, 617, 422, 901, 900, 899, 616, 795])).
% 1.53/1.70 tff(909,plain,
% 1.53/1.70 (c1_1(a838)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[908, 898, 431])).
% 1.53/1.70 tff(910,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(911,plain,
% 1.53/1.70 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807)) <=> (c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(912,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793)))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[911])).
% 1.53/1.70 tff(913,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793))),
% 1.53/1.70 inference(transitivity,[status(thm)],[912, 910])).
% 1.53/1.70 tff(914,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(915,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a793)) | c3_1(a793)),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[914, 913])).
% 1.53/1.70 tff(916,plain,
% 1.53/1.70 ((~c3_1(a808)) | c3_1(a793)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[915, 130, 617, 797, 796, 901, 900, 899, 616, 795])).
% 1.53/1.70 tff(917,plain,
% 1.53/1.70 (~c3_1(a808)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[916, 898])).
% 1.53/1.70 tff(918,plain,
% 1.53/1.70 (~hskp11),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[812, 917])).
% 1.53/1.70 tff(919,plain,
% 1.53/1.70 (~c1_1(a796)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[676, 918, 572])).
% 1.53/1.70 tff(920,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a838) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a838)) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a838) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a838)) | (~c1_1(a838)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(921,plain,
% 1.53/1.70 ((hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a838) | (~c3_1(a838)) | (~c1_1(a838))) <=> (hskp8 | c0_1(a838) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a838)) | (~c1_1(a838)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(922,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a838) | (~c3_1(a838)) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a838) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a838)) | (~c1_1(a838))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[921])).
% 1.53/1.70 tff(923,plain,
% 1.53/1.70 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a838) | (~c3_1(a838)) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a838) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a838)) | (~c1_1(a838)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[922, 920])).
% 1.53/1.70 tff(924,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a796) | (~c3_1(a796)) | (~c2_1(a796)) | c0_1(a838) | (~c3_1(a838)) | (~c1_1(a838)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(925,plain,
% 1.53/1.70 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a838) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | c1_1(a796) | (~c3_1(a838)) | (~c1_1(a838))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[924, 923])).
% 1.53/1.70 tff(926,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[925, 130, 818, 613, 618, 571, 431, 687, 919, 909])).
% 1.53/1.70 tff(927,plain,(hskp8 | (~c2_1(a796)) | (~c3_1(a796)) | c0_1(a838) | (~c3_1(a838)) | (~c0_1(a793)) | c2_1(a838) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c1_1(a793) | c1_1(a808) | c2_1(a808) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(928,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[927, 897, 896, 618, 288, 571, 617, 422, 818, 821, 820, 616, 771, 777, 817, 570, 614, 613])).
% 1.53/1.70 tff(929,plain,(hskp8 | (~c3_1(a796)) | c0_1(a833) | c0_1(a838) | (~c0_1(a793)) | c2_1(a838) | c1_1(a793) | (~c1_1(a833)) | (~c2_1(a793)) | (~c2_1(a796)) | (~c0_1(a796)) | c2_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(930,plain,
% 1.53/1.70 (hskp8),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[929, 571, 288, 568, 612, 422, 604, 570, 598, 569, 567, 276, 321])).
% 1.53/1.70 tff(931,plain,
% 1.53/1.70 (~c3_1(a805)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[414, 930])).
% 1.53/1.70 tff(932,plain,
% 1.53/1.70 (hskp11),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[764, 572, 569, 568, 567, 570, 288, 276, 598, 604, 612])).
% 1.53/1.70 tff(933,plain,
% 1.53/1.70 (~c2_1(a808)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[776, 932])).
% 1.53/1.70 tff(934,plain,
% 1.53/1.70 (~c2_1(a805)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[420, 930])).
% 1.53/1.70 tff(935,plain,
% 1.53/1.70 (~c1_1(a808)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[770, 932])).
% 1.53/1.70 tff(936,plain,
% 1.53/1.70 (c1_1(a805)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[429, 930])).
% 1.53/1.70 tff(937,plain,
% 1.53/1.70 (c3_1(a808)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[812, 932])).
% 1.53/1.70 tff(938,assumption,(~c3_1(a805)), introduced(assumption)).
% 1.53/1.70 tff(939,assumption,(~c2_1(a805)), introduced(assumption)).
% 1.53/1.70 tff(940,assumption,(c1_1(a805)), introduced(assumption)).
% 1.53/1.70 tff(941,assumption,(c3_1(a808)), introduced(assumption)).
% 1.53/1.70 tff(942,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a832) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a832) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(943,plain,
% 1.53/1.70 (((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c3_1(a832) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(944,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a832) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)) | (~c2_1(a832)) | (~c0_1(a832))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[943])).
% 1.53/1.70 tff(945,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a832) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[944, 942])).
% 1.53/1.70 tff(946,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(947,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a832) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)) | (~c2_1(a832)) | (~c0_1(a832))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[946, 945])).
% 1.53/1.70 tff(948,plain,
% 1.53/1.70 ((~c0_1(a808)) | (~c0_1(a832))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[947, 130, 391, 941, 940, 22, 796, 939, 938, 299])).
% 1.53/1.70 tff(949,plain,
% 1.53/1.70 (~c0_1(a808)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[948, 408])).
% 1.53/1.70 tff(950,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | (~c0_1(a832)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(951,plain,
% 1.53/1.70 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805)) <=> (c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | (~c0_1(a832)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(952,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | (~c0_1(a832))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[951])).
% 1.53/1.70 tff(953,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | (~c0_1(a832)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[952, 950])).
% 1.53/1.70 tff(954,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(955,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | (~c0_1(a832))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[954, 953])).
% 1.53/1.70 tff(956,plain,
% 1.53/1.70 (c0_1(a805) | (~c0_1(a832))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[955, 130, 941, 289, 22, 797, 796, 939, 938, 795])).
% 1.53/1.70 tff(957,plain,
% 1.53/1.70 (c0_1(a805)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[956, 408])).
% 1.53/1.70 tff(958,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a832) | c1_1(a808) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a832) | c1_1(a808) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(959,plain,
% 1.53/1.70 (((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (c1_1(a832) | c1_1(a808) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(960,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a832) | c1_1(a808) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)) | (~c0_1(a832))))),
% 1.53/1.70 inference(monotonicity,[status(thm)],[959])).
% 1.53/1.70 tff(961,plain,
% 1.53/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a832) | c1_1(a808) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.53/1.70 inference(transitivity,[status(thm)],[960, 958])).
% 1.53/1.70 tff(962,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 1.53/1.70 inference(quant_inst,[status(thm)],[])).
% 1.53/1.70 tff(963,plain,
% 1.53/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a832) | c1_1(a808) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)) | (~c0_1(a832))),
% 1.53/1.70 inference(modus_ponens,[status(thm)],[962, 961])).
% 1.53/1.70 tff(964,plain,
% 1.53/1.70 ((~c0_1(a805)) | c0_1(a808) | (~c0_1(a832))),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[963, 130, 391, 941, 940, 289, 797, 939, 287])).
% 1.53/1.70 tff(965,plain,
% 1.53/1.70 ($false),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[964, 957, 949, 408])).
% 1.53/1.70 tff(966,plain,((~c0_1(a832)) | (~c2_1(a832)) | (~c3_1(a808)) | (~c1_1(a805)) | c1_1(a832) | c1_1(a808) | c2_1(a805) | c3_1(a832) | c2_1(a808) | c3_1(a805)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.70 tff(967,plain,
% 1.53/1.70 (~c0_1(a832)),
% 1.53/1.70 inference(unit_resolution,[status(thm)],[966, 937, 391, 936, 289, 935, 934, 22, 933, 931])).
% 1.53/1.70 tff(968,plain,
% 1.53/1.70 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 1.53/1.70 inference(bind,[status(th)],[])).
% 1.53/1.70 tff(969,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.70 inference(quant_intro,[status(thm)],[968])).
% 1.53/1.70 tff(970,plain,
% 1.53/1.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.70 inference(rewrite,[status(thm)],[])).
% 1.53/1.70 tff(971,plain,
% 1.53/1.70 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(972,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[971])).
% 1.53/1.71 tff(973,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.53/1.71 tff(974,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[973, 972])).
% 1.53/1.71 tff(975,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[974, 970])).
% 1.53/1.71 tff(976,plain,(
% 1.53/1.71 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.71 inference(skolemize,[status(sab)],[975])).
% 1.53/1.71 tff(977,plain,
% 1.53/1.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[976, 969])).
% 1.53/1.71 tff(978,plain,
% 1.53/1.71 (c3_1(a833)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[816, 933, 569, 568, 570, 288, 572, 612, 276, 598, 935, 604, 567])).
% 1.53/1.71 tff(979,assumption,(~c0_1(a832)), introduced(assumption)).
% 1.53/1.71 tff(980,plain,
% 1.53/1.71 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(981,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[980])).
% 1.53/1.71 tff(982,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(983,plain,
% 1.53/1.71 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(984,plain,
% 1.53/1.71 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[983])).
% 1.53/1.71 tff(985,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.53/1.71 tff(986,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[985, 984])).
% 1.53/1.71 tff(987,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[986, 982])).
% 1.53/1.71 tff(988,plain,(
% 1.53/1.71 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.71 inference(skolemize,[status(sab)],[987])).
% 1.53/1.71 tff(989,plain,
% 1.53/1.71 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[988, 981])).
% 1.53/1.71 tff(990,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(991,plain,
% 1.53/1.71 ((hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (hskp12 | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(992,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[991])).
% 1.53/1.71 tff(993,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[992, 990])).
% 1.53/1.71 tff(994,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(995,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[994, 993])).
% 1.53/1.71 tff(996,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[995, 130, 730, 391, 288, 276, 22, 989, 979, 669])).
% 1.53/1.71 tff(997,plain,(c0_1(a832) | hskp12 | (~c2_1(a832)) | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(998,plain,
% 1.53/1.71 (hskp12),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[997, 967, 391, 288, 276, 22, 978])).
% 1.53/1.71 tff(999,plain,
% 1.53/1.71 (~c0_1(a809)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[143, 998])).
% 1.53/1.71 tff(1000,plain,
% 1.53/1.71 (c2_1(a809)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[152, 998])).
% 1.53/1.71 tff(1001,plain,
% 1.53/1.71 (c1_1(a809)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[160, 998])).
% 1.53/1.71 tff(1002,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | c0_1(a832))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1003,plain,
% 1.53/1.71 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a832) | c0_1(a832) | c3_1(a832)) <=> (c1_1(a832) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | c0_1(a832))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1004,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | c0_1(a832)))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1003])).
% 1.53/1.71 tff(1005,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | c0_1(a832))),
% 1.53/1.71 inference(transitivity,[status(thm)],[1004, 1002])).
% 1.53/1.71 tff(1006,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a832) | c0_1(a832) | c3_1(a832))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1007,plain,
% 1.53/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | c0_1(a832)),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 1.53/1.71 tff(1008,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1007, 130, 391, 1001, 1000, 289, 22, 999, 977, 967])).
% 1.53/1.71 tff(1009,plain,(c0_1(a838) | (~c2_1(a832)) | c1_1(a832) | c3_1(a832) | c0_1(a833) | c2_1(a833) | c2_1(a838) | (~c1_1(a833)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(1010,plain,
% 1.53/1.71 (c0_1(a838)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1009, 422, 289, 22, 288, 276, 391, 570, 321])).
% 1.53/1.71 tff(1011,assumption,(~hskp0), introduced(assumption)).
% 1.53/1.71 tff(1012,plain,
% 1.53/1.71 (hskp21),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[589, 1011])).
% 1.53/1.71 tff(1013,plain,
% 1.53/1.71 (c3_1(a838)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[398, 1012])).
% 1.53/1.71 tff(1014,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1015,plain,
% 1.53/1.71 ((hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838))) <=> (hskp28 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1016,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1015])).
% 1.53/1.71 tff(1017,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[1016, 1014])).
% 1.53/1.71 tff(1018,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1019,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 1.53/1.71 tff(1020,plain,
% 1.53/1.71 ((~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1019, 130, 321, 422, 332])).
% 1.53/1.71 tff(1021,plain,
% 1.53/1.71 (~c1_1(a838)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1020, 1013, 1010])).
% 1.53/1.71 tff(1022,assumption,(hskp17), introduced(assumption)).
% 1.53/1.71 tff(1023,plain,
% 1.53/1.71 (~c2_1(a825)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[846, 1022])).
% 1.53/1.71 tff(1024,plain,
% 1.53/1.71 (c0_1(a825)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[864, 1022])).
% 1.53/1.71 tff(1025,plain,
% 1.53/1.71 (c1_1(a825)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[856, 1022])).
% 1.53/1.71 tff(1026,assumption,(~c2_1(a825)), introduced(assumption)).
% 1.53/1.71 tff(1027,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a838) | c2_1(a825) | (~ndr1_0) | (~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | c2_1(a825) | (~ndr1_0) | (~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1028,plain,
% 1.53/1.71 ((hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825))) <=> (hskp28 | c2_1(a838) | c2_1(a825) | (~ndr1_0) | (~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1029,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a838) | c2_1(a825) | (~ndr1_0) | (~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1028])).
% 1.53/1.71 tff(1030,plain,
% 1.53/1.71 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | c2_1(a825) | (~ndr1_0) | (~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[1029, 1027])).
% 1.53/1.71 tff(1031,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a825) | (~c1_1(a825)) | (~c0_1(a825)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1032,plain,
% 1.53/1.71 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | c2_1(a825) | (~ndr1_0) | (~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 1.53/1.71 tff(1033,plain,
% 1.53/1.71 ((~c0_1(a825)) | (~c1_1(a825)) | (~c3_1(a838)) | (~c0_1(a838))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1032, 130, 321, 422, 1026, 332])).
% 1.53/1.71 tff(1034,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1033, 1025, 1024, 432, 431])).
% 1.53/1.71 tff(1035,plain,((~hskp17) | (~c0_1(a838)) | (~c3_1(a838)) | hskp28 | c2_1(a838) | c2_1(a825)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(1036,plain,
% 1.53/1.71 ($false),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1035, 1023, 1022, 432, 321, 422, 431])).
% 1.53/1.71 tff(1037,plain,((~hskp17) | (~c0_1(a838)) | hskp28 | c2_1(a838) | (~c3_1(a838))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.71 tff(1038,plain,
% 1.53/1.71 (~hskp17),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1037, 1013, 321, 422, 1010])).
% 1.53/1.71 tff(1039,plain,
% 1.53/1.71 (^[U: $i] : refl((hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(1040,plain,
% 1.53/1.71 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[1039])).
% 1.53/1.71 tff(1041,plain,
% 1.53/1.71 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1042,plain,
% 1.53/1.71 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0) <=> ((hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0))), rewrite(((hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0) <=> (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.53/1.71 inference(bind,[status(th)],[])).
% 1.53/1.71 tff(1043,plain,
% 1.53/1.71 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0) <=> ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.71 inference(quant_intro,[status(thm)],[1042])).
% 1.53/1.71 tff(1044,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp17) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 1.53/1.71 tff(1045,plain,
% 1.53/1.71 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 1.53/1.71 tff(1046,plain,
% 1.53/1.71 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1045, 1041])).
% 1.53/1.71 tff(1047,plain,(
% 1.53/1.71 ![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.71 inference(skolemize,[status(sab)],[1046])).
% 1.53/1.71 tff(1048,plain,
% 1.53/1.71 (![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1047, 1040])).
% 1.53/1.71 tff(1049,plain,
% 1.53/1.71 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1050,plain,
% 1.53/1.71 ((hskp17 | hskp0 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833))) <=> (hskp17 | hskp0 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.53/1.71 inference(rewrite,[status(thm)],[])).
% 1.53/1.71 tff(1051,plain,
% 1.53/1.71 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.53/1.71 inference(monotonicity,[status(thm)],[1050])).
% 1.53/1.71 tff(1052,plain,
% 1.53/1.71 (((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.53/1.71 inference(transitivity,[status(thm)],[1051, 1049])).
% 1.53/1.71 tff(1053,plain,
% 1.53/1.71 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp0 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.53/1.71 inference(quant_inst,[status(thm)],[])).
% 1.53/1.71 tff(1054,plain,
% 1.53/1.71 ((~![U: $i] : (hskp17 | hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp0 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.53/1.71 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 1.53/1.71 tff(1055,plain,
% 1.53/1.71 (hskp17 | hskp0 | (~c3_1(a833))),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1054, 130, 570, 288, 1048])).
% 1.53/1.71 tff(1056,plain,
% 1.53/1.71 (~c3_1(a833)),
% 1.53/1.71 inference(unit_resolution,[status(thm)],[1055, 1038, 1011])).
% 1.53/1.71 tff(1057,plain,
% 1.53/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1058,plain,
% 1.53/1.72 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833)) <=> (c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1059,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1058])).
% 1.53/1.72 tff(1060,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1059, 1057])).
% 1.53/1.72 tff(1061,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1062,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 1.53/1.72 tff(1063,plain,
% 1.53/1.72 ((~c0_1(a832)) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1062, 130, 422, 288, 276, 289, 22, 795])).
% 1.53/1.72 tff(1064,plain,
% 1.53/1.72 (~c0_1(a832)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1063, 1056, 1013, 1021])).
% 1.53/1.72 tff(1065,plain,
% 1.53/1.72 (hskp12),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[745, 1056, 569, 568, 570, 288, 276, 567])).
% 1.53/1.72 tff(1066,plain,
% 1.53/1.72 (~c0_1(a809)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[143, 1065])).
% 1.53/1.72 tff(1067,plain,
% 1.53/1.72 (c2_1(a809)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[152, 1065])).
% 1.53/1.72 tff(1068,plain,
% 1.53/1.72 (c1_1(a809)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[160, 1065])).
% 1.53/1.72 tff(1069,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1007, 130, 391, 1068, 1067, 289, 22, 1066, 977, 1064])).
% 1.53/1.72 tff(1070,plain,(hskp0 | (~c2_1(a832)) | c1_1(a832) | c3_1(a832) | c2_1(a838) | c0_1(a833) | c2_1(a833) | (~c1_1(a833)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(1071,plain,
% 1.53/1.72 (hskp0),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1070, 422, 289, 22, 391, 288, 276, 570, 321])).
% 1.53/1.72 tff(1072,plain,
% 1.53/1.72 (c2_1(a793)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[597, 1071])).
% 1.53/1.72 tff(1073,plain,
% 1.53/1.72 (~c1_1(a793)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[603, 1071])).
% 1.53/1.72 tff(1074,plain,
% 1.53/1.72 (c0_1(a793)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[611, 1071])).
% 1.53/1.72 tff(1075,plain,
% 1.53/1.72 (hskp11),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[764, 629, 569, 568, 567, 570, 288, 276, 614, 616, 617])).
% 1.53/1.72 tff(1076,plain,
% 1.53/1.72 (~c1_1(a808)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[770, 1075])).
% 1.53/1.72 tff(1077,plain,
% 1.53/1.72 (~c2_1(a808)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[776, 1075])).
% 1.53/1.72 tff(1078,plain,
% 1.53/1.72 (c3_1(a833)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[816, 1077, 569, 568, 570, 288, 629, 617, 276, 614, 1076, 616, 567])).
% 1.53/1.72 tff(1079,plain,
% 1.53/1.72 (^[U: $i] : refl((hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.53/1.72 inference(bind,[status(th)],[])).
% 1.53/1.72 tff(1080,plain,
% 1.53/1.72 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.53/1.72 inference(quant_intro,[status(thm)],[1079])).
% 1.53/1.72 tff(1081,plain,
% 1.53/1.72 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1082,plain,
% 1.53/1.72 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp21))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp18) <=> ((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18))), rewrite(((hskp21 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18) <=> (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp18) <=> (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.53/1.72 inference(bind,[status(th)],[])).
% 1.53/1.72 tff(1083,plain,
% 1.53/1.72 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp18) <=> ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.53/1.72 inference(quant_intro,[status(thm)],[1082])).
% 1.53/1.72 tff(1084,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp21) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.53/1.72 tff(1085,plain,
% 1.53/1.72 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 1.53/1.72 tff(1086,plain,
% 1.53/1.72 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1085, 1081])).
% 1.53/1.72 tff(1087,plain,(
% 1.53/1.72 ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.53/1.72 inference(skolemize,[status(sab)],[1086])).
% 1.53/1.72 tff(1088,plain,
% 1.53/1.72 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1087, 1080])).
% 1.53/1.72 tff(1089,plain,
% 1.53/1.72 (c3_1(a808)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[812, 1075])).
% 1.53/1.72 tff(1090,plain,
% 1.53/1.72 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp21 | hskp18 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp21 | hskp18 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1091,plain,
% 1.53/1.72 ((hskp21 | hskp18 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c3_1(a808))) <=> (hskp21 | hskp18 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1092,plain,
% 1.53/1.72 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp21 | hskp18 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1091])).
% 1.53/1.72 tff(1093,plain,
% 1.53/1.72 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp21 | hskp18 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1092, 1090])).
% 1.53/1.72 tff(1094,plain,
% 1.53/1.72 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1095,plain,
% 1.53/1.72 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp21 | hskp18 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.53/1.72 tff(1096,plain,
% 1.53/1.72 (hskp18),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1095, 130, 629, 1089, 1076, 1077, 1088])).
% 1.53/1.72 tff(1097,plain,
% 1.53/1.72 (((~hskp18) | (~c2_1(a828))) <=> ((~hskp18) | (~c2_1(a828)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1098,plain,
% 1.53/1.72 (((~c2_1(a828)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a828)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1099,axiom,((~c2_1(a828)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.53/1.72 tff(1100,plain,
% 1.53/1.72 ((~hskp18) | (~c2_1(a828))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 1.53/1.72 tff(1101,plain,
% 1.53/1.72 ((~hskp18) | (~c2_1(a828))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1100, 1097])).
% 1.53/1.72 tff(1102,plain,
% 1.53/1.72 (~c2_1(a828)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1101, 1096])).
% 1.53/1.72 tff(1103,plain,
% 1.53/1.72 (((~hskp18) | (~c3_1(a828))) <=> ((~hskp18) | (~c3_1(a828)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1104,plain,
% 1.53/1.72 (((~c3_1(a828)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a828)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1105,axiom,((~c3_1(a828)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.53/1.72 tff(1106,plain,
% 1.53/1.72 ((~hskp18) | (~c3_1(a828))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1105, 1104])).
% 1.53/1.72 tff(1107,plain,
% 1.53/1.72 ((~hskp18) | (~c3_1(a828))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1106, 1103])).
% 1.53/1.72 tff(1108,plain,
% 1.53/1.72 (~c3_1(a828)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1107, 1096])).
% 1.53/1.72 tff(1109,plain,
% 1.53/1.72 (((~hskp18) | (~c1_1(a828))) <=> ((~hskp18) | (~c1_1(a828)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1110,plain,
% 1.53/1.72 (((~c1_1(a828)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a828)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1111,axiom,((~c1_1(a828)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.53/1.72 tff(1112,plain,
% 1.53/1.72 ((~hskp18) | (~c1_1(a828))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 1.53/1.72 tff(1113,plain,
% 1.53/1.72 ((~hskp18) | (~c1_1(a828))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1112, 1109])).
% 1.53/1.72 tff(1114,plain,
% 1.53/1.72 (~c1_1(a828)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1113, 1096])).
% 1.53/1.72 tff(1115,assumption,(~c3_1(a828)), introduced(assumption)).
% 1.53/1.72 tff(1116,assumption,(~c2_1(a828)), introduced(assumption)).
% 1.53/1.72 tff(1117,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a793)) | c3_1(a793))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a793)) | c3_1(a793))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1118,plain,
% 1.53/1.72 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828)) <=> (c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a793)) | c3_1(a793))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1119,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a793)) | c3_1(a793)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1118])).
% 1.53/1.72 tff(1120,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a793)) | c3_1(a793))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1119, 1117])).
% 1.53/1.72 tff(1121,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1122,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c1_1(a793) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a793)) | c3_1(a793)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 1.53/1.72 tff(1123,plain,
% 1.53/1.72 (c0_1(a828) | c3_1(a793)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1122, 130, 941, 617, 1116, 1115, 797, 796, 616, 795])).
% 1.53/1.72 tff(1124,plain,
% 1.53/1.72 (c0_1(a828)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1123, 898])).
% 1.53/1.72 tff(1125,assumption,(~c1_1(a828)), introduced(assumption)).
% 1.53/1.72 tff(1126,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a828)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1127,plain,
% 1.53/1.72 (((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807)) <=> (c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a828)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1128,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a828))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1127])).
% 1.53/1.72 tff(1129,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a828)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1128, 1126])).
% 1.53/1.72 tff(1130,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a807) | c0_1(a807) | c3_1(a807))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1131,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a807) | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a828))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 1.53/1.72 tff(1132,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1131, 130, 941, 1125, 1115, 797, 796, 897, 821, 820, 795, 1124])).
% 1.53/1.72 tff(1133,plain,(hskp8 | (~c3_1(a808)) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~c0_1(a793)) | c2_1(a828) | c1_1(a793) | (~c3_1(a833)) | (~c1_1(a833)) | (~c2_1(a793)) | c0_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(1134,plain,
% 1.53/1.72 (hskp8),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1133, 1089, 1114, 1108, 1076, 1077, 617, 1102, 616, 1078, 570, 614, 288, 321])).
% 1.53/1.72 tff(1135,plain,
% 1.53/1.72 (~c3_1(a805)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[414, 1134])).
% 1.53/1.72 tff(1136,plain,
% 1.53/1.72 (~c2_1(a805)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[420, 1134])).
% 1.53/1.72 tff(1137,plain,
% 1.53/1.72 (c1_1(a805)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[429, 1134])).
% 1.53/1.72 tff(1138,plain,
% 1.53/1.72 (~c0_1(a832)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[966, 1137, 391, 1089, 289, 1076, 1136, 22, 1077, 1135])).
% 1.53/1.72 tff(1139,plain,
% 1.53/1.72 (hskp12),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[997, 1138, 391, 288, 276, 22, 1078])).
% 1.53/1.72 tff(1140,plain,
% 1.53/1.72 (~c0_1(a809)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[143, 1139])).
% 1.53/1.72 tff(1141,plain,
% 1.53/1.72 (c2_1(a809)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[152, 1139])).
% 1.53/1.72 tff(1142,plain,
% 1.53/1.72 (c1_1(a809)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[160, 1139])).
% 1.53/1.72 tff(1143,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1007, 130, 391, 1142, 1141, 289, 22, 1140, 977, 1138])).
% 1.53/1.72 tff(1144,plain,(hskp21 | (~c2_1(a832)) | c1_1(a832) | c3_1(a832) | c0_1(a833) | c2_1(a833) | (~c0_1(a793)) | c1_1(a793) | (~c1_1(a833)) | (~c2_1(a793)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(1145,plain,
% 1.53/1.72 (hskp21),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1144, 1074, 289, 22, 288, 276, 391, 1073, 570, 1072, 321])).
% 1.53/1.72 tff(1146,plain,
% 1.53/1.72 (c3_1(a838)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[398, 1145])).
% 1.53/1.72 tff(1147,plain,
% 1.53/1.72 (~c1_1(a838)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1020, 1146, 1010])).
% 1.53/1.72 tff(1148,plain,
% 1.53/1.72 (~c3_1(a793)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[881, 818, 874])).
% 1.53/1.72 tff(1149,assumption,(~c1_1(a838)), introduced(assumption)).
% 1.53/1.72 tff(1150,plain,
% 1.53/1.72 ($false),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[907, 130, 431, 617, 422, 897, 821, 820, 616, 795, 1149, 1148])).
% 1.53/1.72 tff(1151,plain,(hskp8 | (~c3_1(a838)) | (~c0_1(a793)) | c2_1(a838) | c1_1(a793) | c1_1(a838) | (~c1_1(a833)) | (~c2_1(a793)) | c0_1(a833) | c2_1(a833) | (~c2_1(a796)) | (~c3_1(a796)) | (~c0_1(a796)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.72 tff(1152,plain,
% 1.53/1.72 (hskp8),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1151, 1146, 1074, 422, 1073, 1147, 570, 1072, 288, 276, 569, 568, 567, 321])).
% 1.53/1.72 tff(1153,plain,
% 1.53/1.72 (~c2_1(a805)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[420, 1152])).
% 1.53/1.72 tff(1154,plain,
% 1.53/1.72 (c1_1(a805)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[429, 1152])).
% 1.53/1.72 tff(1155,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a838) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1156,plain,
% 1.53/1.72 ((hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805))) <=> (hskp28 | c2_1(a838) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1157,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | c2_1(a838) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1156])).
% 1.53/1.72 tff(1158,plain,
% 1.53/1.72 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1157, 1155])).
% 1.53/1.72 tff(1159,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1160,plain,
% 1.53/1.72 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | c2_1(a838) | c2_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838))),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 1.53/1.72 tff(1161,plain,
% 1.53/1.72 (~c0_1(a805)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1160, 130, 321, 1010, 1146, 1154, 422, 1153, 332])).
% 1.53/1.72 tff(1162,plain,
% 1.53/1.72 (~c3_1(a805)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[414, 1152])).
% 1.53/1.72 tff(1163,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c2_1(a805) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | c0_1(a805) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c2_1(a805) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | c0_1(a805) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1164,plain,
% 1.53/1.72 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a805) | c0_1(a805) | c3_1(a805)) <=> (c2_1(a838) | c2_1(a805) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | c0_1(a805) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1165,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a805) | c0_1(a805) | c3_1(a805))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c2_1(a805) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | c0_1(a805) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1164])).
% 1.53/1.72 tff(1166,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a805) | c0_1(a805) | c3_1(a805))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c2_1(a805) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | c0_1(a805) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 1.53/1.72 inference(transitivity,[status(thm)],[1165, 1163])).
% 1.53/1.72 tff(1167,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a805) | c0_1(a805) | c3_1(a805))),
% 1.53/1.72 inference(quant_inst,[status(thm)],[])).
% 1.53/1.72 tff(1168,plain,
% 1.53/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c2_1(a805) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | c0_1(a805) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)),
% 1.53/1.72 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 1.53/1.72 tff(1169,plain,
% 1.53/1.72 (c0_1(a805) | c3_1(a793)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1168, 130, 1146, 1074, 422, 1153, 1162, 1073, 795, 1147])).
% 1.53/1.72 tff(1170,plain,
% 1.53/1.72 (c3_1(a793)),
% 1.53/1.72 inference(unit_resolution,[status(thm)],[1169, 1161])).
% 1.53/1.72 tff(1171,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a805) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c0_1(a805) | (~c1_1(a805)) | (~c2_1(a793)) | (~c3_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c0_1(a805) | (~c1_1(a805)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1172,plain,
% 1.53/1.72 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c3_1(a805) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c0_1(a805) | (~c1_1(a805)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 1.53/1.72 inference(rewrite,[status(thm)],[])).
% 1.53/1.72 tff(1173,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a805) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c0_1(a805) | (~c1_1(a805)) | (~c2_1(a793)) | (~c3_1(a793))))),
% 1.53/1.72 inference(monotonicity,[status(thm)],[1172])).
% 1.53/1.72 tff(1174,plain,
% 1.53/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c0_1(a805) | (~c1_1(a805)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1173, 1171])).
% 1.53/1.73 tff(1175,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1176,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | c1_1(a793) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c0_1(a805) | (~c1_1(a805)) | (~c2_1(a793)) | (~c3_1(a793))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 1.53/1.73 tff(1177,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1176, 130, 567, 569, 568, 1154, 1072, 1162, 1073, 719, 1170, 1161])).
% 1.53/1.73 tff(1178,plain,(c2_1(a838) | hskp28 | (~c1_1(a833)) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~c2_1(a832))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(1179,plain,
% 1.53/1.73 (c2_1(a838)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1178, 565, 321, 564, 558, 353, 347, 341])).
% 1.53/1.73 tff(1180,plain,
% 1.53/1.73 (~hskp21),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[389, 1179])).
% 1.53/1.73 tff(1181,plain,
% 1.53/1.73 (hskp21 | hskp0),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[588, 130, 341, 353, 347, 582])).
% 1.53/1.73 tff(1182,plain,
% 1.53/1.73 (hskp0),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1181, 1180])).
% 1.53/1.73 tff(1183,plain,
% 1.53/1.73 (c2_1(a793)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[597, 1182])).
% 1.53/1.73 tff(1184,plain,
% 1.53/1.73 (c0_1(a793)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[611, 1182])).
% 1.53/1.73 tff(1185,plain,
% 1.53/1.73 (~c1_1(a793)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[603, 1182])).
% 1.53/1.73 tff(1186,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1144, 1185, 1184, 353, 347, 564, 558, 341, 1180, 565, 1183, 321])).
% 1.53/1.73 tff(1187,plain,(hskp30 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(1188,plain,
% 1.53/1.73 (hskp30),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1187, 321])).
% 1.53/1.73 tff(1189,plain,
% 1.53/1.73 (c3_1(a867)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[30, 1188])).
% 1.53/1.73 tff(1190,plain,
% 1.53/1.73 (c1_1(a867)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[38, 1188])).
% 1.53/1.73 tff(1191,plain,
% 1.53/1.73 (c0_1(a867)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[46, 1188])).
% 1.53/1.73 tff(1192,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)) | (~c1_1(a867)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)) | (~c1_1(a867)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1193,plain,
% 1.53/1.73 ((hskp28 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)) | c2_1(a867) | (~c1_1(a867)) | (~c0_1(a867))) <=> (hskp28 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)) | (~c1_1(a867)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1194,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)) | c2_1(a867) | (~c1_1(a867)) | (~c0_1(a867)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)) | (~c1_1(a867))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1193])).
% 1.53/1.73 tff(1195,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)) | c2_1(a867) | (~c1_1(a867)) | (~c0_1(a867)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)) | (~c1_1(a867)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1194, 1192])).
% 1.53/1.73 tff(1196,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp28 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)) | c2_1(a867) | (~c1_1(a867)) | (~c0_1(a867)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1197,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp28 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)) | (~c1_1(a867))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 1.53/1.73 tff(1198,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1197, 130, 321, 1191, 1190, 1189, 332, 322])).
% 1.53/1.73 tff(1199,plain,(c2_1(a867) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(1200,plain,
% 1.53/1.73 (c2_1(a867)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1199, 321])).
% 1.53/1.73 tff(1201,plain,
% 1.53/1.73 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(1202,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[1201])).
% 1.53/1.73 tff(1203,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1204,plain,
% 1.53/1.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp15) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(1205,plain,
% 1.53/1.73 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[1204])).
% 1.53/1.73 tff(1206,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.53/1.73 tff(1207,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 1.53/1.73 tff(1208,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1207, 1203])).
% 1.53/1.73 tff(1209,plain,(
% 1.53/1.73 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.53/1.73 inference(skolemize,[status(sab)],[1208])).
% 1.53/1.73 tff(1210,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1209, 1202])).
% 1.53/1.73 tff(1211,plain,
% 1.53/1.73 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(1212,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[1211])).
% 1.53/1.73 tff(1213,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1214,plain,
% 1.53/1.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp28) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(1215,plain,
% 1.53/1.73 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[1214])).
% 1.53/1.73 tff(1216,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.53/1.73 tff(1217,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 1.53/1.73 tff(1218,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1217, 1213])).
% 1.53/1.73 tff(1219,plain,(
% 1.53/1.73 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.53/1.73 inference(skolemize,[status(sab)],[1218])).
% 1.53/1.73 tff(1220,plain,
% 1.53/1.73 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1219, 1212])).
% 1.53/1.73 tff(1221,assumption,(hskp21), introduced(assumption)).
% 1.53/1.73 tff(1222,plain,
% 1.53/1.73 (~c2_1(a838)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[389, 1221])).
% 1.53/1.73 tff(1223,plain,
% 1.53/1.73 (^[U: $i] : refl((hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(1224,plain,
% 1.53/1.73 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[1223])).
% 1.53/1.73 tff(1225,plain,
% 1.53/1.73 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1226,plain,
% 1.53/1.73 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp19) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp19))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp19) <=> (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp19) <=> (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.53/1.73 inference(bind,[status(th)],[])).
% 1.53/1.73 tff(1227,plain,
% 1.53/1.73 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp19) <=> ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.73 inference(quant_intro,[status(thm)],[1226])).
% 1.53/1.73 tff(1228,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.53/1.73 tff(1229,plain,
% 1.53/1.73 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 1.53/1.73 tff(1230,plain,
% 1.53/1.73 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1229, 1225])).
% 1.53/1.73 tff(1231,plain,(
% 1.53/1.73 ![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.73 inference(skolemize,[status(sab)],[1230])).
% 1.53/1.73 tff(1232,plain,
% 1.53/1.73 (![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1231, 1224])).
% 1.53/1.73 tff(1233,plain,
% 1.53/1.73 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1234,plain,
% 1.53/1.73 ((hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867))) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1235,plain,
% 1.53/1.73 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1234])).
% 1.53/1.73 tff(1236,plain,
% 1.53/1.73 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1235, 1233])).
% 1.53/1.73 tff(1237,plain,
% 1.53/1.73 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1238,plain,
% 1.53/1.73 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 1.53/1.73 tff(1239,plain,
% 1.53/1.73 (hskp21 | hskp11 | (~c2_1(a867))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1238, 130, 1190, 1189, 628])).
% 1.53/1.73 tff(1240,plain,
% 1.53/1.73 (hskp11),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1239, 629, 1200])).
% 1.53/1.73 tff(1241,plain,
% 1.53/1.73 (~c2_1(a808)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[776, 1240])).
% 1.53/1.73 tff(1242,plain,
% 1.53/1.73 (~c1_1(a808)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[770, 1240])).
% 1.53/1.73 tff(1243,plain,
% 1.53/1.73 (c3_1(a808)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[812, 1240])).
% 1.53/1.73 tff(1244,plain,
% 1.53/1.73 (hskp18),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1095, 130, 629, 1243, 1242, 1241, 1088])).
% 1.53/1.73 tff(1245,plain,
% 1.53/1.73 (~c3_1(a828)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1107, 1244])).
% 1.53/1.73 tff(1246,plain,
% 1.53/1.73 (~c2_1(a828)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1101, 1244])).
% 1.53/1.73 tff(1247,assumption,(hskp15), introduced(assumption)).
% 1.53/1.73 tff(1248,plain,
% 1.53/1.73 (((~hskp15) | (~c1_1(a817))) <=> ((~hskp15) | (~c1_1(a817)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1249,plain,
% 1.53/1.73 (((~c1_1(a817)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a817)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1250,axiom,((~c1_1(a817)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.53/1.73 tff(1251,plain,
% 1.53/1.73 ((~hskp15) | (~c1_1(a817))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1250, 1249])).
% 1.53/1.73 tff(1252,plain,
% 1.53/1.73 ((~hskp15) | (~c1_1(a817))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1251, 1248])).
% 1.53/1.73 tff(1253,plain,
% 1.53/1.73 (~c1_1(a817)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1252, 1247])).
% 1.53/1.73 tff(1254,plain,
% 1.53/1.73 (((~hskp15) | c3_1(a817)) <=> ((~hskp15) | c3_1(a817))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1255,axiom,((~hskp15) | c3_1(a817)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.53/1.73 tff(1256,plain,
% 1.53/1.73 ((~hskp15) | c3_1(a817)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 1.53/1.73 tff(1257,plain,
% 1.53/1.73 ((~hskp15) | c3_1(a817)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1256, 1254])).
% 1.53/1.73 tff(1258,plain,
% 1.53/1.73 ((~hskp15) | c3_1(a817)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1257, 1254])).
% 1.53/1.73 tff(1259,plain,
% 1.53/1.73 ((~hskp15) | c3_1(a817)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1258, 1254])).
% 1.53/1.73 tff(1260,plain,
% 1.53/1.73 ((~hskp15) | c3_1(a817)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1259, 1254])).
% 1.53/1.73 tff(1261,plain,
% 1.53/1.73 (c3_1(a817)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1260, 1247])).
% 1.53/1.73 tff(1262,plain,
% 1.53/1.73 (((~hskp15) | c2_1(a817)) <=> ((~hskp15) | c2_1(a817))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1263,axiom,((~hskp15) | c2_1(a817)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.53/1.73 tff(1264,plain,
% 1.53/1.73 ((~hskp15) | c2_1(a817)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 1.53/1.73 tff(1265,plain,
% 1.53/1.73 ((~hskp15) | c2_1(a817)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1264, 1262])).
% 1.53/1.73 tff(1266,plain,
% 1.53/1.73 ((~hskp15) | c2_1(a817)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1265, 1262])).
% 1.53/1.73 tff(1267,plain,
% 1.53/1.73 ((~hskp15) | c2_1(a817)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1266, 1262])).
% 1.53/1.73 tff(1268,plain,
% 1.53/1.73 ((~hskp15) | c2_1(a817)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1267, 1262])).
% 1.53/1.73 tff(1269,plain,
% 1.53/1.73 (c2_1(a817)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1268, 1247])).
% 1.53/1.73 tff(1270,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a817) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a817)) | (~c3_1(a817)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a817) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a817)) | (~c3_1(a817)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1271,plain,
% 1.53/1.73 ((hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817))) <=> (hskp28 | c1_1(a817) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a817)) | (~c3_1(a817)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1272,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a817) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a817)) | (~c3_1(a817))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1271])).
% 1.53/1.73 tff(1273,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a817) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a817)) | (~c3_1(a817)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1272, 1270])).
% 1.53/1.73 tff(1274,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1275,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a817) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a817)) | (~c3_1(a817))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 1.53/1.73 tff(1276,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1275, 130, 321, 1191, 1190, 1189, 1269, 1261, 1253, 1220])).
% 1.53/1.73 tff(1277,plain,((~hskp15) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.53/1.73 tff(1278,plain,
% 1.53/1.73 (~hskp15),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1277, 321])).
% 1.53/1.73 tff(1279,assumption,(c2_1(a867)), introduced(assumption)).
% 1.53/1.73 tff(1280,assumption,(c2_1(a833)), introduced(assumption)).
% 1.53/1.73 tff(1281,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1282,plain,
% 1.53/1.73 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a833) | (~c3_1(a833)) | (~c2_1(a833))) <=> (c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1283,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a833) | (~c3_1(a833)) | (~c2_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833))))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1282])).
% 1.53/1.73 tff(1284,plain,
% 1.53/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a833) | (~c3_1(a833)) | (~c2_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1283, 1281])).
% 1.53/1.73 tff(1285,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a833) | (~c3_1(a833)) | (~c2_1(a833)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1286,plain,
% 1.53/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833))),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 1.53/1.73 tff(1287,plain,
% 1.53/1.73 ((~c2_1(a833)) | (~c3_1(a833))),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1286, 130, 58, 57, 65, 288, 180, 1279])).
% 1.53/1.73 tff(1288,plain,
% 1.53/1.73 (~c3_1(a833)),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1287, 1280])).
% 1.53/1.73 tff(1289,assumption,(~hskp15), introduced(assumption)).
% 1.53/1.73 tff(1290,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | c3_1(a833))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | c3_1(a833))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1291,plain,
% 1.53/1.73 ((hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a833) | c0_1(a833) | (~c2_1(a833))) <=> (hskp15 | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | c3_1(a833))),
% 1.53/1.73 inference(rewrite,[status(thm)],[])).
% 1.53/1.73 tff(1292,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a833) | c0_1(a833) | (~c2_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | c3_1(a833)))),
% 1.53/1.73 inference(monotonicity,[status(thm)],[1291])).
% 1.53/1.73 tff(1293,plain,
% 1.53/1.73 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a833) | c0_1(a833) | (~c2_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | c3_1(a833))),
% 1.53/1.73 inference(transitivity,[status(thm)],[1292, 1290])).
% 1.53/1.73 tff(1294,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a833) | c0_1(a833) | (~c2_1(a833)))),
% 1.53/1.73 inference(quant_inst,[status(thm)],[])).
% 1.53/1.73 tff(1295,plain,
% 1.53/1.73 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a833) | (~c2_1(a833)) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | c3_1(a833)),
% 1.53/1.73 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 1.53/1.73 tff(1296,plain,
% 1.53/1.73 ($false),
% 1.53/1.73 inference(unit_resolution,[status(thm)],[1295, 130, 1289, 57, 65, 288, 1280, 1210, 1288, 1279])).
% 1.53/1.73 tff(1297,plain,((~c2_1(a833)) | hskp15 | (~c1_1(a867)) | (~c3_1(a867)) | c0_1(a833) | (~c2_1(a867)) | (~c0_1(a867))), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(1298,plain,
% 1.53/1.74 (~c2_1(a833)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1297, 288, 1190, 1189, 1278, 1200, 1191])).
% 1.53/1.74 tff(1299,plain,
% 1.53/1.74 (^[U: $i] : refl((hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(1300,plain,
% 1.53/1.74 (![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[1299])).
% 1.53/1.74 tff(1301,plain,
% 1.53/1.74 (![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1302,plain,
% 1.53/1.74 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp2) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp2))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp2) <=> (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp2) <=> (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(1303,plain,
% 1.53/1.74 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp2) <=> ![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[1302])).
% 1.53/1.74 tff(1304,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.53/1.74 tff(1305,plain,
% 1.53/1.74 (![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 1.53/1.74 tff(1306,plain,
% 1.53/1.74 (![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1305, 1301])).
% 1.53/1.74 tff(1307,plain,(
% 1.53/1.74 ![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.53/1.74 inference(skolemize,[status(sab)],[1306])).
% 1.53/1.74 tff(1308,plain,
% 1.53/1.74 (![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1307, 1300])).
% 1.53/1.74 tff(1309,plain,
% 1.53/1.74 (~c1_1(a828)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1113, 1244])).
% 1.53/1.74 tff(1310,plain,
% 1.53/1.74 (((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))) <=> ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp20 | hskp2 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1311,plain,
% 1.53/1.74 ((hskp20 | hskp2 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | c3_1(a828)) <=> (hskp20 | hskp2 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1312,plain,
% 1.53/1.74 (((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | c3_1(a828))) <=> ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1311])).
% 1.53/1.74 tff(1313,plain,
% 1.53/1.74 (((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | c3_1(a828))) <=> ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp20 | hskp2 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1312, 1310])).
% 1.53/1.74 tff(1314,plain,
% 1.53/1.74 ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | c3_1(a828))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1315,plain,
% 1.53/1.74 ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp20 | hskp2 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 1.53/1.74 tff(1316,plain,
% 1.53/1.74 (hskp2),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1315, 130, 308, 1309, 1246, 1245, 1308])).
% 1.53/1.74 tff(1317,plain,
% 1.53/1.74 (((~hskp2) | (~c3_1(a795))) <=> ((~hskp2) | (~c3_1(a795)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1318,plain,
% 1.53/1.74 (((~c3_1(a795)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a795)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1319,axiom,((~c3_1(a795)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.53/1.74 tff(1320,plain,
% 1.53/1.74 ((~hskp2) | (~c3_1(a795))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 1.53/1.74 tff(1321,plain,
% 1.53/1.74 ((~hskp2) | (~c3_1(a795))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1320, 1317])).
% 1.53/1.74 tff(1322,plain,
% 1.53/1.74 (~c3_1(a795)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1321, 1316])).
% 1.53/1.74 tff(1323,plain,
% 1.53/1.74 (((~hskp2) | (~c1_1(a795))) <=> ((~hskp2) | (~c1_1(a795)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1324,plain,
% 1.53/1.74 (((~c1_1(a795)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a795)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1325,axiom,((~c1_1(a795)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.53/1.74 tff(1326,plain,
% 1.53/1.74 ((~hskp2) | (~c1_1(a795))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 1.53/1.74 tff(1327,plain,
% 1.53/1.74 ((~hskp2) | (~c1_1(a795))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1326, 1323])).
% 1.53/1.74 tff(1328,plain,
% 1.53/1.74 (~c1_1(a795)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1327, 1316])).
% 1.53/1.74 tff(1329,plain,
% 1.53/1.74 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(1330,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[1329])).
% 1.53/1.74 tff(1331,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1332,plain,
% 1.53/1.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(1333,plain,
% 1.53/1.74 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[1332])).
% 1.53/1.74 tff(1334,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 1.53/1.74 tff(1335,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1334, 1333])).
% 1.53/1.74 tff(1336,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1335, 1331])).
% 1.53/1.74 tff(1337,plain,(
% 1.53/1.74 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.53/1.74 inference(skolemize,[status(sab)],[1336])).
% 1.53/1.74 tff(1338,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1337, 1330])).
% 1.53/1.74 tff(1339,assumption,(~c2_1(a793)), introduced(assumption)).
% 1.53/1.74 tff(1340,plain,
% 1.53/1.74 (~hskp0),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[597, 1339])).
% 1.53/1.74 tff(1341,assumption,(~c0_1(a793)), introduced(assumption)).
% 1.53/1.74 tff(1342,plain,
% 1.53/1.74 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1343,plain,
% 1.53/1.74 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795))) <=> (hskp21 | hskp0 | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1344,plain,
% 1.53/1.74 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1343])).
% 1.53/1.74 tff(1345,plain,
% 1.53/1.74 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1344, 1342])).
% 1.53/1.74 tff(1346,plain,
% 1.53/1.74 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1347,plain,
% 1.53/1.74 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1346, 1345])).
% 1.53/1.74 tff(1348,plain,
% 1.53/1.74 (~c2_1(a795)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1347, 130, 629, 1011, 1328, 1322, 582])).
% 1.53/1.74 tff(1349,plain,
% 1.53/1.74 (((~hskp2) | (~c0_1(a795))) <=> ((~hskp2) | (~c0_1(a795)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1350,plain,
% 1.53/1.74 (((~c0_1(a795)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a795)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1351,axiom,((~c0_1(a795)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.53/1.74 tff(1352,plain,
% 1.53/1.74 ((~hskp2) | (~c0_1(a795))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 1.53/1.74 tff(1353,plain,
% 1.53/1.74 ((~hskp2) | (~c0_1(a795))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1352, 1349])).
% 1.53/1.74 tff(1354,plain,
% 1.53/1.74 (~c0_1(a795)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1353, 1316])).
% 1.53/1.74 tff(1355,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a828)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1356,plain,
% 1.53/1.74 (((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795)) <=> (c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a828)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1357,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a828))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1356])).
% 1.53/1.74 tff(1358,plain,
% 1.53/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a828)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1357, 1355])).
% 1.53/1.74 tff(1359,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a828) | c3_1(a828) | (~c0_1(a828)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1360,plain,
% 1.53/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a828))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 1.53/1.74 tff(1361,plain,
% 1.53/1.74 (~c0_1(a828)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1360, 130, 1243, 1309, 1245, 1242, 1241, 1354, 1322, 795, 1348])).
% 1.53/1.74 tff(1362,assumption,(~c2_1(a832)), introduced(assumption)).
% 1.53/1.74 tff(1363,plain,
% 1.53/1.74 (~hskp19),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[340, 1362])).
% 1.53/1.74 tff(1364,plain,
% 1.53/1.74 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1365,plain,
% 1.53/1.74 ((hskp28 | hskp19 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832))) <=> (hskp28 | hskp19 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1366,plain,
% 1.53/1.74 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1365])).
% 1.53/1.74 tff(1367,plain,
% 1.53/1.74 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1366, 1364])).
% 1.53/1.74 tff(1368,plain,
% 1.53/1.74 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1369,plain,
% 1.53/1.74 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 1.53/1.74 tff(1370,plain,
% 1.53/1.74 (hskp19 | c2_1(a832) | (~c1_1(a832))),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1369, 130, 321, 22, 1232])).
% 1.53/1.74 tff(1371,plain,
% 1.53/1.74 (~c1_1(a832)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1370, 1363, 1362])).
% 1.53/1.74 tff(1372,assumption,(hskp7), introduced(assumption)).
% 1.53/1.74 tff(1373,plain,
% 1.53/1.74 (((~hskp7) | (~c2_1(a803))) <=> ((~hskp7) | (~c2_1(a803)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1374,plain,
% 1.53/1.74 (((~c2_1(a803)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a803)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1375,axiom,((~c2_1(a803)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.53/1.74 tff(1376,plain,
% 1.53/1.74 ((~hskp7) | (~c2_1(a803))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 1.53/1.74 tff(1377,plain,
% 1.53/1.74 ((~hskp7) | (~c2_1(a803))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1376, 1373])).
% 1.53/1.74 tff(1378,plain,
% 1.53/1.74 (~c2_1(a803)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1377, 1372])).
% 1.53/1.74 tff(1379,plain,
% 1.53/1.74 (((~hskp7) | c3_1(a803)) <=> ((~hskp7) | c3_1(a803))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1380,axiom,((~hskp7) | c3_1(a803)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.53/1.74 tff(1381,plain,
% 1.53/1.74 ((~hskp7) | c3_1(a803)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 1.53/1.74 tff(1382,plain,
% 1.53/1.74 ((~hskp7) | c3_1(a803)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1381, 1379])).
% 1.53/1.74 tff(1383,plain,
% 1.53/1.74 ((~hskp7) | c3_1(a803)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1382, 1379])).
% 1.53/1.74 tff(1384,plain,
% 1.53/1.74 ((~hskp7) | c3_1(a803)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1383, 1379])).
% 1.53/1.74 tff(1385,plain,
% 1.53/1.74 ((~hskp7) | c3_1(a803)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1384, 1379])).
% 1.53/1.74 tff(1386,plain,
% 1.53/1.74 (c3_1(a803)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1385, 1372])).
% 1.53/1.74 tff(1387,plain,
% 1.53/1.74 (((~hskp7) | c1_1(a803)) <=> ((~hskp7) | c1_1(a803))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1388,axiom,((~hskp7) | c1_1(a803)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.53/1.74 tff(1389,plain,
% 1.53/1.74 ((~hskp7) | c1_1(a803)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 1.53/1.74 tff(1390,plain,
% 1.53/1.74 ((~hskp7) | c1_1(a803)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1389, 1387])).
% 1.53/1.74 tff(1391,plain,
% 1.53/1.74 ((~hskp7) | c1_1(a803)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1390, 1387])).
% 1.53/1.74 tff(1392,plain,
% 1.53/1.74 ((~hskp7) | c1_1(a803)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1391, 1387])).
% 1.53/1.74 tff(1393,plain,
% 1.53/1.74 ((~hskp7) | c1_1(a803)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1392, 1387])).
% 1.53/1.74 tff(1394,plain,
% 1.53/1.74 (c1_1(a803)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1393, 1372])).
% 1.53/1.74 tff(1395,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | c1_1(a832) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | c1_1(a832) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1396,plain,
% 1.53/1.74 ((hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c2_1(a832) | c1_1(a832)) <=> (hskp19 | c2_1(a832) | c1_1(a832) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1397,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | c1_1(a832) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803))))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1396])).
% 1.53/1.74 tff(1398,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | c1_1(a832) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1397, 1395])).
% 1.53/1.74 tff(1399,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c2_1(a832) | c1_1(a832))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1400,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | c1_1(a832) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 1.53/1.74 tff(1401,plain,
% 1.53/1.74 ($false),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1400, 130, 1363, 1362, 1394, 1386, 289, 22, 1378, 10])).
% 1.53/1.74 tff(1402,plain,((~hskp7) | c2_1(a832) | c1_1(a832) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.74 tff(1403,plain,
% 1.53/1.74 (~hskp7),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1402, 1362, 1371, 22])).
% 1.53/1.74 tff(1404,plain,
% 1.53/1.74 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(1405,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[1404])).
% 1.53/1.74 tff(1406,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1407,plain,
% 1.53/1.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.53/1.74 inference(bind,[status(th)],[])).
% 1.53/1.74 tff(1408,plain,
% 1.53/1.74 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.74 inference(quant_intro,[status(thm)],[1407])).
% 1.53/1.74 tff(1409,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.53/1.74 tff(1410,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 1.53/1.74 tff(1411,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1410, 1406])).
% 1.53/1.74 tff(1412,plain,(
% 1.53/1.74 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.74 inference(skolemize,[status(sab)],[1411])).
% 1.53/1.74 tff(1413,plain,
% 1.53/1.74 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1412, 1405])).
% 1.53/1.74 tff(1414,assumption,(hskp11), introduced(assumption)).
% 1.53/1.74 tff(1415,plain,
% 1.53/1.74 (~c1_1(a808)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[770, 1414])).
% 1.53/1.74 tff(1416,plain,
% 1.53/1.74 (c3_1(a808)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[812, 1414])).
% 1.53/1.74 tff(1417,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a808) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a808)) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a808) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a808)) | c0_1(a808))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1418,plain,
% 1.53/1.74 ((hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (hskp7 | c1_1(a808) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a808)) | c0_1(a808))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1419,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a808) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a808)) | c0_1(a808)))),
% 1.53/1.74 inference(monotonicity,[status(thm)],[1418])).
% 1.53/1.74 tff(1420,plain,
% 1.53/1.74 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a808) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a808)) | c0_1(a808))),
% 1.53/1.74 inference(transitivity,[status(thm)],[1419, 1417])).
% 1.53/1.74 tff(1421,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 1.53/1.74 inference(quant_inst,[status(thm)],[])).
% 1.53/1.74 tff(1422,plain,
% 1.53/1.74 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a808) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a808)) | c0_1(a808)),
% 1.53/1.74 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 1.53/1.74 tff(1423,plain,
% 1.53/1.74 (hskp7 | c0_1(a808)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1422, 130, 1190, 1189, 1416, 1415, 1413, 1200])).
% 1.53/1.74 tff(1424,plain,
% 1.53/1.74 (c0_1(a808)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[1423, 1403])).
% 1.53/1.74 tff(1425,plain,
% 1.53/1.74 (~c2_1(a808)),
% 1.53/1.74 inference(unit_resolution,[status(thm)],[776, 1414])).
% 1.53/1.74 tff(1426,plain,
% 1.53/1.74 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a808)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a808)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1427,plain,
% 1.53/1.74 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808))) <=> (hskp20 | hskp9 | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a808)))),
% 1.53/1.74 inference(rewrite,[status(thm)],[])).
% 1.53/1.74 tff(1428,plain,
% 1.53/1.74 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a808))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[1427])).
% 1.53/1.75 tff(1429,plain,
% 1.53/1.75 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a808)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[1428, 1426])).
% 1.53/1.75 tff(1430,plain,
% 1.53/1.75 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(1431,plain,
% 1.53/1.75 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a808))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 1.53/1.75 tff(1432,plain,
% 1.53/1.75 (hskp9 | (~c0_1(a808))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1431, 130, 308, 1416, 1425, 21])).
% 1.53/1.75 tff(1433,plain,
% 1.53/1.75 (hskp9),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1432, 1424])).
% 1.53/1.75 tff(1434,plain,
% 1.53/1.75 (~c3_1(a806)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[63, 1433])).
% 1.53/1.75 tff(1435,plain,
% 1.53/1.75 (c1_1(a806)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[72, 1433])).
% 1.53/1.75 tff(1436,plain,
% 1.53/1.75 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1437,plain,
% 1.53/1.75 ((hskp28 | hskp19 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806))) <=> (hskp28 | hskp19 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1438,plain,
% 1.53/1.75 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[1437])).
% 1.53/1.75 tff(1439,plain,
% 1.53/1.75 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[1438, 1436])).
% 1.53/1.75 tff(1440,plain,
% 1.53/1.75 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(1441,plain,
% 1.53/1.75 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 1.53/1.75 tff(1442,plain,
% 1.53/1.75 (c2_1(a806)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1441, 130, 321, 1363, 1435, 1434, 1232])).
% 1.53/1.75 tff(1443,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1444,plain,
% 1.53/1.75 ((hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1445,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[1444])).
% 1.53/1.75 tff(1446,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[1445, 1443])).
% 1.53/1.75 tff(1447,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(1448,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a833))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 1.53/1.75 tff(1449,plain,
% 1.53/1.75 (hskp7 | (~c3_1(a833))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1448, 130, 1190, 1189, 300, 288, 1413, 1200])).
% 1.53/1.75 tff(1450,plain,
% 1.53/1.75 (~c3_1(a833)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1449, 1403])).
% 1.53/1.75 tff(1451,assumption,(~c2_1(a795)), introduced(assumption)).
% 1.53/1.75 tff(1452,assumption,(~c0_1(a795)), introduced(assumption)).
% 1.53/1.75 tff(1453,assumption,(~c3_1(a795)), introduced(assumption)).
% 1.53/1.75 tff(1454,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a832)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1455,plain,
% 1.53/1.75 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795)) <=> (c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a832)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1456,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a832))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[1455])).
% 1.53/1.75 tff(1457,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a832)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[1456, 1454])).
% 1.53/1.75 tff(1458,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a795) | c0_1(a795) | c3_1(a795))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(1459,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a808)) | (~c0_1(a832))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 1.53/1.75 tff(1460,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1459, 130, 1416, 289, 22, 1415, 1425, 1452, 1453, 795, 408, 1451])).
% 1.53/1.75 tff(1461,plain,((~hskp11) | c1_1(a832) | c3_1(a832) | c0_1(a795) | c3_1(a795) | (~c0_1(a832)) | c2_1(a795)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(1462,plain,
% 1.53/1.75 (~c0_1(a832)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1461, 1371, 22, 1414, 1453, 1452, 1451])).
% 1.53/1.75 tff(1463,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832) | c3_1(a833))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1464,plain,
% 1.53/1.75 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a833) | c2_1(a833) | c0_1(a833) | c2_1(a832) | c1_1(a832) | c0_1(a832)) <=> (c2_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832) | c3_1(a833))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1465,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a833) | c2_1(a833) | c0_1(a833) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832) | c3_1(a833)))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[1464])).
% 1.53/1.75 tff(1466,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a833) | c2_1(a833) | c0_1(a833) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832) | c3_1(a833))),
% 1.53/1.75 inference(transitivity,[status(thm)],[1465, 1463])).
% 1.53/1.75 tff(1467,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a833) | c2_1(a833) | c0_1(a833) | c2_1(a832) | c1_1(a832) | c0_1(a832))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(1468,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832) | c3_1(a833)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 1.53/1.75 tff(1469,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1468, 130, 1362, 1435, 288, 276, 1371, 1434, 228, 1462, 1450, 1442])).
% 1.53/1.75 tff(1470,plain,(c2_1(a832) | c0_1(a833) | c2_1(a833) | hskp28 | c1_1(a833) | c3_1(a832) | (~hskp11) | c3_1(a795) | c0_1(a795) | c2_1(a795)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(1471,plain,
% 1.53/1.75 (c2_1(a832)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1470, 1240, 276, 321, 300, 22, 288, 1322, 1354, 1348])).
% 1.53/1.75 tff(1472,plain,
% 1.53/1.75 (hskp21 | c1_1(a832) | (~c2_1(a832))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[588, 130, 1011, 22, 582])).
% 1.53/1.75 tff(1473,plain,
% 1.53/1.75 (c1_1(a832)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1472, 1471, 629])).
% 1.53/1.75 tff(1474,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~c1_1(a832)) | c3_1(a832) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a832)) | c3_1(a832) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1475,plain,
% 1.53/1.75 (((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a828) | c1_1(a828) | c0_1(a828)) <=> ((~c1_1(a832)) | c3_1(a832) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1476,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a828) | c1_1(a828) | c0_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~c1_1(a832)) | c3_1(a832) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[1475])).
% 1.53/1.75 tff(1477,plain,
% 1.53/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a828) | c1_1(a828) | c0_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a832)) | c3_1(a832) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[1476, 1474])).
% 1.53/1.75 tff(1478,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a828) | c1_1(a828) | c0_1(a828))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(1479,plain,
% 1.53/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a832)) | c3_1(a832) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 1.53/1.75 tff(1480,plain,
% 1.53/1.75 ((~c1_1(a832)) | c0_1(a828) | (~c2_1(a832))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1479, 130, 22, 1309, 1246, 1245, 228])).
% 1.53/1.75 tff(1481,plain,
% 1.53/1.75 ($false),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1480, 1473, 1471, 1361])).
% 1.53/1.75 tff(1482,plain,(hskp21 | c3_1(a832) | hskp0 | c2_1(a833) | hskp28 | c1_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.75 tff(1483,plain,
% 1.53/1.75 (hskp21),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1482, 22, 1340, 276, 321, 300, 288])).
% 1.53/1.75 tff(1484,plain,
% 1.53/1.75 (c0_1(a838)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[406, 1483])).
% 1.53/1.75 tff(1485,plain,
% 1.53/1.75 (~hskp21),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[398, 887])).
% 1.53/1.75 tff(1486,plain,
% 1.53/1.75 (hskp11),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1239, 1485, 1200])).
% 1.53/1.75 tff(1487,plain,
% 1.53/1.75 (~c2_1(a808)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[776, 1486])).
% 1.53/1.75 tff(1488,plain,
% 1.53/1.75 (~c1_1(a808)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[770, 1486])).
% 1.53/1.75 tff(1489,plain,
% 1.53/1.75 (c3_1(a808)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[812, 1486])).
% 1.53/1.75 tff(1490,plain,
% 1.53/1.75 (hskp18),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1095, 130, 1485, 1489, 1488, 1487, 1088])).
% 1.53/1.75 tff(1491,plain,
% 1.53/1.75 (~c3_1(a828)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1107, 1490])).
% 1.53/1.75 tff(1492,plain,
% 1.53/1.75 (~c2_1(a828)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1101, 1490])).
% 1.53/1.75 tff(1493,plain,
% 1.53/1.75 (~c1_1(a828)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1113, 1490])).
% 1.53/1.75 tff(1494,plain,
% 1.53/1.75 (hskp2),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1315, 130, 310, 1493, 1492, 1491, 1308])).
% 1.53/1.75 tff(1495,plain,
% 1.53/1.75 (~c3_1(a795)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1321, 1494])).
% 1.53/1.75 tff(1496,plain,
% 1.53/1.75 (~c1_1(a795)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1327, 1494])).
% 1.53/1.75 tff(1497,plain,
% 1.53/1.75 (~c2_1(a795)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1347, 130, 1485, 1011, 1496, 1495, 582])).
% 1.53/1.75 tff(1498,plain,
% 1.53/1.75 (~c0_1(a795)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1353, 1494])).
% 1.53/1.75 tff(1499,plain,
% 1.53/1.75 (~c0_1(a828)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1360, 130, 1489, 1493, 1491, 1488, 1487, 1498, 1495, 795, 1497])).
% 1.53/1.75 tff(1500,plain,
% 1.53/1.75 (~c0_1(a832)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1461, 1371, 22, 1486, 1495, 1498, 1497])).
% 1.53/1.75 tff(1501,assumption,(~hskp19), introduced(assumption)).
% 1.53/1.75 tff(1502,plain,
% 1.53/1.75 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c3_1(a838) | c2_1(a838) | (~ndr1_0) | (~c1_1(a838)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c3_1(a838) | c2_1(a838) | (~ndr1_0) | (~c1_1(a838)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1503,plain,
% 1.53/1.75 ((hskp28 | hskp19 | (~ndr1_0) | c2_1(a838) | c3_1(a838) | (~c1_1(a838))) <=> (hskp28 | hskp19 | c3_1(a838) | c2_1(a838) | (~ndr1_0) | (~c1_1(a838)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1504,plain,
% 1.53/1.75 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a838) | c3_1(a838) | (~c1_1(a838)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c3_1(a838) | c2_1(a838) | (~ndr1_0) | (~c1_1(a838))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[1503])).
% 1.53/1.75 tff(1505,plain,
% 1.53/1.75 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a838) | c3_1(a838) | (~c1_1(a838)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c3_1(a838) | c2_1(a838) | (~ndr1_0) | (~c1_1(a838)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[1504, 1502])).
% 1.53/1.75 tff(1506,plain,
% 1.53/1.75 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a838) | c3_1(a838) | (~c1_1(a838)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(1507,plain,
% 1.53/1.75 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c3_1(a838) | c2_1(a838) | (~ndr1_0) | (~c1_1(a838))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 1.53/1.75 tff(1508,plain,
% 1.53/1.75 (hskp19 | c3_1(a838) | (~c1_1(a838))),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1507, 130, 321, 422, 1232])).
% 1.53/1.75 tff(1509,plain,
% 1.53/1.75 (~c1_1(a838)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1508, 1501, 887])).
% 1.53/1.75 tff(1510,assumption,(hskp4), introduced(assumption)).
% 1.53/1.75 tff(1511,plain,
% 1.53/1.75 (((~hskp4) | (~c1_1(a799))) <=> ((~hskp4) | (~c1_1(a799)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1512,plain,
% 1.53/1.75 (((~c1_1(a799)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a799)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1513,axiom,((~c1_1(a799)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.53/1.75 tff(1514,plain,
% 1.53/1.75 ((~hskp4) | (~c1_1(a799))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 1.53/1.75 tff(1515,plain,
% 1.53/1.75 ((~hskp4) | (~c1_1(a799))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1514, 1511])).
% 1.53/1.75 tff(1516,plain,
% 1.53/1.75 (~c1_1(a799)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1515, 1510])).
% 1.53/1.75 tff(1517,plain,
% 1.53/1.75 (((~hskp4) | c3_1(a799)) <=> ((~hskp4) | c3_1(a799))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1518,axiom,((~hskp4) | c3_1(a799)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.53/1.75 tff(1519,plain,
% 1.53/1.75 ((~hskp4) | c3_1(a799)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1518, 1517])).
% 1.53/1.75 tff(1520,plain,
% 1.53/1.75 ((~hskp4) | c3_1(a799)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1519, 1517])).
% 1.53/1.75 tff(1521,plain,
% 1.53/1.75 ((~hskp4) | c3_1(a799)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1520, 1517])).
% 1.53/1.75 tff(1522,plain,
% 1.53/1.75 ((~hskp4) | c3_1(a799)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1521, 1517])).
% 1.53/1.75 tff(1523,plain,
% 1.53/1.75 ((~hskp4) | c3_1(a799)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1522, 1517])).
% 1.53/1.75 tff(1524,plain,
% 1.53/1.75 (c3_1(a799)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1523, 1510])).
% 1.53/1.75 tff(1525,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a799) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a799)) | (~c2_1(a799)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a799) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a799)) | (~c2_1(a799)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1526,plain,
% 1.53/1.75 ((hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799))) <=> (hskp28 | c1_1(a799) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a799)) | (~c2_1(a799)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1527,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a799) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a799)) | (~c2_1(a799))))),
% 1.53/1.75 inference(monotonicity,[status(thm)],[1526])).
% 1.53/1.75 tff(1528,plain,
% 1.53/1.75 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a799) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a799)) | (~c2_1(a799)))),
% 1.53/1.75 inference(transitivity,[status(thm)],[1527, 1525])).
% 1.53/1.75 tff(1529,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)))),
% 1.53/1.75 inference(quant_inst,[status(thm)],[])).
% 1.53/1.75 tff(1530,plain,
% 1.53/1.75 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a799) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a799)) | (~c2_1(a799))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1529, 1528])).
% 1.53/1.75 tff(1531,plain,
% 1.53/1.75 (~c2_1(a799)),
% 1.53/1.75 inference(unit_resolution,[status(thm)],[1530, 130, 321, 1191, 1190, 1189, 1524, 1516, 1220])).
% 1.53/1.75 tff(1532,plain,
% 1.53/1.75 (^[U: $i] : refl((hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 1.53/1.75 inference(bind,[status(th)],[])).
% 1.53/1.75 tff(1533,plain,
% 1.53/1.75 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.75 inference(quant_intro,[status(thm)],[1532])).
% 1.53/1.75 tff(1534,plain,
% 1.53/1.75 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1535,plain,
% 1.53/1.75 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp1) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp1))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp1) <=> (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp1) <=> (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 1.53/1.75 inference(bind,[status(th)],[])).
% 1.53/1.75 tff(1536,plain,
% 1.53/1.75 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp1) <=> ![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.75 inference(quant_intro,[status(thm)],[1535])).
% 1.53/1.75 tff(1537,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp20) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.53/1.75 tff(1538,plain,
% 1.53/1.75 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 1.53/1.75 tff(1539,plain,
% 1.53/1.75 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1538, 1534])).
% 1.53/1.75 tff(1540,plain,(
% 1.53/1.75 ![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.75 inference(skolemize,[status(sab)],[1539])).
% 1.53/1.75 tff(1541,plain,
% 1.53/1.75 (![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1540, 1533])).
% 1.53/1.75 tff(1542,plain,
% 1.53/1.75 (((~hskp4) | c0_1(a799)) <=> ((~hskp4) | c0_1(a799))),
% 1.53/1.75 inference(rewrite,[status(thm)],[])).
% 1.53/1.75 tff(1543,axiom,((~hskp4) | c0_1(a799)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.53/1.75 tff(1544,plain,
% 1.53/1.75 ((~hskp4) | c0_1(a799)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 1.53/1.75 tff(1545,plain,
% 1.53/1.75 ((~hskp4) | c0_1(a799)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1544, 1542])).
% 1.53/1.75 tff(1546,plain,
% 1.53/1.75 ((~hskp4) | c0_1(a799)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1545, 1542])).
% 1.53/1.75 tff(1547,plain,
% 1.53/1.75 ((~hskp4) | c0_1(a799)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1546, 1542])).
% 1.53/1.75 tff(1548,plain,
% 1.53/1.75 ((~hskp4) | c0_1(a799)),
% 1.53/1.75 inference(modus_ponens,[status(thm)],[1547, 1542])).
% 1.53/1.75 tff(1549,plain,
% 1.53/1.75 (c0_1(a799)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1548, 1510])).
% 1.53/1.76 tff(1550,plain,
% 1.53/1.76 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a799) | (~ndr1_0) | (~c0_1(a799)) | c2_1(a799))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a799) | (~ndr1_0) | (~c0_1(a799)) | c2_1(a799))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1551,plain,
% 1.53/1.76 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a799) | c1_1(a799) | (~c0_1(a799))) <=> (hskp20 | hskp1 | c1_1(a799) | (~ndr1_0) | (~c0_1(a799)) | c2_1(a799))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1552,plain,
% 1.53/1.76 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a799) | c1_1(a799) | (~c0_1(a799)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a799) | (~ndr1_0) | (~c0_1(a799)) | c2_1(a799)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[1551])).
% 1.53/1.76 tff(1553,plain,
% 1.53/1.76 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a799) | c1_1(a799) | (~c0_1(a799)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a799) | (~ndr1_0) | (~c0_1(a799)) | c2_1(a799))),
% 1.53/1.76 inference(transitivity,[status(thm)],[1552, 1550])).
% 1.53/1.76 tff(1554,plain,
% 1.53/1.76 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a799) | c1_1(a799) | (~c0_1(a799)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(1555,plain,
% 1.53/1.76 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a799) | (~ndr1_0) | (~c0_1(a799)) | c2_1(a799)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 1.53/1.76 tff(1556,plain,
% 1.53/1.76 (hskp1 | c2_1(a799)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1555, 130, 310, 1549, 1516, 1541])).
% 1.53/1.76 tff(1557,plain,
% 1.53/1.76 (hskp1),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1556, 1531])).
% 1.53/1.76 tff(1558,plain,
% 1.53/1.76 (~c2_1(a794)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[250, 1557])).
% 1.53/1.76 tff(1559,plain,
% 1.53/1.76 (c3_1(a794)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[258, 1557])).
% 1.53/1.76 tff(1560,plain,
% 1.53/1.76 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c3_1(a838) | c2_1(a838) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c1_1(a838))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c3_1(a838) | c2_1(a838) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c1_1(a838))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1561,plain,
% 1.53/1.76 ((hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a838) | c2_1(a838) | c1_1(a838)) <=> (hskp19 | c3_1(a838) | c2_1(a838) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c1_1(a838))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1562,plain,
% 1.53/1.76 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a838) | c2_1(a838) | c1_1(a838))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c3_1(a838) | c2_1(a838) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c1_1(a838)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[1561])).
% 1.53/1.76 tff(1563,plain,
% 1.53/1.76 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a838) | c2_1(a838) | c1_1(a838))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c3_1(a838) | c2_1(a838) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c1_1(a838))),
% 1.53/1.76 inference(transitivity,[status(thm)],[1562, 1560])).
% 1.53/1.76 tff(1564,plain,
% 1.53/1.76 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a838) | c2_1(a838) | c1_1(a838))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(1565,plain,
% 1.53/1.76 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c3_1(a838) | c2_1(a838) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c1_1(a838)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 1.53/1.76 tff(1566,plain,
% 1.53/1.76 (~c1_1(a794)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1565, 130, 1501, 887, 1559, 422, 1558, 10, 1509])).
% 1.53/1.76 tff(1567,plain,
% 1.53/1.76 (~c0_1(a794)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[264, 1557])).
% 1.53/1.76 tff(1568,plain,
% 1.53/1.76 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | (~c0_1(a799)) | (~c3_1(a799)) | c2_1(a799))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~ndr1_0) | (~c0_1(a799)) | (~c3_1(a799)) | c2_1(a799))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1569,plain,
% 1.53/1.76 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a799) | (~c3_1(a799)) | (~c0_1(a799))) <=> (hskp20 | hskp9 | (~ndr1_0) | (~c0_1(a799)) | (~c3_1(a799)) | c2_1(a799))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1570,plain,
% 1.53/1.76 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a799) | (~c3_1(a799)) | (~c0_1(a799)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | (~c0_1(a799)) | (~c3_1(a799)) | c2_1(a799)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[1569])).
% 1.53/1.76 tff(1571,plain,
% 1.53/1.76 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a799) | (~c3_1(a799)) | (~c0_1(a799)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~ndr1_0) | (~c0_1(a799)) | (~c3_1(a799)) | c2_1(a799))),
% 1.53/1.76 inference(transitivity,[status(thm)],[1570, 1568])).
% 1.53/1.76 tff(1572,plain,
% 1.53/1.76 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a799) | (~c3_1(a799)) | (~c0_1(a799)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(1573,plain,
% 1.53/1.76 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~ndr1_0) | (~c0_1(a799)) | (~c3_1(a799)) | c2_1(a799)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 1.53/1.76 tff(1574,plain,
% 1.53/1.76 (hskp9 | c2_1(a799)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1573, 130, 310, 1549, 1524, 21])).
% 1.53/1.76 tff(1575,plain,
% 1.53/1.76 (hskp9),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1574, 1531])).
% 1.53/1.76 tff(1576,plain,
% 1.53/1.76 (~c3_1(a806)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[63, 1575])).
% 1.53/1.76 tff(1577,plain,
% 1.53/1.76 (c0_1(a806)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[55, 1575])).
% 1.53/1.76 tff(1578,plain,
% 1.53/1.76 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c0_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1579,plain,
% 1.53/1.76 ((hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a794) | c1_1(a794) | c0_1(a794)) <=> (hskp0 | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1580,plain,
% 1.53/1.76 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a794) | c1_1(a794) | c0_1(a794))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c0_1(a806))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[1579])).
% 1.53/1.76 tff(1581,plain,
% 1.53/1.76 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a794) | c1_1(a794) | c0_1(a794))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[1580, 1578])).
% 1.53/1.76 tff(1582,plain,
% 1.53/1.76 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a794) | c1_1(a794) | c0_1(a794))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(1583,plain,
% 1.53/1.76 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c0_1(a806))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1582, 1581])).
% 1.53/1.76 tff(1584,plain,
% 1.53/1.76 (~c2_1(a806)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1583, 130, 1011, 1577, 1576, 1567, 1558, 1338, 1566])).
% 1.53/1.76 tff(1585,plain,
% 1.53/1.76 (c1_1(a806)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[72, 1575])).
% 1.53/1.76 tff(1586,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1441, 130, 321, 1501, 1585, 1576, 1232, 1584])).
% 1.53/1.76 tff(1587,plain,((~hskp4) | hskp28 | hskp19 | hskp0 | c3_1(a838) | c2_1(a838) | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(1588,plain,
% 1.53/1.76 (~hskp4),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1587, 1363, 321, 1011, 887, 422, 310])).
% 1.53/1.76 tff(1589,plain,
% 1.53/1.76 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))),
% 1.53/1.76 inference(bind,[status(th)],[])).
% 1.53/1.76 tff(1590,plain,
% 1.53/1.76 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.53/1.76 inference(quant_intro,[status(thm)],[1589])).
% 1.53/1.76 tff(1591,plain,
% 1.53/1.76 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1592,plain,
% 1.53/1.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))))),
% 1.53/1.76 inference(bind,[status(th)],[])).
% 1.53/1.76 tff(1593,plain,
% 1.53/1.76 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.53/1.76 inference(quant_intro,[status(thm)],[1592])).
% 1.53/1.76 tff(1594,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.53/1.76 tff(1595,plain,
% 1.53/1.76 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 1.53/1.76 tff(1596,plain,
% 1.53/1.76 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1595, 1591])).
% 1.53/1.76 tff(1597,plain,(
% 1.53/1.76 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.53/1.76 inference(skolemize,[status(sab)],[1596])).
% 1.53/1.76 tff(1598,plain,
% 1.53/1.76 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1597, 1590])).
% 1.53/1.76 tff(1599,plain,
% 1.53/1.76 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp4 | hskp3 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp4 | hskp3 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1600,plain,
% 1.53/1.76 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832)) <=> (hskp4 | hskp3 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1601,plain,
% 1.53/1.76 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp4 | hskp3 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[1600])).
% 1.53/1.76 tff(1602,plain,
% 1.53/1.76 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp4 | hskp3 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 1.53/1.76 inference(transitivity,[status(thm)],[1601, 1599])).
% 1.53/1.76 tff(1603,plain,
% 1.53/1.76 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a832) | c0_1(a832) | c3_1(a832))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(1604,plain,
% 1.53/1.76 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp4 | hskp3 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | c0_1(a832)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 1.53/1.76 tff(1605,plain,
% 1.53/1.76 (hskp4 | hskp3 | c1_1(a832) | c0_1(a832)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1604, 130, 22, 1598])).
% 1.53/1.76 tff(1606,plain,
% 1.53/1.76 (hskp3),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1605, 1588, 1371, 1500])).
% 1.53/1.76 tff(1607,plain,
% 1.53/1.76 (~c3_1(a798)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[492, 1606])).
% 1.53/1.76 tff(1608,plain,
% 1.53/1.76 (c2_1(a798)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[506, 1606])).
% 1.53/1.76 tff(1609,plain,
% 1.53/1.76 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c3_1(a798) | (~ndr1_0) | c1_1(a798) | (~c2_1(a798)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c3_1(a798) | (~ndr1_0) | c1_1(a798) | (~c2_1(a798)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1610,plain,
% 1.53/1.76 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a798) | c3_1(a798) | (~c2_1(a798))) <=> (hskp21 | hskp0 | c3_1(a798) | (~ndr1_0) | c1_1(a798) | (~c2_1(a798)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1611,plain,
% 1.53/1.76 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a798) | c3_1(a798) | (~c2_1(a798)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c3_1(a798) | (~ndr1_0) | c1_1(a798) | (~c2_1(a798))))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[1610])).
% 1.53/1.76 tff(1612,plain,
% 1.53/1.76 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a798) | c3_1(a798) | (~c2_1(a798)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c3_1(a798) | (~ndr1_0) | c1_1(a798) | (~c2_1(a798)))),
% 1.53/1.76 inference(transitivity,[status(thm)],[1611, 1609])).
% 1.53/1.76 tff(1613,plain,
% 1.53/1.76 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a798) | c3_1(a798) | (~c2_1(a798)))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(1614,plain,
% 1.53/1.76 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c3_1(a798) | (~ndr1_0) | c1_1(a798) | (~c2_1(a798))),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1613, 1612])).
% 1.53/1.76 tff(1615,plain,
% 1.53/1.76 (c1_1(a798)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1614, 130, 1485, 1011, 1608, 1607, 582])).
% 1.53/1.76 tff(1616,plain,
% 1.53/1.76 (~c1_1(a838)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1508, 1363, 887])).
% 1.53/1.76 tff(1617,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a838) | c2_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | (~c0_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a838) | c2_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | (~c0_1(a838)) | c1_1(a838))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1618,plain,
% 1.53/1.76 (((~ndr1_0) | c1_1(a838) | c3_1(a838) | (~c0_1(a838)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832)) <=> (c3_1(a838) | c2_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | (~c0_1(a838)) | c1_1(a838))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1619,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a838) | c3_1(a838) | (~c0_1(a838)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a838) | c2_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | (~c0_1(a838)) | c1_1(a838)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[1618])).
% 1.53/1.76 tff(1620,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a838) | c3_1(a838) | (~c0_1(a838)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a838) | c2_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | (~c0_1(a838)) | c1_1(a838))),
% 1.53/1.76 inference(transitivity,[status(thm)],[1619, 1617])).
% 1.53/1.76 tff(1621,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a838) | c3_1(a838) | (~c0_1(a838)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(1622,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a838) | c2_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | (~c0_1(a838)) | c1_1(a838)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 1.53/1.76 tff(1623,plain,
% 1.53/1.76 (~c0_1(a838)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1622, 130, 887, 1362, 1489, 22, 1488, 1487, 795, 1500, 1616])).
% 1.53/1.76 tff(1624,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a838) | c3_1(a838) | c2_1(a832) | c2_1(a838) | c1_1(a832) | c3_1(a798) | (~ndr1_0) | (~c1_1(a798)) | (~c2_1(a798)) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a838) | c3_1(a838) | c2_1(a832) | c2_1(a838) | c1_1(a832) | c3_1(a798) | (~ndr1_0) | (~c1_1(a798)) | (~c2_1(a798)) | c0_1(a832))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1625,plain,
% 1.53/1.76 (((~ndr1_0) | c3_1(a798) | (~c1_1(a798)) | (~c2_1(a798)) | c3_1(a838) | c2_1(a838) | c0_1(a838) | c2_1(a832) | c1_1(a832) | c0_1(a832)) <=> (c0_1(a838) | c3_1(a838) | c2_1(a832) | c2_1(a838) | c1_1(a832) | c3_1(a798) | (~ndr1_0) | (~c1_1(a798)) | (~c2_1(a798)) | c0_1(a832))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.76 tff(1626,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a798) | (~c1_1(a798)) | (~c2_1(a798)) | c3_1(a838) | c2_1(a838) | c0_1(a838) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a838) | c3_1(a838) | c2_1(a832) | c2_1(a838) | c1_1(a832) | c3_1(a798) | (~ndr1_0) | (~c1_1(a798)) | (~c2_1(a798)) | c0_1(a832)))),
% 1.53/1.76 inference(monotonicity,[status(thm)],[1625])).
% 1.53/1.76 tff(1627,plain,
% 1.53/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a798) | (~c1_1(a798)) | (~c2_1(a798)) | c3_1(a838) | c2_1(a838) | c0_1(a838) | c2_1(a832) | c1_1(a832) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a838) | c3_1(a838) | c2_1(a832) | c2_1(a838) | c1_1(a832) | c3_1(a798) | (~ndr1_0) | (~c1_1(a798)) | (~c2_1(a798)) | c0_1(a832))),
% 1.53/1.76 inference(transitivity,[status(thm)],[1626, 1624])).
% 1.53/1.76 tff(1628,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a798) | (~c1_1(a798)) | (~c2_1(a798)) | c3_1(a838) | c2_1(a838) | c0_1(a838) | c2_1(a832) | c1_1(a832) | c0_1(a832))),
% 1.53/1.76 inference(quant_inst,[status(thm)],[])).
% 1.53/1.76 tff(1629,plain,
% 1.53/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a838) | c3_1(a838) | c2_1(a832) | c2_1(a838) | c1_1(a832) | c3_1(a798) | (~ndr1_0) | (~c1_1(a798)) | (~c2_1(a798)) | c0_1(a832)),
% 1.53/1.76 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 1.53/1.76 tff(1630,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1629, 130, 1623, 887, 1362, 1608, 422, 1371, 1607, 228, 1500, 1615])).
% 1.53/1.76 tff(1631,plain,(c2_1(a832) | c3_1(a838) | c2_1(a838) | hskp0 | c3_1(a832) | hskp28 | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(1632,plain,
% 1.53/1.76 (c2_1(a832)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1631, 887, 422, 1011, 22, 321, 310])).
% 1.53/1.76 tff(1633,plain,
% 1.53/1.76 (c1_1(a832)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1472, 1632, 1485])).
% 1.53/1.76 tff(1634,plain,
% 1.53/1.76 ((~c1_1(a832)) | c0_1(a828) | (~c2_1(a832))),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1479, 130, 22, 1493, 1492, 1491, 228])).
% 1.53/1.76 tff(1635,plain,
% 1.53/1.76 ($false),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1634, 1633, 1632, 1499])).
% 1.53/1.76 tff(1636,plain,(c3_1(a838) | c3_1(a832) | hskp0 | c2_1(a838) | hskp28 | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.53/1.76 tff(1637,plain,
% 1.53/1.76 (c3_1(a838)),
% 1.53/1.76 inference(unit_resolution,[status(thm)],[1636, 22, 1340, 422, 321, 308])).
% 1.53/1.76 tff(1638,plain,
% 1.53/1.76 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.53/1.76 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(1639,plain,
% 1.53/1.77 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838))) <=> (hskp20 | hskp9 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(1640,plain,
% 1.53/1.77 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[1639])).
% 1.53/1.77 tff(1641,plain,
% 1.53/1.77 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[1640, 1638])).
% 1.53/1.77 tff(1642,plain,
% 1.53/1.77 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(1643,plain,
% 1.53/1.77 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a838) | (~ndr1_0) | (~c3_1(a838)) | (~c0_1(a838))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 1.53/1.77 tff(1644,plain,
% 1.53/1.77 (hskp9 | (~c3_1(a838)) | (~c0_1(a838))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1643, 130, 308, 422, 21])).
% 1.53/1.77 tff(1645,plain,
% 1.53/1.77 (hskp9),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1644, 1484, 1637])).
% 1.53/1.77 tff(1646,plain,
% 1.53/1.77 (~c3_1(a806)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[63, 1645])).
% 1.53/1.77 tff(1647,plain,
% 1.53/1.77 (c0_1(a806)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[55, 1645])).
% 1.53/1.77 tff(1648,plain,
% 1.53/1.77 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a793) | c2_1(a793) | c3_1(a806) | c1_1(a793) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a793) | c2_1(a793) | c3_1(a806) | c1_1(a793) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(1649,plain,
% 1.53/1.77 ((hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a793) | c1_1(a793) | c0_1(a793)) <=> (hskp0 | c0_1(a793) | c2_1(a793) | c3_1(a806) | c1_1(a793) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(1650,plain,
% 1.53/1.77 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a793) | c1_1(a793) | c0_1(a793))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a793) | c2_1(a793) | c3_1(a806) | c1_1(a793) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[1649])).
% 1.53/1.77 tff(1651,plain,
% 1.53/1.77 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a793) | c1_1(a793) | c0_1(a793))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a793) | c2_1(a793) | c3_1(a806) | c1_1(a793) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[1650, 1648])).
% 1.53/1.77 tff(1652,plain,
% 1.53/1.77 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a793) | c1_1(a793) | c0_1(a793))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(1653,plain,
% 1.53/1.77 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a793) | c2_1(a793) | c3_1(a806) | c1_1(a793) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 1.53/1.77 tff(1654,plain,
% 1.53/1.77 (~c2_1(a806)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1653, 130, 1340, 1647, 1341, 1339, 1646, 616, 1338])).
% 1.53/1.77 tff(1655,plain,
% 1.53/1.77 (c1_1(a806)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[72, 1645])).
% 1.53/1.77 tff(1656,plain,
% 1.53/1.77 (hskp19 | c2_1(a806)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1441, 130, 321, 1655, 1646, 1232])).
% 1.53/1.77 tff(1657,plain,
% 1.53/1.77 (hskp19),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1656, 1654])).
% 1.53/1.77 tff(1658,plain,
% 1.53/1.77 (c2_1(a832)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[340, 1657])).
% 1.53/1.77 tff(1659,plain,
% 1.53/1.77 (~hskp17),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1037, 1484, 321, 422, 1637])).
% 1.53/1.77 tff(1660,plain,
% 1.53/1.77 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp8 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(1661,plain,
% 1.53/1.77 ((hskp17 | hskp8 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806))) <=> (hskp17 | hskp8 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(1662,plain,
% 1.53/1.77 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[1661])).
% 1.53/1.77 tff(1663,plain,
% 1.53/1.77 (((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806)))) <=> ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp8 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)))),
% 1.53/1.77 inference(transitivity,[status(thm)],[1662, 1660])).
% 1.53/1.77 tff(1664,plain,
% 1.53/1.77 ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp17 | hskp8 | (~ndr1_0) | c2_1(a806) | c3_1(a806) | (~c1_1(a806)))),
% 1.53/1.77 inference(quant_inst,[status(thm)],[])).
% 1.53/1.77 tff(1665,plain,
% 1.53/1.77 ((~![U: $i] : (hskp17 | hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp17 | hskp8 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806))),
% 1.53/1.77 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 1.53/1.77 tff(1666,plain,
% 1.53/1.77 (hskp8 | c2_1(a806)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1665, 130, 1659, 1655, 1646, 833])).
% 1.53/1.77 tff(1667,plain,
% 1.53/1.77 (hskp8),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1666, 1654])).
% 1.53/1.77 tff(1668,plain,
% 1.53/1.77 (~c0_1(a832)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[440, 1667, 1637, 1658, 422, 22, 1484])).
% 1.53/1.77 tff(1669,plain,
% 1.53/1.77 (hskp12 | c2_1(a806)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[136, 130, 1191, 1190, 1189, 1655, 1646, 95])).
% 1.53/1.77 tff(1670,plain,
% 1.53/1.77 (hskp12),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1669, 1654])).
% 1.53/1.77 tff(1671,plain,
% 1.53/1.77 (~c0_1(a809)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[143, 1670])).
% 1.53/1.77 tff(1672,plain,
% 1.53/1.77 (~c1_1(a832)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[352, 1657])).
% 1.53/1.77 tff(1673,plain,
% 1.53/1.77 (c2_1(a809)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[152, 1670])).
% 1.53/1.77 tff(1674,plain,
% 1.53/1.77 (c1_1(a809)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[160, 1670])).
% 1.53/1.77 tff(1675,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1007, 130, 1658, 1674, 1673, 1672, 22, 1671, 977, 1668])).
% 1.53/1.77 tff(1676,plain,(c3_1(a832) | c2_1(a838) | hskp28 | c0_1(a793) | c2_1(a793) | c1_1(a793) | c2_1(a833) | c1_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(1677,plain,
% 1.53/1.77 (c3_1(a832)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1676, 422, 321, 1341, 1339, 616, 276, 300, 288])).
% 1.53/1.77 tff(1678,plain,
% 1.53/1.77 (~hskp19),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[346, 1677])).
% 1.53/1.77 tff(1679,plain,
% 1.53/1.77 (~c2_1(a806)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1653, 130, 1340, 56, 1341, 1339, 64, 616, 1338])).
% 1.53/1.77 tff(1680,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1441, 130, 321, 1501, 73, 64, 1232, 1679])).
% 1.53/1.77 tff(1681,plain,((~hskp9) | hskp28 | hskp19 | c0_1(a793) | c2_1(a793) | c1_1(a793)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(1682,plain,
% 1.53/1.77 (~hskp9),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1681, 1678, 321, 1341, 1339, 616])).
% 1.53/1.77 tff(1683,plain,
% 1.53/1.77 (c0_1(a838)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[406, 1221])).
% 1.53/1.77 tff(1684,plain,
% 1.53/1.77 (c3_1(a838)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[398, 1221])).
% 1.53/1.77 tff(1685,plain,
% 1.53/1.77 (hskp9 | (~c3_1(a838)) | (~c0_1(a838))),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1643, 130, 310, 422, 21])).
% 1.53/1.77 tff(1686,plain,
% 1.53/1.77 ($false),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1685, 1684, 1683, 11])).
% 1.53/1.77 tff(1687,plain,((~hskp21) | hskp9 | hskp20 | c2_1(a838)), inference(lemma,lemma(discharge,[]))).
% 1.53/1.77 tff(1688,plain,
% 1.53/1.77 (~hskp21),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1687, 1682, 308, 422])).
% 1.53/1.77 tff(1689,plain,
% 1.53/1.77 (hskp11),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1239, 1688, 1200])).
% 1.53/1.77 tff(1690,plain,
% 1.53/1.77 (~c2_1(a808)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[776, 1689])).
% 1.53/1.77 tff(1691,plain,
% 1.53/1.77 (c3_1(a808)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[812, 1689])).
% 1.53/1.77 tff(1692,plain,
% 1.53/1.77 (~c0_1(a808)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1431, 130, 308, 1682, 1691, 1690, 21])).
% 1.53/1.77 tff(1693,plain,
% 1.53/1.77 (~c1_1(a808)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[770, 1689])).
% 1.53/1.77 tff(1694,plain,
% 1.53/1.77 (hskp7),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1422, 130, 1190, 1189, 1691, 1693, 1413, 1200, 1692])).
% 1.53/1.77 tff(1695,plain,
% 1.53/1.77 (~c2_1(a803)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1377, 1694])).
% 1.53/1.77 tff(1696,plain,
% 1.53/1.77 (hskp18),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1095, 130, 1688, 1691, 1693, 1690, 1088])).
% 1.53/1.77 tff(1697,plain,
% 1.53/1.77 (~c3_1(a828)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1107, 1696])).
% 1.53/1.77 tff(1698,plain,
% 1.53/1.77 (~c2_1(a828)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1101, 1696])).
% 1.53/1.77 tff(1699,plain,
% 1.53/1.77 (~c1_1(a828)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1113, 1696])).
% 1.53/1.77 tff(1700,plain,
% 1.53/1.77 (c3_1(a803)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1385, 1694])).
% 1.53/1.77 tff(1701,plain,
% 1.53/1.77 (c1_1(a803)),
% 1.53/1.77 inference(unit_resolution,[status(thm)],[1393, 1694])).
% 1.53/1.77 tff(1702,plain,
% 1.53/1.77 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(1703,plain,
% 1.53/1.77 ((hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.53/1.77 inference(rewrite,[status(thm)],[])).
% 1.53/1.77 tff(1704,plain,
% 1.53/1.77 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803))))),
% 1.53/1.77 inference(monotonicity,[status(thm)],[1703])).
% 1.53/1.77 tff(1705,plain,
% 1.53/1.77 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.61/1.77 inference(transitivity,[status(thm)],[1704, 1702])).
% 1.61/1.77 tff(1706,plain,
% 1.61/1.77 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 1.61/1.77 inference(quant_inst,[status(thm)],[])).
% 1.61/1.77 tff(1707,plain,
% 1.61/1.77 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803))),
% 1.61/1.77 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 1.61/1.77 tff(1708,plain,
% 1.61/1.77 ($false),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1707, 130, 1678, 1701, 1700, 1699, 1698, 1697, 1695, 10])).
% 1.61/1.77 tff(1709,plain,(c2_1(a838) | hskp28 | c0_1(a793) | c2_1(a793) | c1_1(a793) | c2_1(a833) | c1_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.77 tff(1710,plain,
% 1.61/1.77 (c2_1(a838)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1709, 1341, 321, 1339, 616, 276, 300, 288])).
% 1.61/1.77 tff(1711,plain,
% 1.61/1.77 (~hskp21),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[389, 1710])).
% 1.61/1.77 tff(1712,plain,
% 1.61/1.77 (hskp11),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1239, 1711, 1200])).
% 1.61/1.77 tff(1713,plain,
% 1.61/1.77 (~c2_1(a808)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[776, 1712])).
% 1.61/1.77 tff(1714,plain,
% 1.61/1.77 (c3_1(a808)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[812, 1712])).
% 1.61/1.77 tff(1715,plain,
% 1.61/1.77 (c3_1(a832)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1482, 1711, 1340, 276, 321, 300, 288])).
% 1.61/1.77 tff(1716,plain,
% 1.61/1.77 (~hskp19),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[346, 1715])).
% 1.61/1.77 tff(1717,plain,
% 1.61/1.77 (~hskp9),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1681, 1716, 321, 1341, 1339, 616])).
% 1.61/1.77 tff(1718,plain,
% 1.61/1.77 (~c0_1(a808)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1431, 130, 308, 1717, 1714, 1713, 21])).
% 1.61/1.77 tff(1719,plain,
% 1.61/1.77 (~c1_1(a808)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[770, 1712])).
% 1.61/1.77 tff(1720,plain,
% 1.61/1.77 (hskp7),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1422, 130, 1190, 1189, 1714, 1719, 1413, 1200, 1718])).
% 1.61/1.77 tff(1721,plain,
% 1.61/1.77 (~c2_1(a803)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1377, 1720])).
% 1.61/1.77 tff(1722,plain,
% 1.61/1.77 (hskp18),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1095, 130, 1711, 1714, 1719, 1713, 1088])).
% 1.61/1.77 tff(1723,plain,
% 1.61/1.77 (~c3_1(a828)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1107, 1722])).
% 1.61/1.77 tff(1724,plain,
% 1.61/1.77 (~c2_1(a828)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1101, 1722])).
% 1.61/1.77 tff(1725,plain,
% 1.61/1.77 (~c1_1(a828)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1113, 1722])).
% 1.61/1.77 tff(1726,plain,
% 1.61/1.77 (c3_1(a803)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1385, 1720])).
% 1.61/1.77 tff(1727,plain,
% 1.61/1.77 (c1_1(a803)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1393, 1720])).
% 1.61/1.77 tff(1728,plain,
% 1.61/1.77 ($false),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1707, 130, 1716, 1727, 1726, 1725, 1724, 1723, 1721, 10])).
% 1.61/1.77 tff(1729,plain,(c0_1(a793) | hskp28 | c2_1(a793) | c1_1(a793) | c2_1(a833) | c1_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.77 tff(1730,plain,
% 1.61/1.77 (c0_1(a793)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1729, 1339, 321, 616, 276, 300, 288])).
% 1.61/1.77 tff(1731,plain,
% 1.61/1.77 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a793) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a793) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)))),
% 1.61/1.77 inference(rewrite,[status(thm)],[])).
% 1.61/1.77 tff(1732,plain,
% 1.61/1.77 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a793) | c1_1(a793) | (~c0_1(a793))) <=> (hskp20 | hskp1 | c2_1(a793) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)))),
% 1.61/1.77 inference(rewrite,[status(thm)],[])).
% 1.61/1.77 tff(1733,plain,
% 1.61/1.77 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a793) | c1_1(a793) | (~c0_1(a793)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a793) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793))))),
% 1.61/1.77 inference(monotonicity,[status(thm)],[1732])).
% 1.61/1.77 tff(1734,plain,
% 1.61/1.77 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a793) | c1_1(a793) | (~c0_1(a793)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a793) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793)))),
% 1.61/1.77 inference(transitivity,[status(thm)],[1733, 1731])).
% 1.61/1.77 tff(1735,plain,
% 1.61/1.77 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a793) | c1_1(a793) | (~c0_1(a793)))),
% 1.61/1.77 inference(quant_inst,[status(thm)],[])).
% 1.61/1.77 tff(1736,plain,
% 1.61/1.77 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a793) | c1_1(a793) | (~ndr1_0) | (~c0_1(a793))),
% 1.61/1.77 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 1.61/1.77 tff(1737,plain,
% 1.61/1.77 (hskp1 | c2_1(a793) | (~c0_1(a793))),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1736, 130, 308, 616, 1541])).
% 1.61/1.77 tff(1738,plain,
% 1.61/1.77 (hskp1),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1737, 1730, 1339])).
% 1.61/1.77 tff(1739,plain,
% 1.61/1.77 (~c2_1(a794)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[250, 1738])).
% 1.61/1.77 tff(1740,plain,
% 1.61/1.77 (~c0_1(a794)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[264, 1738])).
% 1.61/1.77 tff(1741,plain,
% 1.61/1.77 (c3_1(a794)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[258, 1738])).
% 1.61/1.77 tff(1742,assumption,(~c2_1(a794)), introduced(assumption)).
% 1.61/1.77 tff(1743,assumption,(c3_1(a794)), introduced(assumption)).
% 1.61/1.77 tff(1744,plain,
% 1.61/1.77 (c3_1(a832)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1482, 629, 1011, 276, 321, 300, 288])).
% 1.61/1.77 tff(1745,plain,
% 1.61/1.77 (~hskp19),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[346, 1744])).
% 1.61/1.77 tff(1746,plain,
% 1.61/1.77 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)))),
% 1.61/1.77 inference(rewrite,[status(thm)],[])).
% 1.61/1.77 tff(1747,plain,
% 1.61/1.77 ((hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)))),
% 1.61/1.77 inference(rewrite,[status(thm)],[])).
% 1.61/1.77 tff(1748,plain,
% 1.61/1.77 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794))))),
% 1.61/1.77 inference(monotonicity,[status(thm)],[1747])).
% 1.61/1.77 tff(1749,plain,
% 1.61/1.77 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)))),
% 1.61/1.77 inference(transitivity,[status(thm)],[1748, 1746])).
% 1.61/1.77 tff(1750,plain,
% 1.61/1.77 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 1.61/1.77 inference(quant_inst,[status(thm)],[])).
% 1.61/1.77 tff(1751,plain,
% 1.61/1.77 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a828) | c2_1(a828) | c3_1(a828) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794))),
% 1.61/1.77 inference(modus_ponens,[status(thm)],[1750, 1749])).
% 1.61/1.77 tff(1752,plain,
% 1.61/1.77 (~c1_1(a794)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1751, 130, 1745, 1743, 1309, 1246, 1245, 1742, 10])).
% 1.61/1.77 tff(1753,assumption,(~c0_1(a794)), introduced(assumption)).
% 1.61/1.77 tff(1754,plain,
% 1.61/1.77 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 1.61/1.77 inference(rewrite,[status(thm)],[])).
% 1.61/1.77 tff(1755,plain,
% 1.61/1.77 ((hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 1.61/1.77 inference(rewrite,[status(thm)],[])).
% 1.61/1.77 tff(1756,plain,
% 1.61/1.77 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867))))),
% 1.61/1.77 inference(monotonicity,[status(thm)],[1755])).
% 1.61/1.77 tff(1757,plain,
% 1.61/1.77 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 1.61/1.77 inference(transitivity,[status(thm)],[1756, 1754])).
% 1.61/1.77 tff(1758,plain,
% 1.61/1.77 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 1.61/1.77 inference(quant_inst,[status(thm)],[])).
% 1.61/1.77 tff(1759,plain,
% 1.61/1.77 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867))),
% 1.61/1.77 inference(modus_ponens,[status(thm)],[1758, 1757])).
% 1.61/1.77 tff(1760,plain,
% 1.61/1.77 (hskp7),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1759, 130, 1190, 1189, 1743, 1753, 1413, 1200, 1752])).
% 1.61/1.77 tff(1761,plain,
% 1.61/1.77 (~c2_1(a803)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1377, 1760])).
% 1.61/1.77 tff(1762,plain,
% 1.61/1.77 (c3_1(a803)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1385, 1760])).
% 1.61/1.77 tff(1763,plain,
% 1.61/1.77 (c1_1(a803)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1393, 1760])).
% 1.61/1.77 tff(1764,plain,
% 1.61/1.77 ($false),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1707, 130, 1745, 1763, 1762, 1309, 1246, 1245, 1761, 10])).
% 1.61/1.77 tff(1765,plain,(hskp21 | (~c3_1(a794)) | c0_1(a794) | c2_1(a794) | hskp0 | c2_1(a833) | hskp28 | c1_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.77 tff(1766,plain,
% 1.61/1.77 (hskp21),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1765, 1741, 1740, 1739, 1340, 276, 321, 300, 288])).
% 1.61/1.77 tff(1767,plain,
% 1.61/1.77 (~c2_1(a838)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[389, 1766])).
% 1.61/1.77 tff(1768,plain,
% 1.61/1.77 (hskp9),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1687, 1766, 308, 1767])).
% 1.61/1.77 tff(1769,plain,
% 1.61/1.77 (~c3_1(a806)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[63, 1768])).
% 1.61/1.77 tff(1770,plain,
% 1.61/1.77 (c0_1(a806)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[55, 1768])).
% 1.61/1.77 tff(1771,plain,
% 1.61/1.77 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.61/1.77 inference(rewrite,[status(thm)],[])).
% 1.61/1.77 tff(1772,plain,
% 1.61/1.77 ((hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a833) | c1_1(a833) | c0_1(a833)) <=> (hskp0 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.61/1.77 inference(rewrite,[status(thm)],[])).
% 1.61/1.77 tff(1773,plain,
% 1.61/1.77 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a833) | c1_1(a833) | c0_1(a833))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806))))),
% 1.61/1.77 inference(monotonicity,[status(thm)],[1772])).
% 1.61/1.77 tff(1774,plain,
% 1.61/1.77 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a833) | c1_1(a833) | c0_1(a833))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.61/1.77 inference(transitivity,[status(thm)],[1773, 1771])).
% 1.61/1.77 tff(1775,plain,
% 1.61/1.77 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a833) | c1_1(a833) | c0_1(a833))),
% 1.61/1.77 inference(quant_inst,[status(thm)],[])).
% 1.61/1.77 tff(1776,plain,
% 1.61/1.77 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806))),
% 1.61/1.77 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 1.61/1.77 tff(1777,plain,
% 1.61/1.77 (~c2_1(a806)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1776, 130, 1340, 300, 1770, 288, 276, 1769, 1338])).
% 1.61/1.77 tff(1778,plain,
% 1.61/1.77 (c1_1(a806)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[72, 1768])).
% 1.61/1.77 tff(1779,plain,
% 1.61/1.77 (hskp12 | c2_1(a806)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[136, 130, 1191, 1190, 1189, 1778, 1769, 95])).
% 1.61/1.77 tff(1780,plain,
% 1.61/1.77 (hskp12),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1779, 1777])).
% 1.61/1.77 tff(1781,plain,
% 1.61/1.77 (~c0_1(a809)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[143, 1780])).
% 1.61/1.77 tff(1782,plain,
% 1.61/1.77 (c2_1(a809)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[152, 1780])).
% 1.61/1.77 tff(1783,plain,
% 1.61/1.77 (c1_1(a809)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[160, 1780])).
% 1.61/1.77 tff(1784,plain,
% 1.61/1.77 ($false),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[167, 130, 1783, 1782, 1770, 1778, 1781, 1769, 84, 1777])).
% 1.61/1.77 tff(1785,plain,(c2_1(a793) | c1_1(a833) | c0_1(a833) | c2_1(a833) | hskp28 | c1_1(a793)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.77 tff(1786,plain,
% 1.61/1.77 (c2_1(a793)),
% 1.61/1.77 inference(unit_resolution,[status(thm)],[1785, 616, 288, 276, 321, 300])).
% 1.61/1.77 tff(1787,plain,
% 1.61/1.77 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c3_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 1.61/1.77 inference(rewrite,[status(thm)],[])).
% 1.61/1.77 tff(1788,plain,
% 1.61/1.77 ((hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793))) <=> (hskp28 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 1.61/1.77 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(1789,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c3_1(a793))))),
% 1.61/1.78 inference(monotonicity,[status(thm)],[1788])).
% 1.61/1.78 tff(1790,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c3_1(a793)))),
% 1.61/1.78 inference(transitivity,[status(thm)],[1789, 1787])).
% 1.61/1.78 tff(1791,plain,
% 1.61/1.78 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp28 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c1_1(a793) | (~c3_1(a793)) | (~c2_1(a793)))),
% 1.61/1.78 inference(quant_inst,[status(thm)],[])).
% 1.61/1.78 tff(1792,plain,
% 1.61/1.78 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp28 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c3_1(a793))),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 1.61/1.78 tff(1793,plain,
% 1.61/1.78 ((~c2_1(a793)) | (~c3_1(a793))),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[1792, 130, 321, 1191, 1190, 1189, 616, 1220])).
% 1.61/1.78 tff(1794,plain,
% 1.61/1.78 (~c3_1(a793)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[1793, 1786])).
% 1.61/1.78 tff(1795,plain,
% 1.61/1.78 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c1_1(a793) | (~ndr1_0) | (~c2_1(a793)) | c3_1(a793))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a793) | (~ndr1_0) | (~c2_1(a793)) | c3_1(a793))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(1796,plain,
% 1.61/1.78 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793))) <=> (hskp21 | hskp0 | c1_1(a793) | (~ndr1_0) | (~c2_1(a793)) | c3_1(a793))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(1797,plain,
% 1.61/1.78 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | c1_1(a793) | (~ndr1_0) | (~c2_1(a793)) | c3_1(a793)))),
% 1.61/1.78 inference(monotonicity,[status(thm)],[1796])).
% 1.61/1.78 tff(1798,plain,
% 1.61/1.78 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a793) | (~ndr1_0) | (~c2_1(a793)) | c3_1(a793))),
% 1.61/1.78 inference(transitivity,[status(thm)],[1797, 1795])).
% 1.61/1.78 tff(1799,plain,
% 1.61/1.78 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)))),
% 1.61/1.78 inference(quant_inst,[status(thm)],[])).
% 1.61/1.78 tff(1800,plain,
% 1.61/1.78 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp21 | hskp0 | c1_1(a793) | (~ndr1_0) | (~c2_1(a793)) | c3_1(a793)),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1799, 1798])).
% 1.61/1.78 tff(1801,plain,
% 1.61/1.78 (hskp21 | hskp0 | (~c2_1(a793)) | c3_1(a793)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[1800, 130, 616, 582])).
% 1.61/1.78 tff(1802,plain,
% 1.61/1.78 (hskp0),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[1801, 629, 1786, 1794])).
% 1.61/1.78 tff(1803,plain,
% 1.61/1.78 (c0_1(a793)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[611, 1802])).
% 1.61/1.78 tff(1804,plain,
% 1.61/1.78 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.61/1.78 inference(bind,[status(th)],[])).
% 1.61/1.78 tff(1805,plain,
% 1.61/1.78 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.61/1.78 inference(quant_intro,[status(thm)],[1804])).
% 1.61/1.78 tff(1806,plain,
% 1.61/1.78 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(1807,plain,
% 1.61/1.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.61/1.78 inference(bind,[status(th)],[])).
% 1.61/1.78 tff(1808,plain,
% 1.61/1.78 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.61/1.78 inference(quant_intro,[status(thm)],[1807])).
% 1.61/1.78 tff(1809,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.61/1.78 tff(1810,plain,
% 1.61/1.78 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1809, 1808])).
% 1.61/1.78 tff(1811,plain,
% 1.61/1.78 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1810, 1806])).
% 1.61/1.78 tff(1812,plain,(
% 1.61/1.78 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.61/1.78 inference(skolemize,[status(sab)],[1811])).
% 1.61/1.78 tff(1813,plain,
% 1.61/1.78 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1812, 1805])).
% 1.61/1.78 tff(1814,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a793)) | c3_1(a793))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a793)) | c3_1(a793))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(1815,plain,
% 1.61/1.78 ((hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | c1_1(a793) | (~c0_1(a793))) <=> (hskp22 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a793)) | c3_1(a793))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(1816,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | c1_1(a793) | (~c0_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a793)) | c3_1(a793)))),
% 1.61/1.78 inference(monotonicity,[status(thm)],[1815])).
% 1.61/1.78 tff(1817,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | c1_1(a793) | (~c0_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a793)) | c3_1(a793))),
% 1.61/1.78 inference(transitivity,[status(thm)],[1816, 1814])).
% 1.61/1.78 tff(1818,plain,
% 1.61/1.78 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | c1_1(a793) | (~c0_1(a793)))),
% 1.61/1.78 inference(quant_inst,[status(thm)],[])).
% 1.61/1.78 tff(1819,plain,
% 1.61/1.78 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a793) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a793)) | c3_1(a793)),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 1.61/1.78 tff(1820,plain,
% 1.61/1.78 (hskp22 | (~c0_1(a793))),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[1819, 130, 1191, 1190, 1189, 616, 1813, 1794])).
% 1.61/1.78 tff(1821,plain,
% 1.61/1.78 (hskp22),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[1820, 1803])).
% 1.61/1.78 tff(1822,plain,
% 1.61/1.78 (((~hskp22) | (~c0_1(a840))) <=> ((~hskp22) | (~c0_1(a840)))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(1823,plain,
% 1.61/1.78 (((~c0_1(a840)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a840)))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(1824,axiom,((~c0_1(a840)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.61/1.78 tff(1825,plain,
% 1.61/1.78 ((~hskp22) | (~c0_1(a840))),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 1.61/1.78 tff(1826,plain,
% 1.61/1.78 ((~hskp22) | (~c0_1(a840))),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1825, 1822])).
% 1.61/1.78 tff(1827,plain,
% 1.61/1.78 (~c0_1(a840)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[1826, 1821])).
% 1.61/1.78 tff(1828,plain,
% 1.61/1.78 (((~hskp22) | c3_1(a840)) <=> ((~hskp22) | c3_1(a840))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(1829,axiom,((~hskp22) | c3_1(a840)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.61/1.78 tff(1830,plain,
% 1.61/1.78 ((~hskp22) | c3_1(a840)),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 1.61/1.78 tff(1831,plain,
% 1.61/1.78 ((~hskp22) | c3_1(a840)),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1830, 1828])).
% 1.61/1.78 tff(1832,plain,
% 1.61/1.78 ((~hskp22) | c3_1(a840)),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1831, 1828])).
% 1.61/1.78 tff(1833,plain,
% 1.61/1.78 ((~hskp22) | c3_1(a840)),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1832, 1828])).
% 1.61/1.78 tff(1834,plain,
% 1.61/1.78 ((~hskp22) | c3_1(a840)),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[1833, 1828])).
% 1.61/1.78 tff(1835,plain,
% 1.61/1.78 (c3_1(a840)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[1834, 1821])).
% 1.61/1.78 tff(1836,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a840) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a840)) | (~c3_1(a840)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a840) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a840)) | (~c3_1(a840)))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1837,plain,
% 1.62/1.78 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a840) | (~c3_1(a840)) | (~c2_1(a840))) <=> (c0_1(a840) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a840)) | (~c3_1(a840)))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1838,plain,
% 1.62/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a840) | (~c3_1(a840)) | (~c2_1(a840)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a840) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a840)) | (~c3_1(a840))))),
% 1.62/1.78 inference(monotonicity,[status(thm)],[1837])).
% 1.62/1.78 tff(1839,plain,
% 1.62/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a840) | (~c3_1(a840)) | (~c2_1(a840)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a840) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a840)) | (~c3_1(a840)))),
% 1.62/1.78 inference(transitivity,[status(thm)],[1838, 1836])).
% 1.62/1.78 tff(1840,plain,
% 1.62/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a840) | (~c3_1(a840)) | (~c2_1(a840)))),
% 1.62/1.78 inference(quant_inst,[status(thm)],[])).
% 1.62/1.78 tff(1841,plain,
% 1.62/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a840) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a840)) | (~c3_1(a840))),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 1.62/1.78 tff(1842,plain,
% 1.62/1.78 (~c2_1(a840)),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[1841, 130, 1191, 1190, 1189, 1835, 1827, 180, 1200])).
% 1.62/1.78 tff(1843,plain,
% 1.62/1.78 (c3_1(a833)),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[803, 130, 1243, 1803, 288, 276, 1242, 1241, 616, 795, 1794])).
% 1.62/1.78 tff(1844,plain,
% 1.62/1.78 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.62/1.78 inference(bind,[status(th)],[])).
% 1.62/1.78 tff(1845,plain,
% 1.62/1.78 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.78 inference(quant_intro,[status(thm)],[1844])).
% 1.62/1.78 tff(1846,plain,
% 1.62/1.78 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1847,plain,
% 1.62/1.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.62/1.78 inference(bind,[status(th)],[])).
% 1.62/1.78 tff(1848,plain,
% 1.62/1.78 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.78 inference(quant_intro,[status(thm)],[1847])).
% 1.62/1.78 tff(1849,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 1.62/1.78 tff(1850,plain,
% 1.62/1.78 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 1.62/1.78 tff(1851,plain,
% 1.62/1.78 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1850, 1846])).
% 1.62/1.78 tff(1852,plain,(
% 1.62/1.78 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.78 inference(skolemize,[status(sab)],[1851])).
% 1.62/1.78 tff(1853,plain,
% 1.62/1.78 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1852, 1845])).
% 1.62/1.78 tff(1854,plain,
% 1.62/1.78 (((~hskp22) | c1_1(a840)) <=> ((~hskp22) | c1_1(a840))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1855,axiom,((~hskp22) | c1_1(a840)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.62/1.78 tff(1856,plain,
% 1.62/1.78 ((~hskp22) | c1_1(a840)),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1855, 1854])).
% 1.62/1.78 tff(1857,plain,
% 1.62/1.78 ((~hskp22) | c1_1(a840)),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1856, 1854])).
% 1.62/1.78 tff(1858,plain,
% 1.62/1.78 ((~hskp22) | c1_1(a840)),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1857, 1854])).
% 1.62/1.78 tff(1859,plain,
% 1.62/1.78 ((~hskp22) | c1_1(a840)),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1858, 1854])).
% 1.62/1.78 tff(1860,plain,
% 1.62/1.78 ((~hskp22) | c1_1(a840)),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1859, 1854])).
% 1.62/1.78 tff(1861,plain,
% 1.62/1.78 (c1_1(a840)),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[1860, 1821])).
% 1.62/1.78 tff(1862,plain,
% 1.62/1.78 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | c2_1(a840) | (~c1_1(a840)) | (~c3_1(a840)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | c2_1(a840) | (~c1_1(a840)) | (~c3_1(a840)))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1863,plain,
% 1.62/1.78 ((hskp6 | (~ndr1_0) | c2_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (hskp6 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | c2_1(a840) | (~c1_1(a840)) | (~c3_1(a840)))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1864,plain,
% 1.62/1.78 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | c2_1(a840) | (~c1_1(a840)) | (~c3_1(a840))))),
% 1.62/1.78 inference(monotonicity,[status(thm)],[1863])).
% 1.62/1.78 tff(1865,plain,
% 1.62/1.78 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | c2_1(a840) | (~c1_1(a840)) | (~c3_1(a840)))),
% 1.62/1.78 inference(transitivity,[status(thm)],[1864, 1862])).
% 1.62/1.78 tff(1866,plain,
% 1.62/1.78 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.62/1.78 inference(quant_inst,[status(thm)],[])).
% 1.62/1.78 tff(1867,plain,
% 1.62/1.78 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | c2_1(a840) | (~c1_1(a840)) | (~c3_1(a840))),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 1.62/1.78 tff(1868,plain,
% 1.62/1.78 (hskp6),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[1867, 130, 1861, 1835, 300, 288, 1853, 1843, 1842])).
% 1.62/1.78 tff(1869,plain,
% 1.62/1.78 (((~hskp6) | (~c0_1(a802))) <=> ((~hskp6) | (~c0_1(a802)))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1870,plain,
% 1.62/1.78 (((~c0_1(a802)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a802)))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1871,axiom,((~c0_1(a802)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.62/1.78 tff(1872,plain,
% 1.62/1.78 ((~hskp6) | (~c0_1(a802))),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 1.62/1.78 tff(1873,plain,
% 1.62/1.78 ((~hskp6) | (~c0_1(a802))),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1872, 1869])).
% 1.62/1.78 tff(1874,plain,
% 1.62/1.78 (~c0_1(a802)),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[1873, 1868])).
% 1.62/1.78 tff(1875,plain,
% 1.62/1.78 (((~hskp6) | c2_1(a802)) <=> ((~hskp6) | c2_1(a802))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1876,axiom,((~hskp6) | c2_1(a802)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.62/1.78 tff(1877,plain,
% 1.62/1.78 ((~hskp6) | c2_1(a802)),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1876, 1875])).
% 1.62/1.78 tff(1878,plain,
% 1.62/1.78 ((~hskp6) | c2_1(a802)),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1877, 1875])).
% 1.62/1.78 tff(1879,plain,
% 1.62/1.78 ((~hskp6) | c2_1(a802)),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1878, 1875])).
% 1.62/1.78 tff(1880,plain,
% 1.62/1.78 ((~hskp6) | c2_1(a802)),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1879, 1875])).
% 1.62/1.78 tff(1881,plain,
% 1.62/1.78 ((~hskp6) | c2_1(a802)),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1880, 1875])).
% 1.62/1.78 tff(1882,plain,
% 1.62/1.78 (c2_1(a802)),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[1881, 1868])).
% 1.62/1.78 tff(1883,plain,
% 1.62/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1884,plain,
% 1.62/1.78 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802))) <=> (c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1885,plain,
% 1.62/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802))))),
% 1.62/1.78 inference(monotonicity,[status(thm)],[1884])).
% 1.62/1.78 tff(1886,plain,
% 1.62/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)))),
% 1.62/1.78 inference(transitivity,[status(thm)],[1885, 1883])).
% 1.62/1.78 tff(1887,plain,
% 1.62/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))),
% 1.62/1.78 inference(quant_inst,[status(thm)],[])).
% 1.62/1.78 tff(1888,plain,
% 1.62/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802))),
% 1.62/1.78 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 1.62/1.78 tff(1889,plain,
% 1.62/1.78 (~c3_1(a802)),
% 1.62/1.78 inference(unit_resolution,[status(thm)],[1888, 130, 1191, 1190, 1189, 1882, 1874, 180, 1200])).
% 1.62/1.78 tff(1890,plain,
% 1.62/1.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c0_1(a793)) | c3_1(a793))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c0_1(a793)) | c3_1(a793))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1891,plain,
% 1.62/1.78 ((hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | (~c0_1(a793)) | (~c2_1(a793))) <=> (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c0_1(a793)) | c3_1(a793))),
% 1.62/1.78 inference(rewrite,[status(thm)],[])).
% 1.62/1.78 tff(1892,plain,
% 1.62/1.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | (~c0_1(a793)) | (~c2_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c0_1(a793)) | c3_1(a793)))),
% 1.62/1.78 inference(monotonicity,[status(thm)],[1891])).
% 1.62/1.78 tff(1893,plain,
% 1.62/1.78 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | (~c0_1(a793)) | (~c2_1(a793)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c0_1(a793)) | c3_1(a793))),
% 1.62/1.79 inference(transitivity,[status(thm)],[1892, 1890])).
% 1.62/1.79 tff(1894,plain,
% 1.62/1.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a793) | (~c0_1(a793)) | (~c2_1(a793)))),
% 1.62/1.79 inference(quant_inst,[status(thm)],[])).
% 1.62/1.79 tff(1895,plain,
% 1.62/1.79 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a793)) | (~c0_1(a793)) | c3_1(a793)),
% 1.62/1.79 inference(modus_ponens,[status(thm)],[1894, 1893])).
% 1.62/1.79 tff(1896,plain,
% 1.62/1.79 (hskp5 | (~c0_1(a793))),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1895, 130, 1191, 1190, 1189, 1786, 190, 1794])).
% 1.62/1.79 tff(1897,plain,
% 1.62/1.79 (hskp5),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1896, 1803])).
% 1.62/1.79 tff(1898,plain,
% 1.62/1.79 (~c1_1(a800)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[233, 1897])).
% 1.62/1.79 tff(1899,plain,
% 1.62/1.79 (~c0_1(a800)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[202, 1897])).
% 1.62/1.79 tff(1900,plain,
% 1.62/1.79 (c3_1(a800)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[210, 1897])).
% 1.62/1.79 tff(1901,plain,
% 1.62/1.79 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)))),
% 1.62/1.79 inference(rewrite,[status(thm)],[])).
% 1.62/1.79 tff(1902,plain,
% 1.62/1.79 ((hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)))),
% 1.62/1.79 inference(rewrite,[status(thm)],[])).
% 1.62/1.79 tff(1903,plain,
% 1.62/1.79 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a800))))),
% 1.62/1.79 inference(monotonicity,[status(thm)],[1902])).
% 1.62/1.79 tff(1904,plain,
% 1.62/1.79 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a800)))),
% 1.62/1.79 inference(transitivity,[status(thm)],[1903, 1901])).
% 1.62/1.79 tff(1905,plain,
% 1.62/1.79 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 1.62/1.79 inference(quant_inst,[status(thm)],[])).
% 1.62/1.79 tff(1906,plain,
% 1.62/1.79 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a800))),
% 1.62/1.79 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 1.62/1.79 tff(1907,plain,
% 1.62/1.79 (hskp7),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1906, 130, 1190, 1189, 1900, 1899, 1898, 1413, 1200])).
% 1.62/1.79 tff(1908,plain,
% 1.62/1.79 (~c2_1(a803)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1377, 1907])).
% 1.62/1.79 tff(1909,plain,
% 1.62/1.79 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.62/1.79 inference(bind,[status(th)],[])).
% 1.62/1.79 tff(1910,plain,
% 1.62/1.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.79 inference(quant_intro,[status(thm)],[1909])).
% 1.62/1.79 tff(1911,plain,
% 1.62/1.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.79 inference(rewrite,[status(thm)],[])).
% 1.62/1.79 tff(1912,plain,
% 1.62/1.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.62/1.79 inference(bind,[status(th)],[])).
% 1.62/1.79 tff(1913,plain,
% 1.62/1.79 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.79 inference(quant_intro,[status(thm)],[1912])).
% 1.62/1.79 tff(1914,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.62/1.79 tff(1915,plain,
% 1.62/1.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.79 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 1.62/1.79 tff(1916,plain,
% 1.62/1.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.79 inference(modus_ponens,[status(thm)],[1915, 1911])).
% 1.62/1.79 tff(1917,plain,(
% 1.62/1.79 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.79 inference(skolemize,[status(sab)],[1916])).
% 1.62/1.79 tff(1918,plain,
% 1.62/1.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.62/1.79 inference(modus_ponens,[status(thm)],[1917, 1910])).
% 1.62/1.79 tff(1919,plain,
% 1.62/1.79 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a793)) | c3_1(a793))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a793)) | c3_1(a793))),
% 1.62/1.79 inference(rewrite,[status(thm)],[])).
% 1.62/1.79 tff(1920,plain,
% 1.62/1.79 ((hskp4 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (hskp4 | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a793)) | c3_1(a793))),
% 1.62/1.79 inference(rewrite,[status(thm)],[])).
% 1.62/1.79 tff(1921,plain,
% 1.62/1.79 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a793)) | c3_1(a793)))),
% 1.62/1.79 inference(monotonicity,[status(thm)],[1920])).
% 1.62/1.79 tff(1922,plain,
% 1.62/1.79 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a793)) | c3_1(a793))),
% 1.62/1.79 inference(transitivity,[status(thm)],[1921, 1919])).
% 1.62/1.79 tff(1923,plain,
% 1.62/1.79 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 1.62/1.79 inference(quant_inst,[status(thm)],[])).
% 1.62/1.79 tff(1924,plain,
% 1.62/1.79 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a793)) | c3_1(a793)),
% 1.62/1.79 inference(modus_ponens,[status(thm)],[1923, 1922])).
% 1.62/1.79 tff(1925,plain,
% 1.62/1.79 (hskp4),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1924, 130, 1900, 1786, 1899, 1898, 616, 1918, 1794])).
% 1.62/1.79 tff(1926,plain,
% 1.62/1.79 (~c1_1(a799)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1515, 1925])).
% 1.62/1.79 tff(1927,plain,
% 1.62/1.79 (c3_1(a799)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1523, 1925])).
% 1.62/1.79 tff(1928,plain,
% 1.62/1.79 (~c2_1(a799)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1530, 130, 321, 1191, 1190, 1189, 1927, 1926, 1220])).
% 1.62/1.79 tff(1929,plain,
% 1.62/1.79 (c0_1(a799)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1548, 1925])).
% 1.62/1.79 tff(1930,plain,
% 1.62/1.79 (hskp9 | c2_1(a799)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1573, 130, 308, 1929, 1927, 21])).
% 1.62/1.79 tff(1931,plain,
% 1.62/1.79 (hskp9),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1930, 1928])).
% 1.62/1.79 tff(1932,plain,
% 1.62/1.79 (~c3_1(a806)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[63, 1931])).
% 1.62/1.79 tff(1933,plain,
% 1.62/1.79 (c3_1(a803)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1385, 1907])).
% 1.62/1.79 tff(1934,plain,
% 1.62/1.79 (c1_1(a803)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1393, 1907])).
% 1.62/1.79 tff(1935,plain,
% 1.62/1.79 (c1_1(a806)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[72, 1931])).
% 1.62/1.79 tff(1936,plain,
% 1.62/1.79 (c0_1(a806)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[55, 1931])).
% 1.62/1.79 tff(1937,plain,
% 1.62/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a806) | c2_1(a803) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a806) | c2_1(a803) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 1.62/1.79 inference(rewrite,[status(thm)],[])).
% 1.62/1.79 tff(1938,plain,
% 1.62/1.79 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a802) | c3_1(a802) | (~c2_1(a802))) <=> (c3_1(a806) | c2_1(a803) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 1.62/1.79 inference(rewrite,[status(thm)],[])).
% 1.62/1.79 tff(1939,plain,
% 1.62/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a806) | c2_1(a803) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806))))),
% 1.62/1.79 inference(monotonicity,[status(thm)],[1938])).
% 1.62/1.79 tff(1940,plain,
% 1.62/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a806) | c2_1(a803) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 1.62/1.79 inference(transitivity,[status(thm)],[1939, 1937])).
% 1.62/1.79 tff(1941,plain,
% 1.62/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)))),
% 1.62/1.79 inference(quant_inst,[status(thm)],[])).
% 1.62/1.79 tff(1942,plain,
% 1.62/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a806) | c2_1(a803) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806))),
% 1.62/1.79 inference(modus_ponens,[status(thm)],[1941, 1940])).
% 1.62/1.79 tff(1943,plain,
% 1.62/1.79 ($false),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1942, 130, 1936, 1935, 1934, 1933, 1882, 1932, 1908, 1874, 275, 1889])).
% 1.62/1.79 tff(1944,plain,(hskp21 | hskp28 | c1_1(a833) | c0_1(a833) | c2_1(a833) | c1_1(a793)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.79 tff(1945,plain,
% 1.62/1.79 (hskp21),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1944, 616, 300, 288, 276, 321])).
% 1.62/1.79 tff(1946,plain,
% 1.62/1.79 (~c2_1(a838)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[389, 1945])).
% 1.62/1.79 tff(1947,plain,
% 1.62/1.79 (hskp9),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1687, 1945, 308, 1946])).
% 1.62/1.79 tff(1948,plain,
% 1.62/1.79 (~c3_1(a806)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[63, 1947])).
% 1.62/1.79 tff(1949,plain,
% 1.62/1.79 (c1_1(a806)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[72, 1947])).
% 1.62/1.79 tff(1950,plain,
% 1.62/1.79 (c0_1(a806)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[55, 1947])).
% 1.62/1.79 tff(1951,plain,
% 1.62/1.79 (c2_1(a806)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[169, 1950, 1949, 1948, 1191, 1190, 1189])).
% 1.62/1.79 tff(1952,plain,
% 1.62/1.79 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.62/1.79 inference(bind,[status(th)],[])).
% 1.62/1.79 tff(1953,plain,
% 1.62/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.62/1.79 inference(quant_intro,[status(thm)],[1952])).
% 1.62/1.79 tff(1954,plain,
% 1.62/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.62/1.79 inference(rewrite,[status(thm)],[])).
% 1.62/1.79 tff(1955,plain,
% 1.62/1.79 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.62/1.79 inference(bind,[status(th)],[])).
% 1.62/1.79 tff(1956,plain,
% 1.62/1.79 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.62/1.79 inference(quant_intro,[status(thm)],[1955])).
% 1.62/1.79 tff(1957,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.62/1.79 tff(1958,plain,
% 1.62/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.62/1.79 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 1.62/1.79 tff(1959,plain,
% 1.62/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.62/1.79 inference(modus_ponens,[status(thm)],[1958, 1954])).
% 1.62/1.79 tff(1960,plain,(
% 1.62/1.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.62/1.79 inference(skolemize,[status(sab)],[1959])).
% 1.62/1.79 tff(1961,plain,
% 1.62/1.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.62/1.79 inference(modus_ponens,[status(thm)],[1960, 1953])).
% 1.62/1.79 tff(1962,plain,
% 1.62/1.79 (c3_1(a838)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[398, 1945])).
% 1.62/1.79 tff(1963,plain,
% 1.62/1.79 (c0_1(a838)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[406, 1945])).
% 1.62/1.79 tff(1964,plain,
% 1.62/1.79 (~c1_1(a838)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1019, 130, 321, 1963, 1962, 1946, 332])).
% 1.62/1.79 tff(1965,plain,
% 1.62/1.79 (hskp0 | (~c2_1(a806))),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1776, 130, 300, 1950, 288, 276, 1948, 1338])).
% 1.62/1.79 tff(1966,plain,
% 1.62/1.79 (hskp0),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1965, 1951])).
% 1.62/1.79 tff(1967,plain,
% 1.62/1.79 (c0_1(a793)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[611, 1966])).
% 1.62/1.79 tff(1968,plain,
% 1.62/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a793) | (~ndr1_0) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a793) | (~ndr1_0) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 1.62/1.79 inference(rewrite,[status(thm)],[])).
% 1.62/1.79 tff(1969,plain,
% 1.62/1.79 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833)) <=> (c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a793) | (~ndr1_0) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 1.62/1.79 inference(rewrite,[status(thm)],[])).
% 1.62/1.79 tff(1970,plain,
% 1.62/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a793) | (~ndr1_0) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)))),
% 1.62/1.79 inference(monotonicity,[status(thm)],[1969])).
% 1.62/1.79 tff(1971,plain,
% 1.62/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a793) | (~ndr1_0) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 1.62/1.79 inference(transitivity,[status(thm)],[1970, 1968])).
% 1.62/1.79 tff(1972,plain,
% 1.62/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a833) | c0_1(a833) | c3_1(a833))),
% 1.62/1.79 inference(quant_inst,[status(thm)],[])).
% 1.62/1.79 tff(1973,plain,
% 1.62/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a833) | c2_1(a833) | c1_1(a793) | (~ndr1_0) | c3_1(a833) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)),
% 1.62/1.79 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 1.62/1.79 tff(1974,plain,
% 1.62/1.79 (c3_1(a833) | (~c0_1(a793)) | c1_1(a838)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1973, 130, 1962, 1946, 288, 276, 616, 795, 1794])).
% 1.62/1.79 tff(1975,plain,
% 1.62/1.79 (c3_1(a833)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1974, 1967, 1964])).
% 1.62/1.79 tff(1976,plain,
% 1.62/1.79 (hskp7),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1449, 1975])).
% 1.62/1.79 tff(1977,plain,
% 1.62/1.79 (~c2_1(a803)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1377, 1976])).
% 1.62/1.79 tff(1978,plain,
% 1.62/1.79 (hskp22),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1820, 1967])).
% 1.62/1.79 tff(1979,plain,
% 1.62/1.79 (~c0_1(a840)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1826, 1978])).
% 1.62/1.79 tff(1980,plain,
% 1.62/1.79 (c3_1(a803)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1385, 1976])).
% 1.62/1.79 tff(1981,plain,
% 1.62/1.79 (c3_1(a840)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1834, 1978])).
% 1.62/1.79 tff(1982,plain,
% 1.62/1.79 (c1_1(a840)),
% 1.62/1.79 inference(unit_resolution,[status(thm)],[1860, 1978])).
% 1.62/1.79 tff(1983,plain,
% 1.62/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a840) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c2_1(a806)) | (~c1_1(a806)) | (~c1_1(a840)) | (~c3_1(a840)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a840) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c2_1(a806)) | (~c1_1(a806)) | (~c1_1(a840)) | (~c3_1(a840)))),
% 1.62/1.79 inference(rewrite,[status(thm)],[])).
% 1.62/1.79 tff(1984,plain,
% 1.62/1.79 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803))) <=> (c0_1(a840) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c2_1(a806)) | (~c1_1(a806)) | (~c1_1(a840)) | (~c3_1(a840)))),
% 1.62/1.79 inference(rewrite,[status(thm)],[])).
% 1.62/1.79 tff(1985,plain,
% 1.62/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a840) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c2_1(a806)) | (~c1_1(a806)) | (~c1_1(a840)) | (~c3_1(a840))))),
% 1.62/1.79 inference(monotonicity,[status(thm)],[1984])).
% 1.62/1.79 tff(1986,plain,
% 1.62/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a840) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c2_1(a806)) | (~c1_1(a806)) | (~c1_1(a840)) | (~c3_1(a840)))),
% 1.62/1.79 inference(transitivity,[status(thm)],[1985, 1983])).
% 1.62/1.79 tff(1987,plain,
% 1.62/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(1988,plain,
% 1.62/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a840) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c2_1(a806)) | (~c1_1(a806)) | (~c1_1(a840)) | (~c3_1(a840))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 1.62/1.80 tff(1989,plain,
% 1.62/1.80 (c0_1(a803)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1988, 130, 1982, 1981, 1949, 1980, 1979, 1948, 1977, 1961, 1951])).
% 1.62/1.80 tff(1990,plain,
% 1.62/1.80 (c1_1(a803)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1393, 1976])).
% 1.62/1.80 tff(1991,plain,
% 1.62/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a833) | c0_1(a833) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a833) | c0_1(a833) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(1992,plain,
% 1.62/1.80 (((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c1_1(a833) | c0_1(a833) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(1993,plain,
% 1.62/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a833) | c0_1(a833) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a833)) | (~c2_1(a793)) | (~c0_1(a793))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[1992])).
% 1.62/1.80 tff(1994,plain,
% 1.62/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a833) | c0_1(a833) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 1.62/1.80 inference(transitivity,[status(thm)],[1993, 1991])).
% 1.62/1.80 tff(1995,plain,
% 1.62/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(1996,plain,
% 1.62/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a833) | c0_1(a833) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a833)) | (~c2_1(a793)) | (~c0_1(a793))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[1995, 1994])).
% 1.62/1.80 tff(1997,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1996, 130, 300, 1990, 1967, 1786, 288, 1977, 616, 287, 1975, 1989])).
% 1.62/1.80 tff(1998,plain,(c1_1(a793) | c1_1(a833) | c0_1(a833) | c2_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(1999,plain,
% 1.62/1.80 (c1_1(a793)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1998, 276, 288, 300, 321])).
% 1.62/1.80 tff(2000,plain,
% 1.62/1.80 (~hskp0),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[603, 1999])).
% 1.62/1.80 tff(2001,plain,
% 1.62/1.80 (~c2_1(a795)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1347, 130, 629, 2000, 1328, 1322, 582])).
% 1.62/1.80 tff(2002,plain,
% 1.62/1.80 (~c0_1(a828)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1360, 130, 1243, 1309, 1245, 1242, 1241, 1354, 1322, 795, 2001])).
% 1.62/1.80 tff(2003,plain,
% 1.62/1.80 (c3_1(a832)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1482, 629, 2000, 276, 321, 300, 288])).
% 1.62/1.80 tff(2004,plain,
% 1.62/1.80 (~hskp19),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[346, 2003])).
% 1.62/1.80 tff(2005,plain,
% 1.62/1.80 (hskp9 | (~c0_1(a808))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1431, 130, 310, 941, 796, 21])).
% 1.62/1.80 tff(2006,plain,
% 1.62/1.80 (~c0_1(a808)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2005, 11])).
% 1.62/1.80 tff(2007,plain,
% 1.62/1.80 (hskp7 | c0_1(a808)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1422, 130, 1190, 1189, 941, 797, 1413, 1200])).
% 1.62/1.80 tff(2008,plain,
% 1.62/1.80 (hskp7),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2007, 2006])).
% 1.62/1.80 tff(2009,plain,
% 1.62/1.80 (~c2_1(a803)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1377, 2008])).
% 1.62/1.80 tff(2010,assumption,(~c0_1(a828)), introduced(assumption)).
% 1.62/1.80 tff(2011,plain,
% 1.62/1.80 (^[U: $i] : refl((hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 1.62/1.80 inference(bind,[status(th)],[])).
% 1.62/1.80 tff(2012,plain,
% 1.62/1.80 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.62/1.80 inference(quant_intro,[status(thm)],[2011])).
% 1.62/1.80 tff(2013,plain,
% 1.62/1.80 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2014,plain,
% 1.62/1.80 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp10) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp10) <=> (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp10) <=> (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 1.62/1.80 inference(bind,[status(th)],[])).
% 1.62/1.80 tff(2015,plain,
% 1.62/1.80 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp10) <=> ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.62/1.80 inference(quant_intro,[status(thm)],[2014])).
% 1.62/1.80 tff(2016,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp9) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.62/1.80 tff(2017,plain,
% 1.62/1.80 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 1.62/1.80 tff(2018,plain,
% 1.62/1.80 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[2017, 2013])).
% 1.62/1.80 tff(2019,plain,(
% 1.62/1.80 ![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.62/1.80 inference(skolemize,[status(sab)],[2018])).
% 1.62/1.80 tff(2020,plain,
% 1.62/1.80 (![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[2019, 2012])).
% 1.62/1.80 tff(2021,plain,
% 1.62/1.80 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp9 | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp9 | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2022,plain,
% 1.62/1.80 ((hskp10 | hskp9 | (~ndr1_0) | c2_1(a828) | c0_1(a828) | c3_1(a828)) <=> (hskp10 | hskp9 | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2023,plain,
% 1.62/1.80 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp9 | (~ndr1_0) | c2_1(a828) | c0_1(a828) | c3_1(a828))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp9 | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828)))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[2022])).
% 1.62/1.80 tff(2024,plain,
% 1.62/1.80 (((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp9 | (~ndr1_0) | c2_1(a828) | c0_1(a828) | c3_1(a828))) <=> ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp9 | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828))),
% 1.62/1.80 inference(transitivity,[status(thm)],[2023, 2021])).
% 1.62/1.80 tff(2025,plain,
% 1.62/1.80 ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp10 | hskp9 | (~ndr1_0) | c2_1(a828) | c0_1(a828) | c3_1(a828))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(2026,plain,
% 1.62/1.80 ((~![U: $i] : (hskp10 | hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp10 | hskp9 | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828)),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 1.62/1.80 tff(2027,plain,
% 1.62/1.80 (hskp10 | hskp9 | c0_1(a828)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2026, 130, 1116, 1115, 2020])).
% 1.62/1.80 tff(2028,plain,
% 1.62/1.80 (hskp10),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2027, 11, 2010])).
% 1.62/1.80 tff(2029,plain,
% 1.62/1.80 (~c3_1(a807)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[455, 2028])).
% 1.62/1.80 tff(2030,plain,
% 1.62/1.80 (~c2_1(a807)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[498, 2028])).
% 1.62/1.80 tff(2031,plain,
% 1.62/1.80 (c3_1(a803)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1385, 2008])).
% 1.62/1.80 tff(2032,plain,
% 1.62/1.80 (c1_1(a803)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1393, 2008])).
% 1.62/1.80 tff(2033,plain,
% 1.62/1.80 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a807) | c3_1(a807) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a807))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a807) | c3_1(a807) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a807))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2034,plain,
% 1.62/1.80 ((hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a807) | c2_1(a807) | c1_1(a807)) <=> (hskp19 | c2_1(a807) | c3_1(a807) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a807))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2035,plain,
% 1.62/1.80 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a807) | c2_1(a807) | c1_1(a807))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a807) | c3_1(a807) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a807)))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[2034])).
% 1.62/1.80 tff(2036,plain,
% 1.62/1.80 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a807) | c2_1(a807) | c1_1(a807))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a807) | c3_1(a807) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a807))),
% 1.62/1.80 inference(transitivity,[status(thm)],[2035, 2033])).
% 1.62/1.80 tff(2037,plain,
% 1.62/1.80 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a807) | c2_1(a807) | c1_1(a807))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(2038,plain,
% 1.62/1.80 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a807) | c3_1(a807) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a807)),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 1.62/1.80 tff(2039,plain,
% 1.62/1.80 (c1_1(a807)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2038, 130, 1501, 2032, 2031, 2030, 2029, 2009, 10])).
% 1.62/1.80 tff(2040,plain,
% 1.62/1.80 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c1_1(a807)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c1_1(a807)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2041,plain,
% 1.62/1.80 ((hskp28 | hskp19 | (~ndr1_0) | c2_1(a807) | c3_1(a807) | (~c1_1(a807))) <=> (hskp28 | hskp19 | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c1_1(a807)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2042,plain,
% 1.62/1.80 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a807) | c3_1(a807) | (~c1_1(a807)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c1_1(a807))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[2041])).
% 1.62/1.80 tff(2043,plain,
% 1.62/1.80 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a807) | c3_1(a807) | (~c1_1(a807)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c1_1(a807)))),
% 1.62/1.80 inference(transitivity,[status(thm)],[2042, 2040])).
% 1.62/1.80 tff(2044,plain,
% 1.62/1.80 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a807) | c3_1(a807) | (~c1_1(a807)))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(2045,plain,
% 1.62/1.80 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a807) | c3_1(a807) | (~ndr1_0) | (~c1_1(a807))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 1.62/1.80 tff(2046,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2045, 130, 321, 1501, 2030, 2029, 1232, 2039])).
% 1.62/1.80 tff(2047,plain,(hskp9 | hskp28 | hskp19 | (~c3_1(a808)) | c1_1(a808) | c0_1(a828) | c2_1(a828) | c3_1(a828) | hskp20 | c2_1(a808)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(2048,plain,
% 1.62/1.80 (hskp9),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2047, 2004, 321, 1243, 1242, 2002, 1246, 1245, 308, 1241])).
% 1.62/1.80 tff(2049,plain,
% 1.62/1.80 (c0_1(a806)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[55, 2048])).
% 1.62/1.80 tff(2050,plain,
% 1.62/1.80 (c1_1(a806)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[72, 2048])).
% 1.62/1.80 tff(2051,plain,
% 1.62/1.80 (~c3_1(a806)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[63, 2048])).
% 1.62/1.80 tff(2052,plain,
% 1.62/1.80 (c2_1(a806)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[169, 2051, 2050, 2049, 1191, 1190, 1189])).
% 1.62/1.80 tff(2053,plain,
% 1.62/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a833) | c0_1(a833) | c2_1(a833) | c2_1(a828) | c3_1(a828) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a833) | c0_1(a833) | c2_1(a833) | c2_1(a828) | c3_1(a828) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a828))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2054,plain,
% 1.62/1.80 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833)) <=> (c1_1(a833) | c0_1(a833) | c2_1(a833) | c2_1(a828) | c3_1(a828) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a828))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2055,plain,
% 1.62/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a833) | c0_1(a833) | c2_1(a833) | c2_1(a828) | c3_1(a828) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a828)))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[2054])).
% 1.62/1.80 tff(2056,plain,
% 1.62/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a833) | c0_1(a833) | c2_1(a833) | c2_1(a828) | c3_1(a828) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a828))),
% 1.62/1.80 inference(transitivity,[status(thm)],[2055, 2053])).
% 1.62/1.80 tff(2057,plain,
% 1.62/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(2058,plain,
% 1.62/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a833) | c0_1(a833) | c2_1(a833) | c2_1(a828) | c3_1(a828) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a828)),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 1.62/1.80 tff(2059,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2058, 130, 300, 2050, 288, 276, 1246, 1245, 2051, 228, 2002, 2052])).
% 1.62/1.80 tff(2060,plain,(hskp21 | c1_1(a833) | c0_1(a833) | c2_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(2061,plain,
% 1.62/1.80 (hskp21),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2060, 276, 288, 300, 321])).
% 1.62/1.80 tff(2062,plain,
% 1.62/1.80 (~c2_1(a838)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[389, 2061])).
% 1.62/1.80 tff(2063,plain,
% 1.62/1.80 (hskp9),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1687, 2061, 308, 2062])).
% 1.62/1.80 tff(2064,plain,
% 1.62/1.80 (c0_1(a806)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[55, 2063])).
% 1.62/1.80 tff(2065,plain,
% 1.62/1.80 (c1_1(a806)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[72, 2063])).
% 1.62/1.80 tff(2066,plain,
% 1.62/1.80 (~c3_1(a806)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[63, 2063])).
% 1.62/1.80 tff(2067,plain,
% 1.62/1.80 (c2_1(a806)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[169, 2066, 2065, 2064, 1191, 1190, 1189])).
% 1.62/1.80 tff(2068,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1776, 130, 2000, 300, 2064, 288, 276, 2066, 1338, 2067])).
% 1.62/1.80 tff(2069,plain,(c2_1(a833) | c1_1(a833) | c0_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(2070,plain,
% 1.62/1.80 (c1_1(a833)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2069, 1298, 288, 321])).
% 1.62/1.80 tff(2071,plain,
% 1.62/1.80 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2072,plain,
% 1.62/1.80 ((hskp28 | hskp19 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (hskp28 | hskp19 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2073,plain,
% 1.62/1.80 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[2072])).
% 1.62/1.80 tff(2074,plain,
% 1.62/1.80 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 1.62/1.80 inference(transitivity,[status(thm)],[2073, 2071])).
% 1.62/1.80 tff(2075,plain,
% 1.62/1.80 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(2076,plain,
% 1.62/1.80 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[2075, 2074])).
% 1.62/1.80 tff(2077,plain,
% 1.62/1.80 (hskp19 | c3_1(a833)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2076, 130, 321, 570, 276, 1232])).
% 1.62/1.80 tff(2078,plain,
% 1.62/1.80 (c3_1(a833)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2077, 1501])).
% 1.62/1.80 tff(2079,plain,
% 1.62/1.80 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2080,plain,
% 1.62/1.80 ((hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (hskp19 | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2081,plain,
% 1.62/1.80 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[2080])).
% 1.62/1.80 tff(2082,plain,
% 1.62/1.80 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.62/1.80 inference(transitivity,[status(thm)],[2081, 2079])).
% 1.62/1.80 tff(2083,plain,
% 1.62/1.80 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(2084,plain,
% 1.62/1.80 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[2083, 2082])).
% 1.62/1.80 tff(2085,plain,
% 1.62/1.80 (hskp19 | (~c3_1(a833))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2084, 130, 570, 276, 1125, 1116, 1115, 10])).
% 1.62/1.80 tff(2086,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2085, 2078, 1501])).
% 1.62/1.80 tff(2087,plain,(hskp19 | (~c1_1(a833)) | c2_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(2088,plain,
% 1.62/1.80 (hskp19),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2087, 1309, 1298, 2070, 1246, 1245, 321])).
% 1.62/1.80 tff(2089,plain,
% 1.62/1.80 (~c3_1(a832)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[346, 2088])).
% 1.62/1.80 tff(2090,plain,
% 1.62/1.80 (c2_1(a832)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[340, 2088])).
% 1.62/1.80 tff(2091,plain,
% 1.62/1.80 (~c1_1(a832)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[352, 2088])).
% 1.62/1.80 tff(2092,plain,
% 1.62/1.80 (hskp0),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[588, 130, 629, 2090, 2091, 2089, 582])).
% 1.62/1.80 tff(2093,plain,
% 1.62/1.80 (~c1_1(a793)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[603, 2092])).
% 1.62/1.80 tff(2094,plain,
% 1.62/1.80 (c0_1(a793)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[611, 2092])).
% 1.62/1.80 tff(2095,plain,
% 1.62/1.80 (c2_1(a793)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[597, 2092])).
% 1.62/1.80 tff(2096,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1144, 2095, 2094, 2070, 629, 288, 1298, 2093, 2091, 2090, 2089, 321])).
% 1.62/1.80 tff(2097,plain,(hskp21 | c0_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(2098,plain,
% 1.62/1.80 (hskp21),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2097, 288, 321])).
% 1.62/1.80 tff(2099,plain,
% 1.62/1.80 (c3_1(a838)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[398, 2098])).
% 1.62/1.80 tff(2100,assumption,(hskp19), introduced(assumption)).
% 1.62/1.80 tff(2101,plain,
% 1.62/1.80 (c2_1(a832)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[340, 2100])).
% 1.62/1.80 tff(2102,plain,
% 1.62/1.80 (~c2_1(a838)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[389, 2098])).
% 1.62/1.80 tff(2103,plain,
% 1.62/1.80 (~c1_1(a832)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[352, 2100])).
% 1.62/1.80 tff(2104,plain,
% 1.62/1.80 (~c3_1(a832)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[346, 2100])).
% 1.62/1.80 tff(2105,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1178, 2104, 2103, 321, 288, 1298, 2070, 2102, 2101])).
% 1.62/1.80 tff(2106,plain,((~hskp19) | hskp28 | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(2107,plain,
% 1.62/1.80 (~hskp19),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2106, 288, 321])).
% 1.62/1.80 tff(2108,plain,
% 1.62/1.80 (^[U: $i] : refl((hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))),
% 1.62/1.80 inference(bind,[status(th)],[])).
% 1.62/1.80 tff(2109,plain,
% 1.62/1.80 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.62/1.80 inference(quant_intro,[status(thm)],[2108])).
% 1.62/1.80 tff(2110,plain,
% 1.62/1.80 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(2111,plain,
% 1.62/1.80 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp27))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19) <=> ((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp19))), rewrite(((hskp27 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U))) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.62/1.81 inference(bind,[status(th)],[])).
% 1.62/1.81 tff(2112,plain,
% 1.62/1.81 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19) <=> ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.62/1.81 inference(quant_intro,[status(thm)],[2111])).
% 1.62/1.81 tff(2113,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp27) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 1.62/1.81 tff(2114,plain,
% 1.62/1.81 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2113, 2112])).
% 1.62/1.81 tff(2115,plain,
% 1.62/1.81 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2114, 2110])).
% 1.62/1.81 tff(2116,plain,(
% 1.62/1.81 ![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.62/1.81 inference(skolemize,[status(sab)],[2115])).
% 1.62/1.81 tff(2117,plain,
% 1.62/1.81 (![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2116, 2109])).
% 1.62/1.81 tff(2118,plain,
% 1.62/1.81 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2119,plain,
% 1.62/1.81 ((hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867))) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2120,plain,
% 1.62/1.81 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[2119])).
% 1.62/1.81 tff(2121,plain,
% 1.62/1.81 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)))),
% 1.62/1.81 inference(transitivity,[status(thm)],[2120, 2118])).
% 1.62/1.81 tff(2122,plain,
% 1.62/1.81 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(2123,plain,
% 1.62/1.81 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 1.62/1.81 tff(2124,plain,
% 1.62/1.81 (hskp27 | hskp19 | (~c2_1(a867))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2123, 130, 1190, 1189, 2117])).
% 1.62/1.81 tff(2125,plain,
% 1.62/1.81 (hskp27),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2124, 2107, 1200])).
% 1.62/1.81 tff(2126,plain,
% 1.62/1.81 (c3_1(a796)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[531, 2125])).
% 1.62/1.81 tff(2127,plain,
% 1.62/1.81 (c2_1(a796)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[539, 2125])).
% 1.62/1.81 tff(2128,plain,
% 1.62/1.81 (c0_1(a838)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[406, 2098])).
% 1.62/1.81 tff(2129,plain,
% 1.62/1.81 (~hskp17),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1037, 2128, 321, 2102, 2099])).
% 1.62/1.81 tff(2130,plain,
% 1.62/1.81 (hskp19 | c3_1(a833)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2076, 130, 321, 2070, 1298, 1232])).
% 1.62/1.81 tff(2131,plain,
% 1.62/1.81 (c3_1(a833)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2130, 2107])).
% 1.62/1.81 tff(2132,plain,
% 1.62/1.81 (hskp17 | hskp0 | (~c3_1(a833)) | (~c1_1(a833))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1054, 130, 288, 1048])).
% 1.62/1.81 tff(2133,plain,
% 1.62/1.81 (hskp0),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2132, 2131, 2070, 2129])).
% 1.62/1.81 tff(2134,plain,
% 1.62/1.81 (c2_1(a793)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[597, 2133])).
% 1.62/1.81 tff(2135,plain,
% 1.62/1.81 (c0_1(a793)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[611, 2133])).
% 1.62/1.81 tff(2136,plain,
% 1.62/1.81 (c0_1(a796)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[547, 2125])).
% 1.62/1.81 tff(2137,plain,
% 1.62/1.81 (~c1_1(a838)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1019, 130, 321, 2128, 2099, 2102, 332])).
% 1.62/1.81 tff(2138,plain,
% 1.62/1.81 (~c1_1(a793)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[603, 2133])).
% 1.62/1.81 tff(2139,plain,
% 1.62/1.81 (hskp8),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1151, 2138, 2070, 2137, 2136, 2102, 2135, 2134, 288, 1298, 2127, 2126, 2099, 321])).
% 1.62/1.81 tff(2140,plain,
% 1.62/1.81 (~c3_1(a805)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[414, 2139])).
% 1.62/1.81 tff(2141,plain,
% 1.62/1.81 (~c2_1(a805)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[420, 2139])).
% 1.62/1.81 tff(2142,plain,
% 1.62/1.81 (c1_1(a805)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[429, 2139])).
% 1.62/1.81 tff(2143,plain,
% 1.62/1.81 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2144,plain,
% 1.62/1.81 ((hskp28 | hskp19 | (~ndr1_0) | c2_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (hskp28 | hskp19 | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2145,plain,
% 1.62/1.81 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[2144])).
% 1.62/1.81 tff(2146,plain,
% 1.62/1.81 (((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805)))),
% 1.62/1.81 inference(transitivity,[status(thm)],[2145, 2143])).
% 1.62/1.81 tff(2147,plain,
% 1.62/1.81 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp28 | hskp19 | (~ndr1_0) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(2148,plain,
% 1.62/1.81 ((~![U: $i] : (hskp28 | hskp19 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp28 | hskp19 | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c1_1(a805))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 1.62/1.81 tff(2149,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2148, 130, 321, 2107, 2142, 2141, 2140, 1232])).
% 1.62/1.81 tff(2150,plain,(c0_1(a833) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(2151,plain,
% 1.62/1.81 (c0_1(a833)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2150, 321])).
% 1.62/1.81 tff(2152,plain,
% 1.62/1.81 (~hskp20),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[563, 2151])).
% 1.62/1.81 tff(2153,plain,
% 1.62/1.81 (hskp9),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1687, 1221, 2152, 1222])).
% 1.62/1.81 tff(2154,plain,
% 1.62/1.81 (c0_1(a806)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[55, 2153])).
% 1.62/1.81 tff(2155,plain,
% 1.62/1.81 (c1_1(a806)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[72, 2153])).
% 1.62/1.81 tff(2156,plain,
% 1.62/1.81 (~c3_1(a806)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[63, 2153])).
% 1.62/1.81 tff(2157,plain,
% 1.62/1.81 (c2_1(a806)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[169, 2156, 2155, 2154, 1191, 1190, 1189])).
% 1.62/1.81 tff(2158,plain,
% 1.62/1.81 (^[U: $i] : refl((hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 1.62/1.81 inference(bind,[status(th)],[])).
% 1.62/1.81 tff(2159,plain,
% 1.62/1.81 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.62/1.81 inference(quant_intro,[status(thm)],[2158])).
% 1.62/1.81 tff(2160,plain,
% 1.62/1.81 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2161,plain,
% 1.62/1.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp16) <=> ((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.62/1.81 inference(bind,[status(th)],[])).
% 1.62/1.81 tff(2162,plain,
% 1.62/1.81 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp16) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.62/1.81 inference(quant_intro,[status(thm)],[2161])).
% 1.62/1.81 tff(2163,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 1.62/1.81 tff(2164,plain,
% 1.62/1.81 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2163, 2162])).
% 1.62/1.81 tff(2165,plain,
% 1.62/1.81 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2164, 2160])).
% 1.62/1.81 tff(2166,plain,(
% 1.62/1.81 ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.62/1.81 inference(skolemize,[status(sab)],[2165])).
% 1.62/1.81 tff(2167,plain,
% 1.62/1.81 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2166, 2159])).
% 1.62/1.81 tff(2168,plain,
% 1.62/1.81 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2169,plain,
% 1.62/1.81 ((hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c0_1(a867))) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2170,plain,
% 1.62/1.81 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[2169])).
% 1.62/1.81 tff(2171,plain,
% 1.62/1.81 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867)))),
% 1.62/1.81 inference(transitivity,[status(thm)],[2170, 2168])).
% 1.62/1.81 tff(2172,plain,
% 1.62/1.81 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c0_1(a867)))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(2173,plain,
% 1.62/1.81 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c2_1(a867))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 1.62/1.81 tff(2174,plain,
% 1.62/1.81 (hskp16 | hskp15 | (~c2_1(a867))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2173, 130, 1191, 1189, 2167])).
% 1.62/1.81 tff(2175,plain,
% 1.62/1.81 (hskp16),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2174, 1278, 1200])).
% 1.62/1.81 tff(2176,plain,
% 1.62/1.81 (((~hskp16) | (~c2_1(a821))) <=> ((~hskp16) | (~c2_1(a821)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2177,plain,
% 1.62/1.81 (((~c2_1(a821)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a821)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2178,axiom,((~c2_1(a821)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.62/1.81 tff(2179,plain,
% 1.62/1.81 ((~hskp16) | (~c2_1(a821))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 1.62/1.81 tff(2180,plain,
% 1.62/1.81 ((~hskp16) | (~c2_1(a821))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2179, 2176])).
% 1.62/1.81 tff(2181,plain,
% 1.62/1.81 (~c2_1(a821)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2180, 2175])).
% 1.62/1.81 tff(2182,plain,
% 1.62/1.81 (((~hskp16) | (~c1_1(a821))) <=> ((~hskp16) | (~c1_1(a821)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2183,plain,
% 1.62/1.81 (((~c1_1(a821)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a821)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2184,axiom,((~c1_1(a821)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.62/1.81 tff(2185,plain,
% 1.62/1.81 ((~hskp16) | (~c1_1(a821))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2184, 2183])).
% 1.62/1.81 tff(2186,plain,
% 1.62/1.81 ((~hskp16) | (~c1_1(a821))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2185, 2182])).
% 1.62/1.81 tff(2187,plain,
% 1.62/1.81 (~c1_1(a821)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2186, 2175])).
% 1.62/1.81 tff(2188,plain,
% 1.62/1.81 (((~hskp16) | (~c0_1(a821))) <=> ((~hskp16) | (~c0_1(a821)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2189,plain,
% 1.62/1.81 (((~c0_1(a821)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a821)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2190,axiom,((~c0_1(a821)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.62/1.81 tff(2191,plain,
% 1.62/1.81 ((~hskp16) | (~c0_1(a821))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 1.62/1.81 tff(2192,plain,
% 1.62/1.81 ((~hskp16) | (~c0_1(a821))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2191, 2188])).
% 1.62/1.81 tff(2193,plain,
% 1.62/1.81 (~c0_1(a821)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2192, 2175])).
% 1.62/1.81 tff(2194,plain,
% 1.62/1.81 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a821) | c1_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a821) | c1_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2195,plain,
% 1.62/1.81 ((hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a821) | c1_1(a821) | c0_1(a821)) <=> (hskp0 | c0_1(a821) | c1_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2196,plain,
% 1.62/1.81 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a821) | c1_1(a821) | c0_1(a821))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a821) | c1_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[2195])).
% 1.62/1.81 tff(2197,plain,
% 1.62/1.81 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a821) | c1_1(a821) | c0_1(a821))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a821) | c1_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)))),
% 1.62/1.81 inference(transitivity,[status(thm)],[2196, 2194])).
% 1.62/1.81 tff(2198,plain,
% 1.62/1.81 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a806) | (~c2_1(a806)) | (~c0_1(a806)) | c2_1(a821) | c1_1(a821) | c0_1(a821))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(2199,plain,
% 1.62/1.81 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a821) | c1_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2198, 2197])).
% 1.62/1.81 tff(2200,plain,
% 1.62/1.81 (hskp0),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2199, 130, 2154, 2193, 2187, 2181, 2156, 1338, 2157])).
% 1.62/1.81 tff(2201,plain,
% 1.62/1.81 (~c1_1(a793)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[603, 2200])).
% 1.62/1.81 tff(2202,plain,
% 1.62/1.81 (c2_1(a793)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[597, 2200])).
% 1.62/1.81 tff(2203,plain,
% 1.62/1.81 (~c3_1(a793)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1792, 130, 321, 1191, 1190, 1189, 2202, 2201, 1220])).
% 1.62/1.81 tff(2204,plain,
% 1.62/1.81 (~c1_1(a838)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1019, 130, 321, 1683, 1684, 1222, 332])).
% 1.62/1.81 tff(2205,plain,
% 1.62/1.81 (c0_1(a793)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[611, 2200])).
% 1.62/1.81 tff(2206,plain,
% 1.62/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a821) | c2_1(a821) | c1_1(a793) | (~ndr1_0) | c3_1(a821) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a821) | c2_1(a821) | c1_1(a793) | (~ndr1_0) | c3_1(a821) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2207,plain,
% 1.62/1.81 (((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a821) | c0_1(a821) | c3_1(a821)) <=> (c2_1(a838) | c0_1(a821) | c2_1(a821) | c1_1(a793) | (~ndr1_0) | c3_1(a821) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2208,plain,
% 1.62/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a821) | c0_1(a821) | c3_1(a821))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a838) | c0_1(a821) | c2_1(a821) | c1_1(a793) | (~ndr1_0) | c3_1(a821) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[2207])).
% 1.62/1.81 tff(2209,plain,
% 1.62/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a821) | c0_1(a821) | c3_1(a821))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a821) | c2_1(a821) | c1_1(a793) | (~ndr1_0) | c3_1(a821) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838))),
% 1.62/1.81 inference(transitivity,[status(thm)],[2208, 2206])).
% 1.62/1.81 tff(2210,plain,
% 1.62/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a793) | c3_1(a793) | (~c0_1(a793)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a821) | c0_1(a821) | c3_1(a821))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(2211,plain,
% 1.62/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a838) | c0_1(a821) | c2_1(a821) | c1_1(a793) | (~ndr1_0) | c3_1(a821) | (~c0_1(a793)) | c3_1(a793) | (~c3_1(a838)) | c1_1(a838)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2210, 2209])).
% 1.62/1.81 tff(2212,plain,
% 1.62/1.81 (c3_1(a821) | c3_1(a793)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2211, 130, 1684, 2205, 1222, 2193, 2181, 2201, 795, 2204])).
% 1.62/1.81 tff(2213,plain,
% 1.62/1.81 (c3_1(a821)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2212, 2203])).
% 1.62/1.81 tff(2214,plain,
% 1.62/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a806)) | (~c1_1(a806)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a806)) | (~c1_1(a806)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2215,plain,
% 1.62/1.81 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a806)) | (~c1_1(a806)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2216,plain,
% 1.62/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a806)) | (~c1_1(a806))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[2215])).
% 1.62/1.81 tff(2217,plain,
% 1.62/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a806)) | (~c1_1(a806)))),
% 1.62/1.81 inference(transitivity,[status(thm)],[2216, 2214])).
% 1.62/1.81 tff(2218,plain,
% 1.62/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(2219,plain,
% 1.62/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a806)) | (~c1_1(a806))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2218, 2217])).
% 1.62/1.81 tff(2220,plain,
% 1.62/1.81 (~c1_1(a794)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2219, 130, 2155, 1743, 2156, 1753, 1742, 1961, 2157])).
% 1.62/1.81 tff(2221,plain,
% 1.62/1.81 (hskp7),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1759, 130, 1190, 1189, 1743, 1753, 1413, 1200, 2220])).
% 1.62/1.81 tff(2222,plain,
% 1.62/1.81 (~c2_1(a803)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1377, 2221])).
% 1.62/1.81 tff(2223,plain,
% 1.62/1.81 (c1_1(a803)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1393, 2221])).
% 1.62/1.81 tff(2224,plain,
% 1.62/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a821) | c1_1(a821) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a821)) | (~c2_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a821) | c1_1(a821) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a821)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2225,plain,
% 1.62/1.81 (((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821))) <=> (c0_1(a821) | c1_1(a821) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a821)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(2226,plain,
% 1.62/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a821) | c1_1(a821) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a821)) | (~c2_1(a793)) | (~c0_1(a793))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[2225])).
% 1.62/1.81 tff(2227,plain,
% 1.62/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a821) | c1_1(a821) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a821)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 1.62/1.81 inference(transitivity,[status(thm)],[2226, 2224])).
% 1.62/1.81 tff(2228,plain,
% 1.62/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(2229,plain,
% 1.62/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a821) | c1_1(a821) | c2_1(a803) | c1_1(a793) | (~ndr1_0) | (~c0_1(a803)) | (~c1_1(a803)) | (~c3_1(a821)) | (~c2_1(a793)) | (~c0_1(a793))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[2228, 2227])).
% 1.62/1.81 tff(2230,plain,
% 1.62/1.81 (~c0_1(a803)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[2229, 130, 2223, 2205, 2202, 2193, 2187, 2222, 2201, 287, 2213])).
% 1.62/1.81 tff(2231,plain,
% 1.62/1.81 (c3_1(a803)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1385, 2221])).
% 1.62/1.81 tff(2232,plain,
% 1.62/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a821)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a821)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(2233,plain,
% 1.62/1.82 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821))) <=> (c0_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a821)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(2234,plain,
% 1.62/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a821))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[2233])).
% 1.62/1.82 tff(2235,plain,
% 1.62/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a821)))),
% 1.62/1.82 inference(transitivity,[status(thm)],[2234, 2232])).
% 1.62/1.82 tff(2236,plain,
% 1.62/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821)))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(2237,plain,
% 1.62/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a821) | c2_1(a821) | c3_1(a806) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a821))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 1.62/1.82 tff(2238,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2237, 130, 2155, 2223, 2231, 2193, 2181, 2156, 1961, 2157, 2213, 2230])).
% 1.62/1.82 tff(2239,plain,((~hskp21) | hskp28 | (~c3_1(a794)) | c0_1(a794) | c2_1(a794)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(2240,plain,
% 1.62/1.82 (~hskp21),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2239, 259, 321, 265, 251])).
% 1.62/1.82 tff(2241,plain,
% 1.62/1.82 (hskp21 | hskp11 | (~c2_1(a867))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1238, 130, 57, 65, 628])).
% 1.62/1.82 tff(2242,plain,
% 1.62/1.82 (hskp11),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2241, 629, 1279])).
% 1.62/1.82 tff(2243,plain,
% 1.62/1.82 (~c2_1(a808)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[776, 2242])).
% 1.62/1.82 tff(2244,plain,
% 1.62/1.82 (~c1_1(a808)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[770, 2242])).
% 1.62/1.82 tff(2245,plain,
% 1.62/1.82 (c3_1(a808)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[812, 2242])).
% 1.62/1.82 tff(2246,assumption,(~hskp18), introduced(assumption)).
% 1.62/1.82 tff(2247,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1095, 130, 629, 2246, 2245, 2244, 2243, 1088])).
% 1.62/1.82 tff(2248,plain,(hskp21 | hskp18 | (~c2_1(a867)) | (~c1_1(a867)) | (~c3_1(a867))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(2249,plain,
% 1.62/1.82 (hskp18),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2248, 2240, 1200, 1190, 1189])).
% 1.62/1.82 tff(2250,assumption,(hskp18), introduced(assumption)).
% 1.62/1.82 tff(2251,plain,
% 1.62/1.82 (~c3_1(a828)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1107, 2250])).
% 1.62/1.82 tff(2252,plain,
% 1.62/1.82 (~c2_1(a828)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1101, 2250])).
% 1.62/1.82 tff(2253,plain,
% 1.62/1.82 (~c1_1(a828)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1113, 2250])).
% 1.62/1.82 tff(2254,plain,
% 1.62/1.82 (~c1_1(a794)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1751, 130, 1501, 1743, 2253, 2252, 2251, 1742, 10])).
% 1.62/1.82 tff(2255,plain,
% 1.62/1.82 (hskp7),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1759, 130, 57, 65, 1743, 1753, 1413, 1279, 2254])).
% 1.62/1.82 tff(2256,plain,
% 1.62/1.82 (~c2_1(a803)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1377, 2255])).
% 1.62/1.82 tff(2257,plain,
% 1.62/1.82 (c3_1(a803)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1385, 2255])).
% 1.62/1.82 tff(2258,plain,
% 1.62/1.82 (c1_1(a803)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1393, 2255])).
% 1.62/1.82 tff(2259,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1707, 130, 1501, 2258, 2257, 2253, 2252, 2251, 2256, 10])).
% 1.62/1.82 tff(2260,plain,((~hskp18) | hskp19 | (~c1_1(a867)) | (~c3_1(a867)) | (~c3_1(a794)) | c0_1(a794) | (~c2_1(a867)) | c2_1(a794)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(2261,plain,
% 1.62/1.82 (hskp19),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2260, 2249, 1190, 1189, 259, 265, 1200, 251])).
% 1.62/1.82 tff(2262,plain,
% 1.62/1.82 (~c3_1(a832)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[346, 2261])).
% 1.62/1.82 tff(2263,plain,
% 1.62/1.82 (c2_1(a832)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[340, 2261])).
% 1.62/1.82 tff(2264,plain,
% 1.62/1.82 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | c0_1(a832))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(2265,plain,
% 1.62/1.82 ((hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832))) <=> (hskp15 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | c0_1(a832))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(2266,plain,
% 1.62/1.82 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | c0_1(a832)))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[2265])).
% 1.62/1.82 tff(2267,plain,
% 1.62/1.82 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | c0_1(a832))),
% 1.62/1.82 inference(transitivity,[status(thm)],[2266, 2264])).
% 1.62/1.82 tff(2268,plain,
% 1.62/1.82 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(2269,plain,
% 1.62/1.82 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | c0_1(a832)),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[2268, 2267])).
% 1.62/1.82 tff(2270,plain,
% 1.62/1.82 (c0_1(a832)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2269, 130, 1278, 1190, 1189, 2263, 2262, 1210, 1200])).
% 1.62/1.82 tff(2271,plain,
% 1.62/1.82 (hskp11),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1239, 2240, 1200])).
% 1.62/1.82 tff(2272,plain,
% 1.62/1.82 (~c2_1(a808)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[776, 2271])).
% 1.62/1.82 tff(2273,plain,
% 1.62/1.82 (~c1_1(a808)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[770, 2271])).
% 1.62/1.82 tff(2274,plain,
% 1.62/1.82 (~c1_1(a832)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[352, 2261])).
% 1.62/1.82 tff(2275,plain,
% 1.62/1.82 (c3_1(a808)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[812, 2271])).
% 1.62/1.82 tff(2276,plain,
% 1.62/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a821) | c2_1(a821) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a821) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a821) | c2_1(a821) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a821) | (~c0_1(a832)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(2277,plain,
% 1.62/1.82 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a821) | c0_1(a821) | c3_1(a821)) <=> (c1_1(a832) | c3_1(a832) | c0_1(a821) | c2_1(a821) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a821) | (~c0_1(a832)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(2278,plain,
% 1.62/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a821) | c0_1(a821) | c3_1(a821))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a821) | c2_1(a821) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a821) | (~c0_1(a832))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[2277])).
% 1.62/1.82 tff(2279,plain,
% 1.62/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a821) | c0_1(a821) | c3_1(a821))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a821) | c2_1(a821) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a821) | (~c0_1(a832)))),
% 1.62/1.82 inference(transitivity,[status(thm)],[2278, 2276])).
% 1.62/1.82 tff(2280,plain,
% 1.62/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a821) | c0_1(a821) | c3_1(a821))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(2281,plain,
% 1.62/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a821) | c2_1(a821) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c3_1(a821) | (~c0_1(a832))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[2280, 2279])).
% 1.62/1.82 tff(2282,plain,
% 1.62/1.82 (c3_1(a821) | (~c0_1(a832))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2281, 130, 2275, 2274, 2262, 2193, 2181, 2273, 2272, 795])).
% 1.62/1.82 tff(2283,plain,
% 1.62/1.82 (c3_1(a821)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2282, 2270])).
% 1.62/1.82 tff(2284,plain,
% 1.62/1.82 (~c3_1(a828)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1107, 2249])).
% 1.62/1.82 tff(2285,plain,
% 1.62/1.82 (~c2_1(a828)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1101, 2249])).
% 1.62/1.82 tff(2286,plain,
% 1.62/1.82 (~c1_1(a828)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1113, 2249])).
% 1.62/1.82 tff(2287,plain,
% 1.62/1.82 (hskp2),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1315, 130, 2152, 2286, 2285, 2284, 1308])).
% 1.62/1.82 tff(2288,plain,
% 1.62/1.82 (~c0_1(a795)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1353, 2287])).
% 1.62/1.82 tff(2289,plain,
% 1.62/1.82 (~c3_1(a795)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1321, 2287])).
% 1.62/1.82 tff(2290,plain,
% 1.62/1.82 (c2_1(a795)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1461, 2289, 2274, 2271, 2270, 2288, 2262])).
% 1.62/1.82 tff(2291,plain,
% 1.62/1.82 (~c1_1(a795)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1327, 2287])).
% 1.62/1.82 tff(2292,assumption,(~c1_1(a795)), introduced(assumption)).
% 1.62/1.82 tff(2293,assumption,(hskp12), introduced(assumption)).
% 1.62/1.82 tff(2294,plain,
% 1.62/1.82 (~c0_1(a809)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[143, 2293])).
% 1.62/1.82 tff(2295,plain,
% 1.62/1.82 (c1_1(a809)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[160, 2293])).
% 1.62/1.82 tff(2296,plain,
% 1.62/1.82 (c2_1(a809)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[152, 2293])).
% 1.62/1.82 tff(2297,assumption,(~c0_1(a809)), introduced(assumption)).
% 1.62/1.82 tff(2298,plain,
% 1.62/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(2299,plain,
% 1.62/1.82 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a795) | c0_1(a795) | c3_1(a795)) <=> (c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(2300,plain,
% 1.62/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[2299])).
% 1.62/1.82 tff(2301,plain,
% 1.62/1.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)))),
% 1.62/1.82 inference(transitivity,[status(thm)],[2300, 2298])).
% 1.62/1.82 tff(2302,plain,
% 1.62/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c1_1(a795) | c0_1(a795) | c3_1(a795))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(2303,plain,
% 1.62/1.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[2302, 2301])).
% 1.62/1.82 tff(2304,plain,
% 1.62/1.82 ((~c2_1(a809)) | (~c1_1(a809))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2303, 130, 391, 289, 22, 2297, 1452, 2292, 1453, 977])).
% 1.62/1.82 tff(2305,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2304, 2296, 2295])).
% 1.62/1.82 tff(2306,plain,((~hskp12) | (~c2_1(a832)) | c1_1(a832) | c3_1(a832) | c0_1(a809) | c0_1(a795) | c1_1(a795) | c3_1(a795)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(2307,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2306, 2294, 2293, 289, 22, 391, 1452, 2292, 1453])).
% 1.62/1.82 tff(2308,plain,((~hskp12) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a795) | c1_1(a795) | c3_1(a795)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(2309,plain,
% 1.62/1.82 (~hskp12),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2308, 2288, 2262, 2291, 2263, 2274, 2289])).
% 1.62/1.82 tff(2310,plain,
% 1.62/1.82 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a821)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a821)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(2311,plain,
% 1.62/1.82 ((hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821))) <=> (hskp12 | c0_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a821)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(2312,plain,
% 1.62/1.82 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a821))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[2311])).
% 1.62/1.82 tff(2313,plain,
% 1.62/1.82 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a821)))),
% 1.62/1.82 inference(transitivity,[status(thm)],[2312, 2310])).
% 1.62/1.82 tff(2314,plain,
% 1.62/1.82 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a821) | c0_1(a821) | (~c3_1(a821)))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(2315,plain,
% 1.62/1.82 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a821))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 1.62/1.82 tff(2316,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2315, 130, 2309, 2193, 2181, 2288, 2289, 989, 2290, 2283])).
% 1.62/1.82 tff(2317,plain,((~hskp1) | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(2318,plain,
% 1.62/1.82 (~hskp1),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[2317, 321])).
% 1.62/1.82 tff(2319,plain,
% 1.62/1.82 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.62/1.82 inference(bind,[status(th)],[])).
% 1.62/1.82 tff(2320,plain,
% 1.62/1.82 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.62/1.82 inference(quant_intro,[status(thm)],[2319])).
% 1.62/1.82 tff(2321,plain,
% 1.62/1.82 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(2322,plain,
% 1.62/1.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.66/1.82 inference(bind,[status(th)],[])).
% 1.66/1.82 tff(2323,plain,
% 1.66/1.82 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.66/1.82 inference(quant_intro,[status(thm)],[2322])).
% 1.66/1.82 tff(2324,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.66/1.82 tff(2325,plain,
% 1.66/1.82 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[2324, 2323])).
% 1.66/1.82 tff(2326,plain,
% 1.66/1.82 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[2325, 2321])).
% 1.66/1.82 tff(2327,plain,(
% 1.66/1.82 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.66/1.82 inference(skolemize,[status(sab)],[2326])).
% 1.66/1.82 tff(2328,plain,
% 1.66/1.82 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[2327, 2320])).
% 1.66/1.82 tff(2329,plain,
% 1.66/1.82 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a821) | c1_1(a821) | c2_1(a821) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a821) | c1_1(a821) | c2_1(a821) | (~ndr1_0))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(2330,plain,
% 1.66/1.82 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a821) | c1_1(a821) | c0_1(a821)) <=> (hskp2 | hskp1 | c0_1(a821) | c1_1(a821) | c2_1(a821) | (~ndr1_0))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(2331,plain,
% 1.66/1.82 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a821) | c1_1(a821) | c0_1(a821))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a821) | c1_1(a821) | c2_1(a821) | (~ndr1_0)))),
% 1.66/1.82 inference(monotonicity,[status(thm)],[2330])).
% 1.66/1.82 tff(2332,plain,
% 1.66/1.82 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a821) | c1_1(a821) | c0_1(a821))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a821) | c1_1(a821) | c2_1(a821) | (~ndr1_0))),
% 1.66/1.82 inference(transitivity,[status(thm)],[2331, 2329])).
% 1.66/1.82 tff(2333,plain,
% 1.66/1.82 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a821) | c1_1(a821) | c0_1(a821))),
% 1.66/1.82 inference(quant_inst,[status(thm)],[])).
% 1.66/1.82 tff(2334,plain,
% 1.66/1.82 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a821) | c1_1(a821) | c2_1(a821) | (~ndr1_0)),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[2333, 2332])).
% 1.66/1.82 tff(2335,plain,
% 1.66/1.82 (hskp2 | hskp1),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[2334, 130, 2193, 2187, 2181, 2328])).
% 1.66/1.82 tff(2336,plain,
% 1.66/1.82 (hskp2),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[2335, 2318])).
% 1.66/1.82 tff(2337,plain,
% 1.66/1.82 (~c3_1(a795)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1321, 2336])).
% 1.66/1.82 tff(2338,plain,
% 1.66/1.82 (~c0_1(a795)),
% 1.66/1.82 inference(unit_resolution,[status(thm)],[1353, 2336])).
% 1.66/1.82 tff(2339,plain,
% 1.66/1.82 (^[U: $i] : refl((hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.66/1.82 inference(bind,[status(th)],[])).
% 1.66/1.82 tff(2340,plain,
% 1.66/1.82 (![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.66/1.82 inference(quant_intro,[status(thm)],[2339])).
% 1.66/1.82 tff(2341,plain,
% 1.66/1.82 (![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(2342,plain,
% 1.66/1.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp1) <=> ((hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp1))), rewrite(((hskp25 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp1) <=> (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.66/1.82 inference(bind,[status(th)],[])).
% 1.66/1.82 tff(2343,plain,
% 1.66/1.82 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp1) <=> ![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.66/1.82 inference(quant_intro,[status(thm)],[2342])).
% 1.66/1.82 tff(2344,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 1.66/1.82 tff(2345,plain,
% 1.66/1.82 (![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[2344, 2343])).
% 1.66/1.82 tff(2346,plain,
% 1.66/1.82 (![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[2345, 2341])).
% 1.66/1.82 tff(2347,plain,(
% 1.66/1.82 ![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.66/1.82 inference(skolemize,[status(sab)],[2346])).
% 1.66/1.82 tff(2348,plain,
% 1.66/1.82 (![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.66/1.82 inference(modus_ponens,[status(thm)],[2347, 2340])).
% 1.66/1.82 tff(2349,plain,
% 1.66/1.82 (((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))) <=> ((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(2350,plain,
% 1.66/1.82 ((hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867))) <=> (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))),
% 1.66/1.82 inference(rewrite,[status(thm)],[])).
% 1.66/1.82 tff(2351,plain,
% 1.66/1.82 (((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867))))),
% 1.66/1.82 inference(monotonicity,[status(thm)],[2350])).
% 1.66/1.82 tff(2352,plain,
% 1.66/1.82 (((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2351, 2349])).
% 1.66/1.83 tff(2353,plain,
% 1.66/1.83 ((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2354,plain,
% 1.66/1.83 ((~![U: $i] : (hskp25 | hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp1 | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2353, 2352])).
% 1.66/1.83 tff(2355,plain,
% 1.66/1.83 (hskp25 | hskp1),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2354, 130, 1191, 1190, 1189, 2348])).
% 1.66/1.83 tff(2356,plain,
% 1.66/1.83 (hskp25),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2355, 2318])).
% 1.66/1.83 tff(2357,plain,
% 1.66/1.83 (((~hskp25) | (~c3_1(a865))) <=> ((~hskp25) | (~c3_1(a865)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2358,plain,
% 1.66/1.83 (((~c3_1(a865)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a865)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2359,axiom,((~c3_1(a865)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.66/1.83 tff(2360,plain,
% 1.66/1.83 ((~hskp25) | (~c3_1(a865))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2359, 2358])).
% 1.66/1.83 tff(2361,plain,
% 1.66/1.83 ((~hskp25) | (~c3_1(a865))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2360, 2357])).
% 1.66/1.83 tff(2362,plain,
% 1.66/1.83 (~c3_1(a865)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2361, 2356])).
% 1.66/1.83 tff(2363,plain,
% 1.66/1.83 (((~hskp25) | c2_1(a865)) <=> ((~hskp25) | c2_1(a865))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2364,axiom,((~hskp25) | c2_1(a865)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.66/1.83 tff(2365,plain,
% 1.66/1.83 ((~hskp25) | c2_1(a865)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2364, 2363])).
% 1.66/1.83 tff(2366,plain,
% 1.66/1.83 ((~hskp25) | c2_1(a865)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2365, 2363])).
% 1.66/1.83 tff(2367,plain,
% 1.66/1.83 ((~hskp25) | c2_1(a865)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2366, 2363])).
% 1.66/1.83 tff(2368,plain,
% 1.66/1.83 ((~hskp25) | c2_1(a865)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2367, 2363])).
% 1.66/1.83 tff(2369,plain,
% 1.66/1.83 ((~hskp25) | c2_1(a865)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2368, 2363])).
% 1.66/1.83 tff(2370,plain,
% 1.66/1.83 (c2_1(a865)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2369, 2356])).
% 1.66/1.83 tff(2371,plain,
% 1.66/1.83 (((~hskp25) | c1_1(a865)) <=> ((~hskp25) | c1_1(a865))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2372,axiom,((~hskp25) | c1_1(a865)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.66/1.83 tff(2373,plain,
% 1.66/1.83 ((~hskp25) | c1_1(a865)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2372, 2371])).
% 1.66/1.83 tff(2374,plain,
% 1.66/1.83 ((~hskp25) | c1_1(a865)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2373, 2371])).
% 1.66/1.83 tff(2375,plain,
% 1.66/1.83 ((~hskp25) | c1_1(a865)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2374, 2371])).
% 1.66/1.83 tff(2376,plain,
% 1.66/1.83 ((~hskp25) | c1_1(a865)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2375, 2371])).
% 1.66/1.83 tff(2377,plain,
% 1.66/1.83 ((~hskp25) | c1_1(a865)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2376, 2371])).
% 1.66/1.83 tff(2378,plain,
% 1.66/1.83 (c1_1(a865)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2377, 2356])).
% 1.66/1.83 tff(2379,plain,
% 1.66/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a865) | c0_1(a821) | c1_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a865) | c0_1(a821) | c1_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c2_1(a865)) | (~c1_1(a865)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2380,plain,
% 1.66/1.83 (((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a821) | c1_1(a821) | c0_1(a821)) <=> (c3_1(a865) | c0_1(a821) | c1_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c2_1(a865)) | (~c1_1(a865)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2381,plain,
% 1.66/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a821) | c1_1(a821) | c0_1(a821))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a865) | c0_1(a821) | c1_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c2_1(a865)) | (~c1_1(a865))))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[2380])).
% 1.66/1.83 tff(2382,plain,
% 1.66/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a821) | c1_1(a821) | c0_1(a821))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a865) | c0_1(a821) | c1_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c2_1(a865)) | (~c1_1(a865)))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2381, 2379])).
% 1.66/1.83 tff(2383,plain,
% 1.66/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a821) | c1_1(a821) | c0_1(a821))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2384,plain,
% 1.66/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a865) | c0_1(a821) | c1_1(a821) | c2_1(a821) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c2_1(a865)) | (~c1_1(a865))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 1.66/1.83 tff(2385,plain,
% 1.66/1.83 (c2_1(a795)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2384, 130, 2378, 2370, 2362, 2193, 2187, 2181, 2338, 2337, 228])).
% 1.66/1.83 tff(2386,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a795)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2387,plain,
% 1.66/1.83 ((hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795))) <=> (hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a795)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2388,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a795))))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[2387])).
% 1.66/1.83 tff(2389,plain,
% 1.66/1.83 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a795)))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2388, 2386])).
% 1.66/1.83 tff(2390,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c2_1(a867)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795)))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2391,plain,
% 1.66/1.83 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c3_1(a867)) | (~c2_1(a867)) | (~c1_1(a867)) | (~c2_1(a795))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 1.66/1.83 tff(2392,plain,
% 1.66/1.83 ($false),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2391, 130, 1278, 1190, 1189, 2338, 2337, 1210, 2385, 1200])).
% 1.66/1.83 tff(2393,plain,(hskp28), inference(lemma,lemma(discharge,[]))).
% 1.66/1.83 tff(2394,plain,
% 1.66/1.83 (((~hskp28) | c3_1(a797)) <=> ((~hskp28) | c3_1(a797))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2395,axiom,((~hskp28) | c3_1(a797)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.66/1.83 tff(2396,plain,
% 1.66/1.83 ((~hskp28) | c3_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2395, 2394])).
% 1.66/1.83 tff(2397,plain,
% 1.66/1.83 ((~hskp28) | c3_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2396, 2394])).
% 1.66/1.83 tff(2398,plain,
% 1.66/1.83 ((~hskp28) | c3_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2397, 2394])).
% 1.66/1.83 tff(2399,plain,
% 1.66/1.83 ((~hskp28) | c3_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2398, 2394])).
% 1.66/1.83 tff(2400,plain,
% 1.66/1.83 ((~hskp28) | c3_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2399, 2394])).
% 1.66/1.83 tff(2401,plain,
% 1.66/1.83 (c3_1(a797)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2400, 2393])).
% 1.66/1.83 tff(2402,plain,
% 1.66/1.83 (((~hskp28) | c2_1(a797)) <=> ((~hskp28) | c2_1(a797))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2403,axiom,((~hskp28) | c2_1(a797)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.66/1.83 tff(2404,plain,
% 1.66/1.83 ((~hskp28) | c2_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 1.66/1.83 tff(2405,plain,
% 1.66/1.83 ((~hskp28) | c2_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2404, 2402])).
% 1.66/1.83 tff(2406,plain,
% 1.66/1.83 ((~hskp28) | c2_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2405, 2402])).
% 1.66/1.83 tff(2407,plain,
% 1.66/1.83 ((~hskp28) | c2_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2406, 2402])).
% 1.66/1.83 tff(2408,plain,
% 1.66/1.83 ((~hskp28) | c2_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2407, 2402])).
% 1.66/1.83 tff(2409,plain,
% 1.66/1.83 (c2_1(a797)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2408, 2393])).
% 1.66/1.83 tff(2410,plain,
% 1.66/1.83 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2411,plain,
% 1.66/1.83 ((hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797))) <=> (hskp30 | hskp20 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2412,plain,
% 1.66/1.83 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797))))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[2411])).
% 1.66/1.83 tff(2413,plain,
% 1.66/1.83 (((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2412, 2410])).
% 1.66/1.83 tff(2414,plain,
% 1.66/1.83 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2415,plain,
% 1.66/1.83 ((~![U: $i] : (hskp30 | hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp30 | hskp20 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 1.66/1.83 tff(2416,plain,
% 1.66/1.83 (hskp30 | hskp20 | (~c0_1(a797))),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2415, 130, 2409, 2401, 320])).
% 1.66/1.83 tff(2417,plain,
% 1.66/1.83 (~c0_1(a797)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2416, 310, 309])).
% 1.66/1.83 tff(2418,plain,
% 1.66/1.83 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.66/1.83 inference(bind,[status(th)],[])).
% 1.66/1.83 tff(2419,plain,
% 1.66/1.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.66/1.83 inference(quant_intro,[status(thm)],[2418])).
% 1.66/1.83 tff(2420,plain,
% 1.66/1.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2421,plain,
% 1.66/1.83 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.66/1.83 inference(bind,[status(th)],[])).
% 1.66/1.83 tff(2422,plain,
% 1.66/1.83 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.66/1.83 inference(quant_intro,[status(thm)],[2421])).
% 1.66/1.83 tff(2423,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.66/1.83 tff(2424,plain,
% 1.66/1.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2423, 2422])).
% 1.66/1.83 tff(2425,plain,
% 1.66/1.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2424, 2420])).
% 1.66/1.83 tff(2426,plain,(
% 1.66/1.83 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.66/1.83 inference(skolemize,[status(sab)],[2425])).
% 1.66/1.83 tff(2427,plain,
% 1.66/1.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2426, 2419])).
% 1.66/1.83 tff(2428,plain,
% 1.66/1.83 (((~hskp28) | c1_1(a797)) <=> ((~hskp28) | c1_1(a797))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2429,axiom,((~hskp28) | c1_1(a797)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.66/1.83 tff(2430,plain,
% 1.66/1.83 ((~hskp28) | c1_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2429, 2428])).
% 1.66/1.83 tff(2431,plain,
% 1.66/1.83 ((~hskp28) | c1_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2430, 2428])).
% 1.66/1.83 tff(2432,plain,
% 1.66/1.83 ((~hskp28) | c1_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2431, 2428])).
% 1.66/1.83 tff(2433,plain,
% 1.66/1.83 ((~hskp28) | c1_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2432, 2428])).
% 1.66/1.83 tff(2434,plain,
% 1.66/1.83 ((~hskp28) | c1_1(a797)),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2433, 2428])).
% 1.66/1.83 tff(2435,plain,
% 1.66/1.83 (c1_1(a797)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2434, 2393])).
% 1.66/1.83 tff(2436,plain,
% 1.66/1.83 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2437,plain,
% 1.66/1.83 ((hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797))) <=> (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2438,plain,
% 1.66/1.83 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797))))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[2437])).
% 1.66/1.83 tff(2439,plain,
% 1.66/1.83 (((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2438, 2436])).
% 1.66/1.83 tff(2440,plain,
% 1.66/1.83 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2441,plain,
% 1.66/1.83 ((~![U: $i] : (hskp21 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp21 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2440, 2439])).
% 1.66/1.83 tff(2442,plain,
% 1.66/1.83 (hskp21 | hskp11),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2441, 130, 2435, 2409, 2401, 628])).
% 1.66/1.83 tff(2443,plain,
% 1.66/1.83 (hskp11),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2442, 629])).
% 1.66/1.83 tff(2444,plain,
% 1.66/1.83 (~c2_1(a808)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[776, 2443])).
% 1.66/1.83 tff(2445,plain,
% 1.66/1.83 (~c1_1(a808)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[770, 2443])).
% 1.66/1.83 tff(2446,plain,
% 1.66/1.83 (c3_1(a808)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[812, 2443])).
% 1.66/1.83 tff(2447,plain,
% 1.66/1.83 (hskp18),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1095, 130, 629, 2446, 2445, 2444, 1088])).
% 1.66/1.83 tff(2448,plain,
% 1.66/1.83 (~c3_1(a828)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1107, 2447])).
% 1.66/1.83 tff(2449,plain,
% 1.66/1.83 (~c2_1(a828)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1101, 2447])).
% 1.66/1.83 tff(2450,plain,
% 1.66/1.83 (~c1_1(a828)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1113, 2447])).
% 1.66/1.83 tff(2451,assumption,(hskp27), introduced(assumption)).
% 1.66/1.83 tff(2452,plain,
% 1.66/1.83 (c3_1(a796)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[531, 2451])).
% 1.66/1.83 tff(2453,plain,
% 1.66/1.83 (c2_1(a796)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[539, 2451])).
% 1.66/1.83 tff(2454,plain,
% 1.66/1.83 (c0_1(a796)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[547, 2451])).
% 1.66/1.83 tff(2455,plain,
% 1.66/1.83 ($false),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[551, 309, 130, 310, 2454, 2453, 2452, 320])).
% 1.66/1.83 tff(2456,plain,((~hskp27) | hskp30 | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.66/1.83 tff(2457,plain,
% 1.66/1.83 (~hskp27),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2456, 310, 309])).
% 1.66/1.83 tff(2458,plain,
% 1.66/1.83 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2459,plain,
% 1.66/1.83 ((hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797))) <=> (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2460,plain,
% 1.66/1.83 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797))))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[2459])).
% 1.66/1.83 tff(2461,plain,
% 1.66/1.83 (((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2460, 2458])).
% 1.66/1.83 tff(2462,plain,
% 1.66/1.83 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2463,plain,
% 1.66/1.83 ((~![U: $i] : (hskp27 | hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)))) | hskp27 | hskp19 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 1.66/1.83 tff(2464,plain,
% 1.66/1.83 (hskp27 | hskp19),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2463, 130, 2435, 2409, 2401, 2117])).
% 1.66/1.83 tff(2465,plain,
% 1.66/1.83 (hskp19),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2464, 2457])).
% 1.66/1.83 tff(2466,plain,
% 1.66/1.83 (~c1_1(a832)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[352, 2465])).
% 1.66/1.83 tff(2467,plain,
% 1.66/1.83 (hskp20 | hskp2),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1315, 130, 1125, 1116, 1115, 1308])).
% 1.66/1.83 tff(2468,plain,
% 1.66/1.83 (hskp2),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2467, 310])).
% 1.66/1.83 tff(2469,plain,
% 1.66/1.83 (~c3_1(a795)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1321, 2468])).
% 1.66/1.83 tff(2470,plain,
% 1.66/1.83 (~c1_1(a795)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1327, 2468])).
% 1.66/1.83 tff(2471,plain,
% 1.66/1.83 (~c0_1(a795)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1353, 2468])).
% 1.66/1.83 tff(2472,plain,
% 1.66/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a795)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a795)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2473,plain,
% 1.66/1.83 (((~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a795) | c0_1(a795) | c3_1(a795)) <=> (c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a795)))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2474,plain,
% 1.66/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a795))))),
% 1.66/1.83 inference(monotonicity,[status(thm)],[2473])).
% 1.66/1.83 tff(2475,plain,
% 1.66/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a795)))),
% 1.66/1.83 inference(transitivity,[status(thm)],[2474, 2472])).
% 1.66/1.83 tff(2476,plain,
% 1.66/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a795) | c3_1(a795) | (~c2_1(a795)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a795) | c0_1(a795) | c3_1(a795))),
% 1.66/1.83 inference(quant_inst,[status(thm)],[])).
% 1.66/1.83 tff(2477,plain,
% 1.66/1.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a795) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a795))),
% 1.66/1.83 inference(modus_ponens,[status(thm)],[2476, 2475])).
% 1.66/1.83 tff(2478,plain,
% 1.66/1.83 (~c2_1(a795)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[2477, 130, 2435, 2409, 2471, 2470, 2469, 977, 2417])).
% 1.66/1.83 tff(2479,plain,
% 1.66/1.83 (~c3_1(a832)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[346, 2465])).
% 1.66/1.83 tff(2480,plain,
% 1.66/1.83 (~c0_1(a832)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[1461, 2479, 1414, 2471, 2469, 2478, 2466])).
% 1.66/1.83 tff(2481,plain,
% 1.66/1.83 (c2_1(a832)),
% 1.66/1.83 inference(unit_resolution,[status(thm)],[340, 2465])).
% 1.66/1.83 tff(2482,plain,
% 1.66/1.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | c0_1(a832))),
% 1.66/1.83 inference(rewrite,[status(thm)],[])).
% 1.66/1.83 tff(2483,plain,
% 1.66/1.83 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a832) | c0_1(a832) | c3_1(a832)) <=> (c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | c0_1(a832))),
% 1.66/1.84 inference(rewrite,[status(thm)],[])).
% 1.66/1.84 tff(2484,plain,
% 1.66/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | c0_1(a832)))),
% 1.66/1.84 inference(monotonicity,[status(thm)],[2483])).
% 1.66/1.84 tff(2485,plain,
% 1.66/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | c0_1(a832))),
% 1.66/1.84 inference(transitivity,[status(thm)],[2484, 2482])).
% 1.66/1.84 tff(2486,plain,
% 1.66/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a832) | c0_1(a832) | c3_1(a832))),
% 1.66/1.84 inference(quant_inst,[status(thm)],[])).
% 1.66/1.84 tff(2487,plain,
% 1.66/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | c0_1(a832)),
% 1.66/1.84 inference(modus_ponens,[status(thm)],[2486, 2485])).
% 1.66/1.84 tff(2488,plain,
% 1.66/1.84 ($false),
% 1.66/1.84 inference(unit_resolution,[status(thm)],[2487, 130, 2435, 2409, 2481, 2466, 2479, 977, 2480, 2417])).
% 1.66/1.84 tff(2489,plain,(hskp20 | (~hskp11) | hskp30 | c1_1(a828) | c2_1(a828) | c3_1(a828)), inference(lemma,lemma(discharge,[]))).
% 1.66/1.84 tff(2490,plain,
% 1.66/1.84 (hskp20),
% 1.66/1.84 inference(unit_resolution,[status(thm)],[2489, 2443, 309, 2450, 2449, 2448])).
% 1.66/1.84 tff(2491,plain,
% 1.66/1.84 (~c0_1(a833)),
% 1.66/1.84 inference(unit_resolution,[status(thm)],[563, 2490])).
% 1.66/1.84 tff(2492,plain,
% 1.66/1.84 (c1_1(a833)),
% 1.66/1.84 inference(unit_resolution,[status(thm)],[307, 2490])).
% 1.66/1.84 tff(2493,plain,
% 1.66/1.84 (~c2_1(a833)),
% 1.66/1.84 inference(unit_resolution,[status(thm)],[557, 2490])).
% 1.66/1.84 tff(2494,plain,
% 1.66/1.84 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.66/1.84 inference(bind,[status(th)],[])).
% 1.66/1.84 tff(2495,plain,
% 1.66/1.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.66/1.84 inference(quant_intro,[status(thm)],[2494])).
% 1.66/1.84 tff(2496,plain,
% 1.66/1.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.66/1.84 inference(rewrite,[status(thm)],[])).
% 1.66/1.84 tff(2497,plain,
% 1.66/1.84 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.66/1.84 inference(bind,[status(th)],[])).
% 1.66/1.84 tff(2498,plain,
% 1.66/1.84 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.66/1.84 inference(quant_intro,[status(thm)],[2497])).
% 1.66/1.84 tff(2499,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.66/1.84 tff(2500,plain,
% 1.66/1.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.66/1.84 inference(modus_ponens,[status(thm)],[2499, 2498])).
% 1.66/1.84 tff(2501,plain,
% 1.66/1.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.66/1.84 inference(modus_ponens,[status(thm)],[2500, 2496])).
% 1.66/1.84 tff(2502,plain,(
% 1.66/1.84 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.66/1.84 inference(skolemize,[status(sab)],[2501])).
% 1.66/1.84 tff(2503,plain,
% 1.66/1.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.66/1.84 inference(modus_ponens,[status(thm)],[2502, 2495])).
% 1.66/1.84 tff(2504,plain,
% 1.66/1.84 (~c3_1(a833)),
% 1.66/1.84 inference(unit_resolution,[status(thm)],[2085, 1501])).
% 1.66/1.84 tff(2505,plain,
% 1.66/1.84 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.66/1.84 inference(bind,[status(th)],[])).
% 1.66/1.84 tff(2506,plain,
% 1.66/1.84 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.66/1.84 inference(quant_intro,[status(thm)],[2505])).
% 1.66/1.84 tff(2507,plain,
% 1.66/1.84 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.66/1.84 inference(rewrite,[status(thm)],[])).
% 1.66/1.84 tff(2508,plain,
% 1.66/1.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.68/1.84 inference(bind,[status(th)],[])).
% 1.68/1.84 tff(2509,plain,
% 1.68/1.84 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.68/1.84 inference(quant_intro,[status(thm)],[2508])).
% 1.68/1.84 tff(2510,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.68/1.84 tff(2511,plain,
% 1.68/1.84 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 1.68/1.84 tff(2512,plain,
% 1.68/1.84 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2511, 2507])).
% 1.68/1.84 tff(2513,plain,(
% 1.68/1.84 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.68/1.84 inference(skolemize,[status(sab)],[2512])).
% 1.68/1.84 tff(2514,plain,
% 1.68/1.84 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2513, 2506])).
% 1.68/1.84 tff(2515,assumption,(~hskp3), introduced(assumption)).
% 1.68/1.84 tff(2516,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2517,plain,
% 1.68/1.84 ((hskp3 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)) | c3_1(a833) | c0_1(a833) | (~c1_1(a833))) <=> (hskp3 | c0_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2518,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)) | c3_1(a833) | c0_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2517])).
% 1.68/1.84 tff(2519,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)) | c3_1(a833) | c0_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[2518, 2516])).
% 1.68/1.84 tff(2520,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)) | c3_1(a833) | c0_1(a833) | (~c1_1(a833)))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(2521,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2520, 2519])).
% 1.68/1.84 tff(2522,plain,
% 1.68/1.84 ($false),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2521, 130, 2515, 570, 288, 276, 2514, 277])).
% 1.68/1.84 tff(2523,plain,(c3_1(a833) | hskp3 | (~c1_1(a833)) | c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.84 tff(2524,plain,
% 1.68/1.84 (hskp3),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2523, 2504, 276, 288, 570])).
% 1.68/1.84 tff(2525,plain,
% 1.68/1.84 (~c3_1(a798)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[492, 2524])).
% 1.68/1.84 tff(2526,plain,
% 1.68/1.84 (hskp27),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2464, 1501])).
% 1.68/1.84 tff(2527,plain,
% 1.68/1.84 (c0_1(a796)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[547, 2526])).
% 1.68/1.84 tff(2528,plain,
% 1.68/1.84 (c2_1(a796)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[539, 2526])).
% 1.68/1.84 tff(2529,plain,
% 1.68/1.84 (c3_1(a796)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[531, 2526])).
% 1.68/1.84 tff(2530,plain,
% 1.68/1.84 (hskp12),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[745, 2529, 276, 570, 2528, 288, 2504, 2527])).
% 1.68/1.84 tff(2531,plain,
% 1.68/1.84 (~c0_1(a809)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[143, 2530])).
% 1.68/1.84 tff(2532,plain,
% 1.68/1.84 (c2_1(a798)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[506, 2524])).
% 1.68/1.84 tff(2533,plain,
% 1.68/1.84 (c0_1(a798)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[514, 2524])).
% 1.68/1.84 tff(2534,plain,
% 1.68/1.84 (c2_1(a809)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[152, 2530])).
% 1.68/1.84 tff(2535,plain,
% 1.68/1.84 (c1_1(a809)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[160, 2530])).
% 1.68/1.84 tff(2536,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a809) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a809) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2537,plain,
% 1.68/1.84 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (c0_1(a809) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2538,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a809) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a809)) | (~c1_1(a809))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2537])).
% 1.68/1.84 tff(2539,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a809) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[2538, 2536])).
% 1.68/1.84 tff(2540,plain,
% 1.68/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(2541,plain,
% 1.68/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a809) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a809)) | (~c1_1(a809))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2540, 2539])).
% 1.68/1.84 tff(2542,plain,
% 1.68/1.84 (c0_1(a808)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2541, 130, 2535, 2534, 941, 2533, 2532, 2531, 796, 2525, 2503])).
% 1.68/1.84 tff(2543,plain,
% 1.68/1.84 (hskp8),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[873, 2527, 276, 2504, 2528, 2529, 288, 570])).
% 1.68/1.84 tff(2544,plain,
% 1.68/1.84 (~c3_1(a805)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[414, 2543])).
% 1.68/1.84 tff(2545,plain,
% 1.68/1.84 (~c2_1(a805)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[420, 2543])).
% 1.68/1.84 tff(2546,plain,
% 1.68/1.84 (c1_1(a805)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[429, 2543])).
% 1.68/1.84 tff(2547,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a808) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a808) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2548,plain,
% 1.68/1.84 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c2_1(a808) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2549,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a808) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808))))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2548])).
% 1.68/1.84 tff(2550,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a808) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808)))),
% 1.68/1.84 inference(transitivity,[status(thm)],[2549, 2547])).
% 1.68/1.84 tff(2551,plain,
% 1.68/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(2552,plain,
% 1.68/1.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a808) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a808)) | (~c0_1(a808))),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2551, 2550])).
% 1.68/1.84 tff(2553,plain,
% 1.68/1.84 ($false),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2552, 130, 941, 2546, 2533, 2532, 796, 2545, 2544, 2525, 299, 2542])).
% 1.68/1.84 tff(2554,plain,(hskp19 | (~c3_1(a808)) | c2_1(a808) | c2_1(a833) | (~c1_1(a833)) | c0_1(a833) | c1_1(a828) | c2_1(a828) | c3_1(a828)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.84 tff(2555,plain,
% 1.68/1.84 (hskp19),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2554, 2446, 2444, 2493, 2492, 2491, 2450, 2449, 2448])).
% 1.68/1.84 tff(2556,plain,
% 1.68/1.84 (~c3_1(a832)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[346, 2555])).
% 1.68/1.84 tff(2557,plain,
% 1.68/1.84 (~c1_1(a832)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[352, 2555])).
% 1.68/1.84 tff(2558,plain,
% 1.68/1.84 (c2_1(a832)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[340, 2555])).
% 1.68/1.84 tff(2559,plain,
% 1.68/1.84 (hskp0),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[588, 130, 629, 2558, 2557, 2556, 582])).
% 1.68/1.84 tff(2560,plain,
% 1.68/1.84 (~c1_1(a793)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[603, 2559])).
% 1.68/1.84 tff(2561,plain,
% 1.68/1.84 (c2_1(a793)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[597, 2559])).
% 1.68/1.84 tff(2562,plain,
% 1.68/1.84 (c0_1(a793)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[611, 2559])).
% 1.68/1.84 tff(2563,plain,
% 1.68/1.84 (hskp19),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2554, 941, 796, 276, 570, 288, 1125, 1116, 1115])).
% 1.68/1.84 tff(2564,plain,
% 1.68/1.84 (~c3_1(a832)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[346, 2563])).
% 1.68/1.84 tff(2565,plain,
% 1.68/1.84 (c2_1(a832)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[340, 2563])).
% 1.68/1.84 tff(2566,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a832)) | c0_1(a832))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2567,plain,
% 1.68/1.84 ((hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832))) <=> (hskp15 | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a832)) | c0_1(a832))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2568,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a832)) | c0_1(a832)))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2567])).
% 1.68/1.84 tff(2569,plain,
% 1.68/1.84 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a832)) | c0_1(a832))),
% 1.68/1.84 inference(transitivity,[status(thm)],[2568, 2566])).
% 1.68/1.84 tff(2570,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))),
% 1.68/1.84 inference(quant_inst,[status(thm)],[])).
% 1.68/1.84 tff(2571,plain,
% 1.68/1.84 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a832)) | c0_1(a832)),
% 1.68/1.84 inference(modus_ponens,[status(thm)],[2570, 2569])).
% 1.68/1.84 tff(2572,plain,
% 1.68/1.84 (hskp15 | c0_1(a832)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2571, 130, 2435, 2409, 2401, 2565, 2564, 1210])).
% 1.68/1.84 tff(2573,plain,
% 1.68/1.84 (c0_1(a832)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[2572, 1289])).
% 1.68/1.84 tff(2574,plain,
% 1.68/1.84 (~c1_1(a832)),
% 1.68/1.84 inference(unit_resolution,[status(thm)],[352, 2563])).
% 1.68/1.84 tff(2575,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a832)) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a832)) | c3_1(a833))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2576,plain,
% 1.68/1.84 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833)) <=> (c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a832)) | c3_1(a833))),
% 1.68/1.84 inference(rewrite,[status(thm)],[])).
% 1.68/1.84 tff(2577,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a832)) | c3_1(a833)))),
% 1.68/1.84 inference(monotonicity,[status(thm)],[2576])).
% 1.68/1.84 tff(2578,plain,
% 1.68/1.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a832)) | c3_1(a833))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2577, 2575])).
% 1.68/1.85 tff(2579,plain,
% 1.68/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a833) | c0_1(a833) | c3_1(a833))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2580,plain,
% 1.68/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c1_1(a832) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | (~c0_1(a832)) | c3_1(a833)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2579, 2578])).
% 1.68/1.85 tff(2581,plain,
% 1.68/1.85 ((~c0_1(a832)) | c3_1(a833)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2580, 130, 941, 288, 276, 2574, 2564, 797, 796, 795])).
% 1.68/1.85 tff(2582,plain,
% 1.68/1.85 (c3_1(a833)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2581, 2573])).
% 1.68/1.85 tff(2583,plain,
% 1.68/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a832)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2584,plain,
% 1.68/1.85 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828)) <=> (c1_1(a832) | c3_1(a832) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a832)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2585,plain,
% 1.68/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a832))))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2584])).
% 1.68/1.85 tff(2586,plain,
% 1.68/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a832)))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2585, 2583])).
% 1.68/1.85 tff(2587,plain,
% 1.68/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a828) | c0_1(a828) | c3_1(a828))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2588,plain,
% 1.68/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c2_1(a828) | c3_1(a828) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a828) | (~c0_1(a832))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2587, 2586])).
% 1.68/1.85 tff(2589,plain,
% 1.68/1.85 (c0_1(a828) | (~c0_1(a832))),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2588, 130, 941, 2574, 2564, 1116, 1115, 797, 796, 795])).
% 1.68/1.85 tff(2590,plain,
% 1.68/1.85 (c0_1(a828)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2589, 2573])).
% 1.68/1.85 tff(2591,plain,
% 1.68/1.85 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 1.68/1.85 inference(bind,[status(th)],[])).
% 1.68/1.85 tff(2592,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(quant_intro,[status(thm)],[2591])).
% 1.68/1.85 tff(2593,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2594,plain,
% 1.68/1.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 1.68/1.85 inference(bind,[status(th)],[])).
% 1.68/1.85 tff(2595,plain,
% 1.68/1.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(quant_intro,[status(thm)],[2594])).
% 1.68/1.85 tff(2596,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.68/1.85 tff(2597,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2596, 2595])).
% 1.68/1.85 tff(2598,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2597, 2593])).
% 1.68/1.85 tff(2599,plain,(
% 1.68/1.85 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(skolemize,[status(sab)],[2598])).
% 1.68/1.85 tff(2600,plain,
% 1.68/1.85 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2599, 2592])).
% 1.68/1.85 tff(2601,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp29 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2602,plain,
% 1.68/1.85 ((hskp29 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (hskp29 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2603,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c0_1(a828))))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2602])).
% 1.68/1.85 tff(2604,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp29 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2603, 2601])).
% 1.68/1.85 tff(2605,plain,
% 1.68/1.85 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2606,plain,
% 1.68/1.85 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp29 | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | (~c0_1(a828))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2605, 2604])).
% 1.68/1.85 tff(2607,plain,
% 1.68/1.85 (hskp29 | (~c0_1(a828))),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2606, 130, 1125, 1116, 1115, 2600])).
% 1.68/1.85 tff(2608,plain,
% 1.68/1.85 (hskp29),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2607, 2590])).
% 1.68/1.85 tff(2609,plain,
% 1.68/1.85 (((~hskp29) | c0_1(a829)) <=> ((~hskp29) | c0_1(a829))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2610,axiom,((~hskp29) | c0_1(a829)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.68/1.85 tff(2611,plain,
% 1.68/1.85 ((~hskp29) | c0_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2610, 2609])).
% 1.68/1.85 tff(2612,plain,
% 1.68/1.85 ((~hskp29) | c0_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2611, 2609])).
% 1.68/1.85 tff(2613,plain,
% 1.68/1.85 ((~hskp29) | c0_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2612, 2609])).
% 1.68/1.85 tff(2614,plain,
% 1.68/1.85 ((~hskp29) | c0_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2613, 2609])).
% 1.68/1.85 tff(2615,plain,
% 1.68/1.85 ((~hskp29) | c0_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2614, 2609])).
% 1.68/1.85 tff(2616,plain,
% 1.68/1.85 (c0_1(a829)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2615, 2608])).
% 1.68/1.85 tff(2617,plain,
% 1.68/1.85 (((~hskp29) | c2_1(a829)) <=> ((~hskp29) | c2_1(a829))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2618,axiom,((~hskp29) | c2_1(a829)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 1.68/1.85 tff(2619,plain,
% 1.68/1.85 ((~hskp29) | c2_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2618, 2617])).
% 1.68/1.85 tff(2620,plain,
% 1.68/1.85 ((~hskp29) | c2_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2619, 2617])).
% 1.68/1.85 tff(2621,plain,
% 1.68/1.85 ((~hskp29) | c2_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2620, 2617])).
% 1.68/1.85 tff(2622,plain,
% 1.68/1.85 ((~hskp29) | c2_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2621, 2617])).
% 1.68/1.85 tff(2623,plain,
% 1.68/1.85 ((~hskp29) | c2_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2622, 2617])).
% 1.68/1.85 tff(2624,plain,
% 1.68/1.85 (c2_1(a829)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2623, 2608])).
% 1.68/1.85 tff(2625,plain,
% 1.68/1.85 (((~hskp29) | c1_1(a829)) <=> ((~hskp29) | c1_1(a829))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2626,axiom,((~hskp29) | c1_1(a829)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 1.68/1.85 tff(2627,plain,
% 1.68/1.85 ((~hskp29) | c1_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2626, 2625])).
% 1.68/1.85 tff(2628,plain,
% 1.68/1.85 ((~hskp29) | c1_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2627, 2625])).
% 1.68/1.85 tff(2629,plain,
% 1.68/1.85 ((~hskp29) | c1_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2628, 2625])).
% 1.68/1.85 tff(2630,plain,
% 1.68/1.85 ((~hskp29) | c1_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2629, 2625])).
% 1.68/1.85 tff(2631,plain,
% 1.68/1.85 ((~hskp29) | c1_1(a829)),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2630, 2625])).
% 1.68/1.85 tff(2632,plain,
% 1.68/1.85 (c1_1(a829)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2631, 2608])).
% 1.68/1.85 tff(2633,assumption,(~hskp16), introduced(assumption)).
% 1.68/1.85 tff(2634,assumption,(c2_1(a829)), introduced(assumption)).
% 1.68/1.85 tff(2635,assumption,(c0_1(a829)), introduced(assumption)).
% 1.68/1.85 tff(2636,plain,
% 1.68/1.85 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a829)) | (~c3_1(a829)) | (~c2_1(a829)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a829)) | (~c3_1(a829)) | (~c2_1(a829)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2637,plain,
% 1.68/1.85 ((hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a829)) | (~c2_1(a829)) | (~c0_1(a829))) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a829)) | (~c3_1(a829)) | (~c2_1(a829)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2638,plain,
% 1.68/1.85 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a829)) | (~c2_1(a829)) | (~c0_1(a829)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a829)) | (~c3_1(a829)) | (~c2_1(a829))))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2637])).
% 1.68/1.85 tff(2639,plain,
% 1.68/1.85 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a829)) | (~c2_1(a829)) | (~c0_1(a829)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a829)) | (~c3_1(a829)) | (~c2_1(a829)))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2638, 2636])).
% 1.68/1.85 tff(2640,plain,
% 1.68/1.85 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a829)) | (~c2_1(a829)) | (~c0_1(a829)))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2641,plain,
% 1.68/1.85 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c0_1(a829)) | (~c3_1(a829)) | (~c2_1(a829))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2640, 2639])).
% 1.68/1.85 tff(2642,plain,
% 1.68/1.85 (hskp16 | (~c3_1(a829))),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2641, 130, 1289, 2635, 2634, 2167])).
% 1.68/1.85 tff(2643,plain,
% 1.68/1.85 (~c3_1(a829)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2642, 2633])).
% 1.68/1.85 tff(2644,plain,
% 1.68/1.85 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2645,plain,
% 1.68/1.85 ((hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797))) <=> (hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2646,plain,
% 1.68/1.85 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797))))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2645])).
% 1.68/1.85 tff(2647,plain,
% 1.68/1.85 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2646, 2644])).
% 1.68/1.85 tff(2648,plain,
% 1.68/1.85 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2649,plain,
% 1.68/1.85 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2648, 2647])).
% 1.68/1.85 tff(2650,plain,
% 1.68/1.85 (hskp16 | hskp15 | (~c0_1(a797))),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2649, 130, 2409, 2401, 2167])).
% 1.68/1.85 tff(2651,plain,
% 1.68/1.85 (~c0_1(a797)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2650, 2633, 1289])).
% 1.68/1.85 tff(2652,assumption,(c1_1(a829)), introduced(assumption)).
% 1.68/1.85 tff(2653,plain,
% 1.68/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a833)) | c3_1(a829) | (~c2_1(a829)) | (~c1_1(a829)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a833)) | c3_1(a829) | (~c2_1(a829)) | (~c1_1(a829)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2654,plain,
% 1.68/1.85 (((~ndr1_0) | c3_1(a829) | (~c1_1(a829)) | (~c2_1(a829)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a833)) | c3_1(a829) | (~c2_1(a829)) | (~c1_1(a829)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2655,plain,
% 1.68/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a829) | (~c1_1(a829)) | (~c2_1(a829)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a833)) | c3_1(a829) | (~c2_1(a829)) | (~c1_1(a829))))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2654])).
% 1.68/1.85 tff(2656,plain,
% 1.68/1.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a829) | (~c1_1(a829)) | (~c2_1(a829)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a833)) | c3_1(a829) | (~c2_1(a829)) | (~c1_1(a829)))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2655, 2653])).
% 1.68/1.85 tff(2657,plain,
% 1.68/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a829) | (~c1_1(a829)) | (~c2_1(a829)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2658,plain,
% 1.68/1.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a833)) | c3_1(a829) | (~c2_1(a829)) | (~c1_1(a829))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2657, 2656])).
% 1.68/1.85 tff(2659,plain,
% 1.68/1.85 ($false),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2658, 130, 2652, 2634, 2435, 2401, 288, 276, 1961, 669, 2651, 2643])).
% 1.68/1.85 tff(2660,plain,(hskp16 | (~c1_1(a829)) | (~c2_1(a829)) | c0_1(a833) | c2_1(a833) | (~c3_1(a833)) | hskp15 | (~c0_1(a829))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.85 tff(2661,plain,
% 1.68/1.85 (hskp16),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2660, 2632, 2624, 288, 276, 2582, 1289, 2616])).
% 1.68/1.85 tff(2662,plain,
% 1.68/1.85 (~c2_1(a821)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2180, 2661])).
% 1.68/1.85 tff(2663,plain,
% 1.68/1.85 (~c0_1(a821)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2192, 2661])).
% 1.68/1.85 tff(2664,plain,
% 1.68/1.85 (c3_1(a821)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2281, 130, 941, 2574, 2564, 2663, 2662, 797, 796, 795, 2573])).
% 1.68/1.85 tff(2665,plain,
% 1.68/1.85 (~c1_1(a821)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2186, 2661])).
% 1.68/1.85 tff(2666,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a833) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2667,plain,
% 1.68/1.85 ((hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821))) <=> (hskp6 | c2_1(a833) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2668,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a833) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2667])).
% 1.68/1.85 tff(2669,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2668, 2666])).
% 1.68/1.85 tff(2670,plain,
% 1.68/1.85 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2671,plain,
% 1.68/1.85 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2670, 2669])).
% 1.68/1.85 tff(2672,plain,
% 1.68/1.85 (hskp6 | (~c3_1(a821))),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2671, 130, 570, 276, 2663, 2665, 1853, 2582])).
% 1.68/1.85 tff(2673,plain,
% 1.68/1.85 (hskp6),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2672, 2664])).
% 1.68/1.85 tff(2674,plain,
% 1.68/1.85 (~c0_1(a802)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[1873, 2673])).
% 1.68/1.85 tff(2675,plain,
% 1.68/1.85 (c2_1(a802)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[1881, 2673])).
% 1.68/1.85 tff(2676,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a833) | c2_1(a833) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a833) | c2_1(a833) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a833)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2677,plain,
% 1.68/1.85 ((hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (hskp12 | c0_1(a833) | c2_1(a833) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a833)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2678,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a833) | c2_1(a833) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a833))))),
% 1.68/1.85 inference(monotonicity,[status(thm)],[2677])).
% 1.68/1.85 tff(2679,plain,
% 1.68/1.85 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a833) | c2_1(a833) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a833)))),
% 1.68/1.85 inference(transitivity,[status(thm)],[2678, 2676])).
% 1.68/1.85 tff(2680,plain,
% 1.68/1.85 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.68/1.85 inference(quant_inst,[status(thm)],[])).
% 1.68/1.85 tff(2681,plain,
% 1.68/1.85 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a833) | c2_1(a833) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a833))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2680, 2679])).
% 1.68/1.85 tff(2682,plain,
% 1.68/1.85 (c3_1(a802)),
% 1.68/1.85 inference(unit_resolution,[status(thm)],[2681, 130, 730, 2675, 288, 276, 2674, 989, 2582])).
% 1.68/1.85 tff(2683,plain,
% 1.68/1.85 (((~hskp6) | (~c1_1(a802))) <=> ((~hskp6) | (~c1_1(a802)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2684,plain,
% 1.68/1.85 (((~c1_1(a802)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a802)))),
% 1.68/1.85 inference(rewrite,[status(thm)],[])).
% 1.68/1.85 tff(2685,axiom,((~c1_1(a802)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.68/1.85 tff(2686,plain,
% 1.68/1.85 ((~hskp6) | (~c1_1(a802))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2685, 2684])).
% 1.68/1.85 tff(2687,plain,
% 1.68/1.85 ((~hskp6) | (~c1_1(a802))),
% 1.68/1.85 inference(modus_ponens,[status(thm)],[2686, 2683])).
% 1.68/1.85 tff(2688,plain,
% 1.68/1.85 (~c1_1(a802)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2687, 2673])).
% 1.68/1.86 tff(2689,plain,
% 1.68/1.86 ($false),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[966, 415, 430, 941, 289, 408, 797, 421, 22, 796, 391])).
% 1.68/1.86 tff(2690,plain,((~hskp8) | (~c3_1(a808)) | c1_1(a832) | (~c0_1(a832)) | c1_1(a808) | c3_1(a832) | c2_1(a808) | (~c2_1(a832))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.86 tff(2691,plain,
% 1.68/1.86 (~hskp8),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2690, 2573, 2574, 941, 797, 2564, 796, 2565])).
% 1.68/1.86 tff(2692,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | c1_1(a802) | (~ndr1_0) | (~c3_1(a802)) | (~c2_1(a802)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a802) | (~ndr1_0) | (~c3_1(a802)) | (~c2_1(a802)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2693,plain,
% 1.68/1.86 ((hskp8 | (~ndr1_0) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833))) <=> (hskp8 | c0_1(a833) | c1_1(a802) | (~ndr1_0) | (~c3_1(a802)) | (~c2_1(a802)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2694,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | c1_1(a802) | (~ndr1_0) | (~c3_1(a802)) | (~c2_1(a802)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2693])).
% 1.68/1.86 tff(2695,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a802) | (~ndr1_0) | (~c3_1(a802)) | (~c2_1(a802)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2694, 2692])).
% 1.68/1.86 tff(2696,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2697,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a802) | (~ndr1_0) | (~c3_1(a802)) | (~c2_1(a802)) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2696, 2695])).
% 1.68/1.86 tff(2698,plain,
% 1.68/1.86 ($false),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2697, 130, 2691, 570, 2675, 288, 2688, 687, 2582, 2682])).
% 1.68/1.86 tff(2699,plain,(hskp15 | (~c1_1(a833)) | c0_1(a833) | hskp12 | c2_1(a833) | (~c3_1(a808)) | c1_1(a808) | c2_1(a808) | c1_1(a828) | c2_1(a828) | c3_1(a828)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.86 tff(2700,plain,
% 1.68/1.86 (hskp15),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2699, 730, 288, 570, 276, 941, 797, 796, 1125, 1116, 1115])).
% 1.68/1.86 tff(2701,plain,
% 1.68/1.86 (~c1_1(a817)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[1252, 2700])).
% 1.68/1.86 tff(2702,plain,
% 1.68/1.86 (c3_1(a817)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[1260, 2700])).
% 1.68/1.86 tff(2703,plain,
% 1.68/1.86 (c2_1(a817)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[1268, 2700])).
% 1.68/1.86 tff(2704,plain,
% 1.68/1.86 (c3_1(a833) | c3_1(a793)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[803, 130, 941, 617, 288, 276, 797, 796, 616, 795])).
% 1.68/1.86 tff(2705,plain,
% 1.68/1.86 (c3_1(a793)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2704, 277])).
% 1.68/1.86 tff(2706,assumption,(~c1_1(a817)), introduced(assumption)).
% 1.68/1.86 tff(2707,assumption,(c3_1(a817)), introduced(assumption)).
% 1.68/1.86 tff(2708,assumption,(c2_1(a817)), introduced(assumption)).
% 1.68/1.86 tff(2709,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)) | (~c3_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)) | (~c3_1(a793)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2710,plain,
% 1.68/1.86 (((~ndr1_0) | (~c3_1(a793)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)) | (~c3_1(a793)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2711,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a793)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)) | (~c3_1(a793))))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2710])).
% 1.68/1.86 tff(2712,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a793)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)) | (~c3_1(a793)))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2711, 2709])).
% 1.68/1.86 tff(2713,plain,
% 1.68/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a793)) | (~c2_1(a793)) | (~c0_1(a793)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2714,plain,
% 1.68/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | c3_1(a833) | (~c1_1(a833)) | (~c2_1(a793)) | (~c0_1(a793)) | (~c3_1(a793))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2713, 2712])).
% 1.68/1.86 tff(2715,plain,
% 1.68/1.86 ($false),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2714, 130, 570, 2708, 2707, 617, 614, 288, 2706, 719, 277, 2705])).
% 1.68/1.86 tff(2716,plain,(c3_1(a833) | (~c1_1(a833)) | (~c2_1(a817)) | (~c3_1(a817)) | (~c0_1(a793)) | (~c2_1(a793)) | c0_1(a833) | c1_1(a817) | (~c3_1(a808)) | c2_1(a833) | c1_1(a808) | c2_1(a808) | c1_1(a793)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.86 tff(2717,plain,
% 1.68/1.86 (c3_1(a833)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2716, 2703, 570, 2702, 617, 614, 288, 2701, 941, 276, 797, 796, 616])).
% 1.68/1.86 tff(2718,plain,
% 1.68/1.86 (c0_1(a832)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[997, 2717, 2565, 288, 276, 2564, 730])).
% 1.68/1.86 tff(2719,plain,
% 1.68/1.86 (~hskp8),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2690, 2718, 2574, 941, 797, 2564, 796, 2565])).
% 1.68/1.86 tff(2720,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2721,plain,
% 1.68/1.86 ((hskp8 | (~ndr1_0) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833))) <=> (hskp8 | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2722,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2721])).
% 1.68/1.86 tff(2723,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2722, 2720])).
% 1.68/1.86 tff(2724,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2725,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a833) | c1_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c3_1(a817)) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2724, 2723])).
% 1.68/1.86 tff(2726,plain,
% 1.68/1.86 ($false),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2725, 130, 2719, 570, 2703, 2702, 288, 2701, 687, 2717])).
% 1.68/1.86 tff(2727,plain,(hskp12 | (~c1_1(a833)) | c0_1(a833) | (~c3_1(a808)) | c1_1(a808) | c2_1(a808) | c2_1(a833) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a793) | c1_1(a828) | c2_1(a828) | c3_1(a828)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.86 tff(2728,plain,
% 1.68/1.86 (hskp12),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2727, 2492, 2491, 2446, 2445, 2444, 2493, 2562, 2561, 2560, 2450, 2449, 2448])).
% 1.68/1.86 tff(2729,plain,
% 1.68/1.86 (~c0_1(a809)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[143, 2728])).
% 1.68/1.86 tff(2730,plain,
% 1.68/1.86 (c2_1(a809)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[152, 2728])).
% 1.68/1.86 tff(2731,plain,
% 1.68/1.86 (c1_1(a809)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[160, 2728])).
% 1.68/1.86 tff(2732,plain,
% 1.68/1.86 (c0_1(a832)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[1007, 130, 2558, 2731, 2730, 2557, 2556, 2729, 977])).
% 1.68/1.86 tff(2733,plain,
% 1.68/1.86 ((~c0_1(a832)) | c3_1(a833)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2580, 130, 2446, 2491, 2493, 2557, 2556, 2445, 2444, 795])).
% 1.68/1.86 tff(2734,plain,
% 1.68/1.86 (c3_1(a833)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2733, 2732])).
% 1.68/1.86 tff(2735,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2736,plain,
% 1.68/1.86 (((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2737,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833))))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2736])).
% 1.68/1.86 tff(2738,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2737, 2735])).
% 1.68/1.86 tff(2739,plain,
% 1.68/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2740,plain,
% 1.68/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2739, 2738])).
% 1.68/1.86 tff(2741,plain,
% 1.68/1.86 ((~c0_1(a832)) | (~c3_1(a833))),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2740, 130, 2558, 2731, 2730, 2491, 2493, 2556, 2729, 2503])).
% 1.68/1.86 tff(2742,plain,
% 1.68/1.86 ($false),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2741, 2734, 2732])).
% 1.68/1.86 tff(2743,plain,(hskp21 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.68/1.86 tff(2744,plain,
% 1.68/1.86 (hskp21),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2743, 309])).
% 1.68/1.86 tff(2745,plain,
% 1.68/1.86 (~c2_1(a838)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[389, 2744])).
% 1.68/1.86 tff(2746,plain,
% 1.68/1.86 (hskp9),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[1687, 310, 2744, 2745])).
% 1.68/1.86 tff(2747,plain,
% 1.68/1.86 (~c3_1(a806)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[63, 2746])).
% 1.68/1.86 tff(2748,plain,
% 1.68/1.86 (c1_1(a806)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[72, 2746])).
% 1.68/1.86 tff(2749,plain,
% 1.68/1.86 (c0_1(a806)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[55, 2746])).
% 1.68/1.86 tff(2750,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a833))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2751,plain,
% 1.68/1.86 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | c3_1(a833)) <=> (c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a833))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2752,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a833)))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2751])).
% 1.68/1.86 tff(2753,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a833))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2752, 2750])).
% 1.68/1.86 tff(2754,plain,
% 1.68/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c1_1(a797)) | c2_1(a833) | c0_1(a833) | c3_1(a833))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2755,plain,
% 1.68/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a806)) | (~c1_1(a806)) | c3_1(a833)),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2754, 2753])).
% 1.68/1.86 tff(2756,plain,
% 1.68/1.86 (c3_1(a833)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2755, 130, 2435, 2401, 2749, 2748, 288, 276, 2747, 2427, 2417])).
% 1.68/1.86 tff(2757,plain,
% 1.68/1.86 (c0_1(a832)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2487, 130, 2435, 2409, 2481, 2466, 2479, 977, 2417])).
% 1.68/1.86 tff(2758,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2759,plain,
% 1.68/1.86 (((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2760,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833))))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2759])).
% 1.68/1.86 tff(2761,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2760, 2758])).
% 1.68/1.86 tff(2762,plain,
% 1.68/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2763,plain,
% 1.68/1.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2762, 2761])).
% 1.68/1.86 tff(2764,plain,
% 1.68/1.86 ((~c0_1(a832)) | (~c3_1(a833))),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2763, 130, 2435, 2409, 2481, 288, 276, 2479, 2503, 2417])).
% 1.68/1.86 tff(2765,plain,
% 1.68/1.86 ($false),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2764, 2757, 2756])).
% 1.68/1.86 tff(2766,plain,(hskp20 | c0_1(a833) | c2_1(a833) | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.68/1.86 tff(2767,plain,
% 1.68/1.86 (hskp30),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2766, 308, 276, 288])).
% 1.68/1.86 tff(2768,plain,
% 1.68/1.86 (c3_1(a867)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[30, 2767])).
% 1.68/1.86 tff(2769,plain,
% 1.68/1.86 (c1_1(a867)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[38, 2767])).
% 1.68/1.86 tff(2770,plain,
% 1.68/1.86 (c0_1(a867)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[46, 2767])).
% 1.68/1.86 tff(2771,plain,
% 1.68/1.86 (c2_1(a806)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[169, 73, 2768, 64, 2770, 2769, 56])).
% 1.68/1.86 tff(2772,plain,
% 1.68/1.86 (hskp0),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[1776, 130, 300, 56, 288, 276, 64, 1338, 2771])).
% 1.68/1.86 tff(2773,plain,
% 1.68/1.86 (~c1_1(a793)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[603, 2772])).
% 1.68/1.86 tff(2774,plain,
% 1.68/1.86 (hskp5),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[196, 130, 2770, 2769, 2768, 56, 64, 190, 2771])).
% 1.68/1.86 tff(2775,plain,
% 1.68/1.86 (~c1_1(a800)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[233, 2774])).
% 1.68/1.86 tff(2776,plain,
% 1.68/1.86 (~c0_1(a800)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[202, 2774])).
% 1.68/1.86 tff(2777,plain,
% 1.68/1.86 (c3_1(a800)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[210, 2774])).
% 1.68/1.86 tff(2778,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a800)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2779,plain,
% 1.68/1.86 ((hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a800)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2780,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a800))))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2779])).
% 1.68/1.86 tff(2781,plain,
% 1.68/1.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a800)))),
% 1.68/1.86 inference(transitivity,[status(thm)],[2780, 2778])).
% 1.68/1.86 tff(2782,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 1.68/1.86 inference(quant_inst,[status(thm)],[])).
% 1.68/1.86 tff(2783,plain,
% 1.68/1.86 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a800))),
% 1.68/1.86 inference(modus_ponens,[status(thm)],[2782, 2781])).
% 1.68/1.86 tff(2784,plain,
% 1.68/1.86 (hskp7),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[2783, 130, 2435, 2409, 2401, 2777, 2776, 2775, 1413])).
% 1.68/1.86 tff(2785,plain,
% 1.68/1.86 (~c2_1(a803)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[1377, 2784])).
% 1.68/1.86 tff(2786,plain,
% 1.68/1.86 (c2_1(a793)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[597, 2772])).
% 1.68/1.86 tff(2787,plain,
% 1.68/1.86 (c0_1(a793)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[611, 2772])).
% 1.68/1.86 tff(2788,plain,
% 1.68/1.86 (c1_1(a803)),
% 1.68/1.86 inference(unit_resolution,[status(thm)],[1393, 2784])).
% 1.68/1.86 tff(2789,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a803) | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a793)) | (~c0_1(a793)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a803) | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2790,plain,
% 1.68/1.86 (((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (c2_1(a803) | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 1.68/1.86 inference(rewrite,[status(thm)],[])).
% 1.68/1.86 tff(2791,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a803) | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a793)) | (~c0_1(a793))))),
% 1.68/1.86 inference(monotonicity,[status(thm)],[2790])).
% 1.68/1.86 tff(2792,plain,
% 1.68/1.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a803) | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a793)) | (~c0_1(a793)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2791, 2789])).
% 1.68/1.87 tff(2793,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a793) | (~c0_1(a793)) | (~c2_1(a793)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2794,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a803) | c0_1(a800) | c1_1(a800) | c1_1(a793) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a793)) | (~c0_1(a793))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2793, 2792])).
% 1.68/1.87 tff(2795,plain,
% 1.68/1.87 (~c0_1(a803)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2794, 130, 2788, 2777, 2787, 2786, 2785, 2776, 2775, 2773, 287])).
% 1.68/1.87 tff(2796,plain,
% 1.68/1.87 (c3_1(a803)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1385, 2784])).
% 1.68/1.87 tff(2797,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2798,plain,
% 1.68/1.87 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803))) <=> (c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2799,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806))))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2798])).
% 1.68/1.87 tff(2800,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2799, 2797])).
% 1.68/1.87 tff(2801,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2802,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a806) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a806)) | (~c1_1(a806))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2801, 2800])).
% 1.68/1.87 tff(2803,plain,
% 1.68/1.87 ($false),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2802, 130, 73, 2788, 2796, 64, 2785, 1961, 2771, 2795])).
% 1.68/1.87 tff(2804,plain,((~hskp9) | c1_1(a833) | c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.87 tff(2805,plain,
% 1.68/1.87 (~hskp9),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2804, 300, 288, 276])).
% 1.68/1.87 tff(2806,plain,
% 1.68/1.87 ($false),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1687, 1222, 1221, 310, 11])).
% 1.68/1.87 tff(2807,plain,((~hskp21) | hskp20 | hskp9), inference(lemma,lemma(discharge,[]))).
% 1.68/1.87 tff(2808,plain,
% 1.68/1.87 (~hskp21),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2807, 308, 2805])).
% 1.68/1.87 tff(2809,plain,
% 1.68/1.87 (hskp11),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2442, 2808])).
% 1.68/1.87 tff(2810,plain,
% 1.68/1.87 (c3_1(a808)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[812, 2809])).
% 1.68/1.87 tff(2811,plain,
% 1.68/1.87 (~hskp7),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1402, 289, 22, 1362])).
% 1.68/1.87 tff(2812,plain,
% 1.68/1.87 (hskp27),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2464, 1363])).
% 1.68/1.87 tff(2813,plain,
% 1.68/1.87 (c3_1(a796)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[531, 2812])).
% 1.68/1.87 tff(2814,plain,
% 1.68/1.87 (c2_1(a796)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[539, 2812])).
% 1.68/1.87 tff(2815,plain,
% 1.68/1.87 (c0_1(a796)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[547, 2812])).
% 1.68/1.87 tff(2816,plain,
% 1.68/1.87 (hskp21),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2442, 630])).
% 1.68/1.87 tff(2817,plain,
% 1.68/1.87 (~c2_1(a838)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[389, 2816])).
% 1.68/1.87 tff(2818,plain,
% 1.68/1.87 (hskp9),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1687, 2816, 310, 2817])).
% 1.68/1.87 tff(2819,plain,
% 1.68/1.87 (c0_1(a806)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[55, 2818])).
% 1.68/1.87 tff(2820,plain,
% 1.68/1.87 (~c3_1(a806)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[63, 2818])).
% 1.68/1.87 tff(2821,plain,
% 1.68/1.87 (c1_1(a806)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[72, 2818])).
% 1.68/1.87 tff(2822,plain,
% 1.68/1.87 (c2_1(a806)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[169, 2821, 65, 2820, 58, 57, 2819])).
% 1.68/1.87 tff(2823,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a869) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a869)) | (~c3_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a869) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a869)) | (~c3_1(a869)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2824,plain,
% 1.68/1.87 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869))) <=> (c0_1(a869) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a869)) | (~c3_1(a869)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2825,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a869) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a869)) | (~c3_1(a869))))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2824])).
% 1.68/1.87 tff(2826,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a869) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a869)) | (~c3_1(a869)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2825, 2823])).
% 1.68/1.87 tff(2827,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2828,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a869) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a869)) | (~c3_1(a869))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2827, 2826])).
% 1.68/1.87 tff(2829,plain,
% 1.68/1.87 ($false),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2828, 130, 58, 57, 65, 661, 653, 2819, 2821, 701, 180, 2822])).
% 1.68/1.87 tff(2830,plain,(hskp11 | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a867)) | hskp20 | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.87 tff(2831,plain,
% 1.68/1.87 (hskp11),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2830, 2815, 2769, 2768, 308, 2770, 2814, 2813])).
% 1.68/1.87 tff(2832,plain,
% 1.68/1.87 (~c1_1(a808)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[770, 2831])).
% 1.68/1.87 tff(2833,plain,
% 1.68/1.87 (c3_1(a808)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[812, 2831])).
% 1.68/1.87 tff(2834,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a808) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a808)) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a808) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a808)) | c0_1(a808))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2835,plain,
% 1.68/1.87 ((hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (hskp7 | c1_1(a808) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a808)) | c0_1(a808))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2836,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a808) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a808)) | c0_1(a808)))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2835])).
% 1.68/1.87 tff(2837,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a808) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a808)) | c0_1(a808))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2836, 2834])).
% 1.68/1.87 tff(2838,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2839,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a808) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a808)) | c0_1(a808)),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 1.68/1.87 tff(2840,plain,
% 1.68/1.87 (hskp7 | c0_1(a808)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2839, 130, 2435, 2409, 2401, 2833, 2832, 1413])).
% 1.68/1.87 tff(2841,plain,
% 1.68/1.87 (c0_1(a808)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2840, 2811])).
% 1.68/1.87 tff(2842,plain,
% 1.68/1.87 (~c2_1(a808)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[776, 2831])).
% 1.68/1.87 tff(2843,plain,
% 1.68/1.87 (hskp9 | (~c0_1(a808))),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1431, 130, 308, 2833, 2842, 21])).
% 1.68/1.87 tff(2844,plain,
% 1.68/1.87 (hskp9),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2843, 2841])).
% 1.68/1.87 tff(2845,plain,
% 1.68/1.87 (c0_1(a806)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[55, 2844])).
% 1.68/1.87 tff(2846,plain,
% 1.68/1.87 (~c3_1(a806)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[63, 2844])).
% 1.68/1.87 tff(2847,plain,
% 1.68/1.87 (c1_1(a806)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[72, 2844])).
% 1.68/1.87 tff(2848,plain,
% 1.68/1.87 (c2_1(a806)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[169, 2847, 2768, 2846, 2770, 2769, 2845])).
% 1.68/1.87 tff(2849,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a833)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2850,plain,
% 1.68/1.87 ((hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a833)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2851,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a833))))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2850])).
% 1.68/1.87 tff(2852,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a833)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2851, 2849])).
% 1.68/1.87 tff(2853,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2854,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a833) | c0_1(a833) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c3_1(a833))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2853, 2852])).
% 1.68/1.87 tff(2855,plain,
% 1.68/1.87 (hskp7 | (~c3_1(a833))),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2854, 130, 2435, 2409, 2401, 300, 288, 1413])).
% 1.68/1.87 tff(2856,plain,
% 1.68/1.87 (~c3_1(a833)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2855, 2811])).
% 1.68/1.87 tff(2857,plain,
% 1.68/1.87 (~c0_1(a832)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2580, 130, 2833, 288, 276, 289, 22, 2832, 2842, 795, 2856])).
% 1.68/1.87 tff(2858,plain,
% 1.68/1.87 ($false),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[1468, 130, 1362, 2847, 288, 276, 289, 2846, 228, 2857, 2856, 2848])).
% 1.68/1.87 tff(2859,plain,(c1_1(a832) | c2_1(a832) | c0_1(a833) | c2_1(a833) | c3_1(a832) | c1_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.87 tff(2860,plain,
% 1.68/1.87 (c1_1(a832)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2859, 1362, 288, 276, 22, 300])).
% 1.68/1.87 tff(2861,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2862,plain,
% 1.68/1.87 ((hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832))) <=> (hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2863,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867))))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2862])).
% 1.68/1.87 tff(2864,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2863, 2861])).
% 1.68/1.87 tff(2865,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2866,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2865, 2864])).
% 1.68/1.87 tff(2867,plain,
% 1.68/1.87 (hskp12 | c2_1(a832) | (~c1_1(a832))),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2866, 130, 2770, 2769, 2768, 22, 95])).
% 1.68/1.87 tff(2868,plain,
% 1.68/1.87 (hskp12),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2867, 2860, 1362])).
% 1.68/1.87 tff(2869,plain,
% 1.68/1.87 (~c0_1(a809)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[143, 2868])).
% 1.68/1.87 tff(2870,plain,
% 1.68/1.87 (c2_1(a809)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[152, 2868])).
% 1.68/1.87 tff(2871,plain,
% 1.68/1.87 (c1_1(a809)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[160, 2868])).
% 1.68/1.87 tff(2872,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a832)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2873,plain,
% 1.68/1.87 (((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809))) <=> (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a832)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2874,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a832))))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2873])).
% 1.68/1.87 tff(2875,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a832)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2874, 2872])).
% 1.68/1.87 tff(2876,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2877,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c0_1(a832))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2876, 2875])).
% 1.68/1.87 tff(2878,plain,
% 1.68/1.87 (~c0_1(a832)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2877, 130, 1362, 2871, 2870, 2860, 22, 2869, 84])).
% 1.68/1.87 tff(2879,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2880,plain,
% 1.68/1.87 ((hskp3 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a832) | (~c1_1(a832))) <=> (hskp3 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2881,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a832) | (~c1_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | c0_1(a832)))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2880])).
% 1.68/1.87 tff(2882,plain,
% 1.68/1.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a832) | (~c1_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | c0_1(a832))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2881, 2879])).
% 1.68/1.87 tff(2883,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)) | c3_1(a832) | c0_1(a832) | (~c1_1(a832)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2884,plain,
% 1.68/1.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | c0_1(a832)),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2883, 2882])).
% 1.68/1.87 tff(2885,plain,
% 1.68/1.87 (hskp3 | (~c1_1(a832)) | c0_1(a832)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2884, 130, 1362, 22, 2514])).
% 1.68/1.87 tff(2886,plain,
% 1.68/1.87 (hskp3),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2885, 2878, 2860])).
% 1.68/1.87 tff(2887,plain,
% 1.68/1.87 (~c3_1(a798)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[492, 2886])).
% 1.68/1.87 tff(2888,plain,
% 1.68/1.87 (c2_1(a798)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[506, 2886])).
% 1.68/1.87 tff(2889,plain,
% 1.68/1.87 (c0_1(a798)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[514, 2886])).
% 1.68/1.87 tff(2890,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2891,plain,
% 1.68/1.87 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832))) <=> (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)))),
% 1.68/1.87 inference(rewrite,[status(thm)],[])).
% 1.68/1.87 tff(2892,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808))))),
% 1.68/1.87 inference(monotonicity,[status(thm)],[2891])).
% 1.68/1.87 tff(2893,plain,
% 1.68/1.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)))),
% 1.68/1.87 inference(transitivity,[status(thm)],[2892, 2890])).
% 1.68/1.87 tff(2894,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))),
% 1.68/1.87 inference(quant_inst,[status(thm)],[])).
% 1.68/1.87 tff(2895,plain,
% 1.68/1.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808))),
% 1.68/1.87 inference(modus_ponens,[status(thm)],[2894, 2893])).
% 1.68/1.87 tff(2896,plain,
% 1.68/1.87 (~c0_1(a808)),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2895, 130, 1362, 2833, 2889, 2888, 2860, 22, 2842, 2887, 299])).
% 1.68/1.87 tff(2897,plain,
% 1.68/1.87 ($false),
% 1.68/1.87 inference(unit_resolution,[status(thm)],[2541, 130, 2871, 2870, 2833, 2889, 2888, 2869, 2842, 2887, 2503, 2896])).
% 1.68/1.87 tff(2898,plain,(c2_1(a832) | c3_1(a832) | c0_1(a833) | c2_1(a833) | c1_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.88 tff(2899,plain,
% 1.68/1.88 (c2_1(a832)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2898, 300, 288, 276, 22])).
% 1.68/1.88 tff(2900,plain,
% 1.68/1.88 (~c2_1(a808)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[776, 2809])).
% 1.68/1.88 tff(2901,plain,
% 1.68/1.88 (~c1_1(a808)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[770, 2809])).
% 1.68/1.88 tff(2902,plain,
% 1.68/1.88 (~c0_1(a808)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1431, 130, 310, 11, 941, 796, 21])).
% 1.68/1.88 tff(2903,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c1_1(a832) | c3_1(a832) | c1_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a832) | c3_1(a832) | c1_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2904,plain,
% 1.68/1.88 ((hskp4 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (hskp4 | c1_1(a832) | c3_1(a832) | c1_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2905,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | c1_1(a832) | c3_1(a832) | c1_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832))))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2904])).
% 1.68/1.88 tff(2906,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a832) | c3_1(a832) | c1_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832)))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2905, 2903])).
% 1.68/1.88 tff(2907,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c2_1(a832)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2908,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp4 | c1_1(a832) | c3_1(a832) | c1_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c2_1(a832))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2907, 2906])).
% 1.68/1.88 tff(2909,plain,
% 1.68/1.88 (hskp4),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2908, 130, 391, 941, 289, 22, 797, 1918, 2902])).
% 1.68/1.88 tff(2910,plain,
% 1.68/1.88 (c3_1(a799)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1523, 2909])).
% 1.68/1.88 tff(2911,plain,
% 1.68/1.88 (c0_1(a799)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1548, 2909])).
% 1.68/1.88 tff(2912,plain,
% 1.68/1.88 (c2_1(a799)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1573, 130, 310, 11, 2911, 2910, 21])).
% 1.68/1.88 tff(2913,plain,
% 1.68/1.88 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2914,plain,
% 1.68/1.88 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867))) <=> (hskp20 | hskp9 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2915,plain,
% 1.68/1.88 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867))))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2914])).
% 1.68/1.88 tff(2916,plain,
% 1.68/1.88 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867)))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2915, 2913])).
% 1.68/1.88 tff(2917,plain,
% 1.68/1.88 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a867) | (~c3_1(a867)) | (~c0_1(a867)))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2918,plain,
% 1.68/1.88 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~ndr1_0) | (~c3_1(a867)) | c2_1(a867) | (~c0_1(a867))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2917, 2916])).
% 1.68/1.88 tff(2919,plain,
% 1.68/1.88 (hskp9 | c2_1(a867)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2918, 130, 310, 58, 65, 21])).
% 1.68/1.88 tff(2920,plain,
% 1.68/1.88 (c2_1(a867)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2919, 11])).
% 1.68/1.88 tff(2921,plain,
% 1.68/1.88 (hskp7),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1422, 130, 57, 65, 941, 797, 1413, 2920, 2902])).
% 1.68/1.88 tff(2922,plain,
% 1.68/1.88 (~c2_1(a803)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1377, 2921])).
% 1.68/1.88 tff(2923,plain,
% 1.68/1.88 (c3_1(a803)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1385, 2921])).
% 1.68/1.88 tff(2924,plain,
% 1.68/1.88 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c0_1(a803)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c0_1(a803)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2925,plain,
% 1.68/1.88 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c0_1(a803))) <=> (hskp20 | hskp9 | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c0_1(a803)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2926,plain,
% 1.68/1.88 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c0_1(a803)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c0_1(a803))))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2925])).
% 1.68/1.88 tff(2927,plain,
% 1.68/1.88 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c0_1(a803)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c0_1(a803)))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2926, 2924])).
% 1.68/1.88 tff(2928,plain,
% 1.68/1.88 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c0_1(a803)))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2929,plain,
% 1.68/1.88 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c0_1(a803))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2928, 2927])).
% 1.68/1.88 tff(2930,plain,
% 1.68/1.88 (~c0_1(a803)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2929, 130, 310, 11, 2923, 2922, 21])).
% 1.68/1.88 tff(2931,plain,
% 1.68/1.88 (~c1_1(a799)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1515, 2909])).
% 1.68/1.88 tff(2932,plain,
% 1.68/1.88 (c1_1(a803)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1393, 2921])).
% 1.68/1.88 tff(2933,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a799) | (~ndr1_0) | (~c3_1(a799)) | (~c2_1(a799)) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a799) | (~ndr1_0) | (~c3_1(a799)) | (~c2_1(a799)) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2934,plain,
% 1.68/1.88 ((hskp8 | (~ndr1_0) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803))) <=> (hskp8 | c1_1(a799) | (~ndr1_0) | (~c3_1(a799)) | (~c2_1(a799)) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2935,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a799) | (~ndr1_0) | (~c3_1(a799)) | (~c2_1(a799)) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803))))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2934])).
% 1.68/1.88 tff(2936,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a799) | (~ndr1_0) | (~c3_1(a799)) | (~c2_1(a799)) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2935, 2933])).
% 1.68/1.88 tff(2937,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a799) | (~c3_1(a799)) | (~c2_1(a799)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2938,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a799) | (~ndr1_0) | (~c3_1(a799)) | (~c2_1(a799)) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2937, 2936])).
% 1.68/1.88 tff(2939,plain,
% 1.68/1.88 (hskp8),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2938, 130, 2932, 2923, 2910, 2931, 687, 2930, 2912])).
% 1.68/1.88 tff(2940,plain,
% 1.68/1.88 (~c3_1(a805)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[414, 2939])).
% 1.68/1.88 tff(2941,plain,
% 1.68/1.88 (~c2_1(a805)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[420, 2939])).
% 1.68/1.88 tff(2942,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a808) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | (~c3_1(a808)) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a808) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | (~c3_1(a808)) | c0_1(a808))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2943,plain,
% 1.68/1.88 ((hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (hskp6 | c1_1(a808) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | (~c3_1(a808)) | c0_1(a808))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2944,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a808) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | (~c3_1(a808)) | c0_1(a808)))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2943])).
% 1.68/1.88 tff(2945,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a808) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | (~c3_1(a808)) | c0_1(a808))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2944, 2942])).
% 1.68/1.88 tff(2946,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2947,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a808) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | (~c3_1(a808)) | c0_1(a808)),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2946, 2945])).
% 1.68/1.88 tff(2948,plain,
% 1.68/1.88 (hskp6),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2947, 130, 941, 2932, 2923, 797, 2922, 1853, 2902])).
% 1.68/1.88 tff(2949,plain,
% 1.68/1.88 (~c0_1(a802)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1873, 2948])).
% 1.68/1.88 tff(2950,plain,
% 1.68/1.88 (c2_1(a802)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1881, 2948])).
% 1.68/1.88 tff(2951,plain,
% 1.68/1.88 (~c3_1(a802)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[1888, 130, 58, 57, 65, 2950, 2949, 180, 2920])).
% 1.68/1.88 tff(2952,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a808) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a808)) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a808) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a808)) | c0_1(a808))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2953,plain,
% 1.68/1.88 ((hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (hskp12 | c2_1(a808) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a808)) | c0_1(a808))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2954,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a808) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a808)) | c0_1(a808)))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2953])).
% 1.68/1.88 tff(2955,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a808) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a808)) | c0_1(a808))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2954, 2952])).
% 1.68/1.88 tff(2956,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a802) | c3_1(a802) | (~c2_1(a802)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2957,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a808) | c0_1(a802) | (~ndr1_0) | c3_1(a802) | (~c2_1(a802)) | (~c3_1(a808)) | c0_1(a808)),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2956, 2955])).
% 1.68/1.88 tff(2958,plain,
% 1.68/1.88 (hskp12),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2957, 130, 941, 2950, 796, 2949, 989, 2902, 2951])).
% 1.68/1.88 tff(2959,plain,
% 1.68/1.88 (~c0_1(a809)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[143, 2958])).
% 1.68/1.88 tff(2960,plain,
% 1.68/1.88 (c1_1(a805)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[429, 2939])).
% 1.68/1.88 tff(2961,plain,
% 1.68/1.88 (c2_1(a809)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[152, 2958])).
% 1.68/1.88 tff(2962,plain,
% 1.68/1.88 (c1_1(a809)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[160, 2958])).
% 1.68/1.88 tff(2963,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a809) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a809) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2964,plain,
% 1.68/1.88 (((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809))) <=> (c0_1(a809) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2965,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a809) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a809)) | (~c1_1(a809))))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2964])).
% 1.68/1.88 tff(2966,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a809) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2965, 2963])).
% 1.68/1.88 tff(2967,plain,
% 1.68/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2968,plain,
% 1.68/1.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a809) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c0_1(a805)) | (~c1_1(a805)) | (~c2_1(a809)) | (~c1_1(a809))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2967, 2966])).
% 1.68/1.88 tff(2969,plain,
% 1.68/1.88 (~c0_1(a805)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2968, 130, 2962, 2961, 2960, 2959, 2941, 2940, 84])).
% 1.68/1.88 tff(2970,plain,
% 1.68/1.88 (~c0_1(a832)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2690, 2939, 941, 289, 797, 22, 796, 391])).
% 1.68/1.88 tff(2971,plain,
% 1.68/1.88 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.68/1.88 inference(bind,[status(th)],[])).
% 1.68/1.88 tff(2972,plain,
% 1.68/1.88 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.68/1.88 inference(quant_intro,[status(thm)],[2971])).
% 1.68/1.88 tff(2973,plain,
% 1.68/1.88 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2974,plain,
% 1.68/1.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.68/1.88 inference(bind,[status(th)],[])).
% 1.68/1.88 tff(2975,plain,
% 1.68/1.88 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.68/1.88 inference(quant_intro,[status(thm)],[2974])).
% 1.68/1.88 tff(2976,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.68/1.88 tff(2977,plain,
% 1.68/1.88 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2976, 2975])).
% 1.68/1.88 tff(2978,plain,
% 1.68/1.88 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2977, 2973])).
% 1.68/1.88 tff(2979,plain,(
% 1.68/1.88 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.68/1.88 inference(skolemize,[status(sab)],[2978])).
% 1.68/1.88 tff(2980,plain,
% 1.68/1.88 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2979, 2972])).
% 1.68/1.88 tff(2981,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a832) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a832) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)) | c0_1(a832))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2982,plain,
% 1.68/1.88 ((hskp14 | (~ndr1_0) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832))) <=> (hskp14 | c3_1(a832) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)) | c0_1(a832))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2983,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a832) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)) | c0_1(a832)))),
% 1.68/1.88 inference(monotonicity,[status(thm)],[2982])).
% 1.68/1.88 tff(2984,plain,
% 1.68/1.88 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a832) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)) | c0_1(a832))),
% 1.68/1.88 inference(transitivity,[status(thm)],[2983, 2981])).
% 1.68/1.88 tff(2985,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a832) | c0_1(a832) | (~c2_1(a832)))),
% 1.68/1.88 inference(quant_inst,[status(thm)],[])).
% 1.68/1.88 tff(2986,plain,
% 1.68/1.88 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a832) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)) | c0_1(a832)),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2985, 2984])).
% 1.68/1.88 tff(2987,plain,
% 1.68/1.88 (hskp14 | c0_1(a832)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2986, 130, 391, 2932, 2923, 22, 2980, 2930])).
% 1.68/1.88 tff(2988,plain,
% 1.68/1.88 (hskp14),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2987, 2970])).
% 1.68/1.88 tff(2989,plain,
% 1.68/1.88 (((~hskp14) | (~c1_1(a816))) <=> ((~hskp14) | (~c1_1(a816)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2990,plain,
% 1.68/1.88 (((~c1_1(a816)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a816)))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2991,axiom,((~c1_1(a816)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.68/1.88 tff(2992,plain,
% 1.68/1.88 ((~hskp14) | (~c1_1(a816))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2991, 2990])).
% 1.68/1.88 tff(2993,plain,
% 1.68/1.88 ((~hskp14) | (~c1_1(a816))),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2992, 2989])).
% 1.68/1.88 tff(2994,plain,
% 1.68/1.88 (~c1_1(a816)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[2993, 2988])).
% 1.68/1.88 tff(2995,plain,
% 1.68/1.88 (((~hskp14) | c0_1(a816)) <=> ((~hskp14) | c0_1(a816))),
% 1.68/1.88 inference(rewrite,[status(thm)],[])).
% 1.68/1.88 tff(2996,axiom,((~hskp14) | c0_1(a816)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.68/1.88 tff(2997,plain,
% 1.68/1.88 ((~hskp14) | c0_1(a816)),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2996, 2995])).
% 1.68/1.88 tff(2998,plain,
% 1.68/1.88 ((~hskp14) | c0_1(a816)),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2997, 2995])).
% 1.68/1.88 tff(2999,plain,
% 1.68/1.88 ((~hskp14) | c0_1(a816)),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2998, 2995])).
% 1.68/1.88 tff(3000,plain,
% 1.68/1.88 ((~hskp14) | c0_1(a816)),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[2999, 2995])).
% 1.68/1.88 tff(3001,plain,
% 1.68/1.88 ((~hskp14) | c0_1(a816)),
% 1.68/1.88 inference(modus_ponens,[status(thm)],[3000, 2995])).
% 1.68/1.88 tff(3002,plain,
% 1.68/1.88 (c0_1(a816)),
% 1.68/1.88 inference(unit_resolution,[status(thm)],[3001, 2988])).
% 1.68/1.88 tff(3003,plain,
% 1.68/1.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a816) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | c3_1(a816) | (~c0_1(a816)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a816) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | c3_1(a816) | (~c0_1(a816)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3004,plain,
% 1.68/1.89 (((~ndr1_0) | c1_1(a816) | c3_1(a816) | (~c0_1(a816)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805)) <=> (c1_1(a816) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | c3_1(a816) | (~c0_1(a816)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3005,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a816) | c3_1(a816) | (~c0_1(a816)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a816) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | c3_1(a816) | (~c0_1(a816))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[3004])).
% 1.68/1.89 tff(3006,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a816) | c3_1(a816) | (~c0_1(a816)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a816) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | c3_1(a816) | (~c0_1(a816)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[3005, 3003])).
% 1.68/1.89 tff(3007,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a816) | c3_1(a816) | (~c0_1(a816)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a805) | c0_1(a805) | c3_1(a805))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(3008,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a816) | c1_1(a808) | c2_1(a808) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | c0_1(a805) | (~c3_1(a808)) | c3_1(a816) | (~c0_1(a816))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[3007, 3006])).
% 1.68/1.89 tff(3009,plain,
% 1.68/1.89 (c3_1(a816)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3008, 130, 3002, 941, 2994, 797, 796, 2941, 2940, 795, 2969])).
% 1.68/1.89 tff(3010,plain,
% 1.68/1.89 (((~hskp14) | (~c2_1(a816))) <=> ((~hskp14) | (~c2_1(a816)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3011,plain,
% 1.68/1.89 (((~c2_1(a816)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a816)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3012,axiom,((~c2_1(a816)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.68/1.89 tff(3013,plain,
% 1.68/1.89 ((~hskp14) | (~c2_1(a816))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[3012, 3011])).
% 1.68/1.89 tff(3014,plain,
% 1.68/1.89 ((~hskp14) | (~c2_1(a816))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[3013, 3010])).
% 1.68/1.89 tff(3015,plain,
% 1.68/1.89 (~c2_1(a816)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3014, 2988])).
% 1.68/1.89 tff(3016,plain,
% 1.68/1.89 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3017,plain,
% 1.68/1.89 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816))) <=> (hskp20 | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3018,plain,
% 1.68/1.89 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[3017])).
% 1.68/1.89 tff(3019,plain,
% 1.68/1.89 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[3018, 3016])).
% 1.68/1.89 tff(3020,plain,
% 1.68/1.89 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(3021,plain,
% 1.68/1.89 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[3020, 3019])).
% 1.68/1.89 tff(3022,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3021, 130, 310, 11, 3002, 3015, 21, 3009])).
% 1.68/1.89 tff(3023,plain,(c1_1(a808) | hskp20 | hskp9 | (~c3_1(a808)) | c2_1(a808) | (~c2_1(a832)) | c3_1(a832) | c1_1(a832) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a867))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(3024,plain,
% 1.68/1.89 (c1_1(a832)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3023, 2901, 2805, 308, 2900, 2899, 22, 2810, 2770, 2769, 2768])).
% 1.68/1.89 tff(3025,plain,
% 1.68/1.89 (~hskp19),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[352, 3024])).
% 1.68/1.89 tff(3026,plain,
% 1.68/1.89 (hskp9 | c2_1(a867)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2918, 130, 308, 2770, 2768, 21])).
% 1.68/1.89 tff(3027,plain,
% 1.68/1.89 (c2_1(a867)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3026, 2805])).
% 1.68/1.89 tff(3028,plain,
% 1.68/1.89 (hskp18),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2248, 2808, 2768, 2769, 3027])).
% 1.68/1.89 tff(3029,plain,
% 1.68/1.89 (~c3_1(a828)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[1107, 3028])).
% 1.68/1.89 tff(3030,plain,
% 1.68/1.89 (~c2_1(a828)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[1101, 3028])).
% 1.68/1.89 tff(3031,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a833) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a833) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3032,plain,
% 1.68/1.89 (((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833)) <=> (c1_1(a833) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3033,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a833) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[3032])).
% 1.68/1.89 tff(3034,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a833) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[3033, 3031])).
% 1.68/1.89 tff(3035,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a828) | c2_1(a828) | c0_1(a828) | c2_1(a833) | c1_1(a833) | c0_1(a833))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(3036,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a833) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c2_1(a828) | c3_1(a828) | (~ndr1_0) | c0_1(a828) | (~c2_1(a832))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[3035, 3034])).
% 1.68/1.89 tff(3037,plain,
% 1.68/1.89 (c0_1(a828)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3036, 130, 300, 2899, 288, 276, 3024, 22, 3030, 3029, 228])).
% 1.68/1.89 tff(3038,plain,
% 1.68/1.89 (~c1_1(a828)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[1113, 3028])).
% 1.68/1.89 tff(3039,plain,
% 1.68/1.89 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3040,plain,
% 1.68/1.89 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828))) <=> (hskp20 | hskp1 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3041,plain,
% 1.68/1.89 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[3040])).
% 1.68/1.89 tff(3042,plain,
% 1.68/1.89 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[3041, 3039])).
% 1.68/1.89 tff(3043,plain,
% 1.68/1.89 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(3044,plain,
% 1.68/1.89 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[3043, 3042])).
% 1.68/1.89 tff(3045,plain,
% 1.68/1.89 (hskp1),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3044, 130, 308, 3038, 3030, 1541, 3037])).
% 1.68/1.89 tff(3046,plain,
% 1.68/1.89 (~c2_1(a794)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[250, 3045])).
% 1.68/1.89 tff(3047,plain,
% 1.68/1.89 (c3_1(a794)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[258, 3045])).
% 1.68/1.89 tff(3048,plain,
% 1.68/1.89 (~c0_1(a794)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[264, 3045])).
% 1.68/1.89 tff(3049,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2260, 3048, 3047, 2769, 2768, 3027, 3028, 3046, 3025])).
% 1.68/1.89 tff(3050,plain,(c1_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(3051,plain,
% 1.68/1.89 (c1_1(a833)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3050, 22, 276, 288])).
% 1.68/1.89 tff(3052,plain,
% 1.68/1.89 (hskp3),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2523, 277, 276, 288, 3051])).
% 1.68/1.89 tff(3053,plain,
% 1.68/1.89 (~c3_1(a798)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[492, 3052])).
% 1.68/1.89 tff(3054,plain,
% 1.68/1.89 (c3_1(a838)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[398, 2816])).
% 1.68/1.89 tff(3055,plain,
% 1.68/1.89 (c0_1(a838)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[406, 2816])).
% 1.68/1.89 tff(3056,plain,
% 1.68/1.89 (hskp3),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2523, 277, 276, 288, 570])).
% 1.68/1.89 tff(3057,plain,
% 1.68/1.89 (~c3_1(a798)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[492, 3056])).
% 1.68/1.89 tff(3058,plain,
% 1.68/1.89 (c2_1(a798)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[506, 3056])).
% 1.68/1.89 tff(3059,plain,
% 1.68/1.89 (c0_1(a798)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[514, 3056])).
% 1.68/1.89 tff(3060,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c2_1(a833) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c3_1(a833) | (~c1_1(a833)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a833) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c3_1(a833) | (~c1_1(a833)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3061,plain,
% 1.68/1.89 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (c2_1(a838) | c2_1(a833) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c3_1(a833) | (~c1_1(a833)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3062,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c2_1(a833) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c3_1(a833) | (~c1_1(a833)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[3061])).
% 1.68/1.89 tff(3063,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a833) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c3_1(a833) | (~c1_1(a833)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[3062, 3060])).
% 1.68/1.89 tff(3064,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(3065,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a833) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c3_1(a833) | (~c1_1(a833)) | (~c3_1(a838)) | (~c0_1(a838))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[3064, 3063])).
% 1.68/1.89 tff(3066,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3065, 130, 432, 431, 570, 3059, 3058, 422, 276, 3057, 299, 277])).
% 1.68/1.89 tff(3067,plain,(c3_1(a833) | (~c0_1(a838)) | (~c3_1(a838)) | (~c1_1(a833)) | c2_1(a838) | c2_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(3068,plain,
% 1.68/1.89 (c3_1(a833)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3067, 3055, 3054, 3051, 2817, 276, 288])).
% 1.68/1.89 tff(3069,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3070,plain,
% 1.68/1.89 ((hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a832) | c2_1(a832) | c1_1(a832)) <=> (hskp19 | c2_1(a832) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3071,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[3070])).
% 1.68/1.89 tff(3072,plain,
% 1.68/1.89 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a832) | c2_1(a832) | c1_1(a832))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[3071, 3069])).
% 1.68/1.89 tff(3073,plain,
% 1.68/1.89 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a832) | c2_1(a832) | c1_1(a832))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(3074,plain,
% 1.68/1.89 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | c2_1(a833) | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[3073, 3072])).
% 1.68/1.89 tff(3075,plain,
% 1.68/1.89 (hskp19 | c2_1(a832) | c1_1(a832) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3074, 130, 276, 22, 10])).
% 1.68/1.89 tff(3076,plain,
% 1.68/1.89 (~c3_1(a833)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3075, 289, 3051, 1362, 1363])).
% 1.68/1.89 tff(3077,plain,
% 1.68/1.89 (hskp8),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[873, 277, 276, 615, 613, 618, 288, 570])).
% 1.68/1.89 tff(3078,plain,
% 1.68/1.89 (~c3_1(a805)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[414, 3077])).
% 1.68/1.89 tff(3079,plain,
% 1.68/1.89 (~c2_1(a805)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[420, 3077])).
% 1.68/1.89 tff(3080,plain,
% 1.68/1.89 (c1_1(a805)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[429, 3077])).
% 1.68/1.89 tff(3081,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3082,plain,
% 1.68/1.89 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c2_1(a838) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.68/1.89 inference(rewrite,[status(thm)],[])).
% 1.68/1.89 tff(3083,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 1.68/1.89 inference(monotonicity,[status(thm)],[3082])).
% 1.68/1.89 tff(3084,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.68/1.89 inference(transitivity,[status(thm)],[3083, 3081])).
% 1.68/1.89 tff(3085,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 1.68/1.89 inference(quant_inst,[status(thm)],[])).
% 1.68/1.89 tff(3086,plain,
% 1.68/1.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c2_1(a805) | c3_1(a805) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c1_1(a805)) | (~c3_1(a838)) | (~c0_1(a838))),
% 1.68/1.89 inference(modus_ponens,[status(thm)],[3085, 3084])).
% 1.68/1.89 tff(3087,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3086, 130, 432, 431, 3080, 3059, 3058, 422, 3079, 3078, 3057, 299])).
% 1.68/1.89 tff(3088,plain,(c3_1(a833) | (~c0_1(a838)) | (~c3_1(a838)) | c2_1(a838) | c2_1(a833) | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796)) | c0_1(a833) | (~c1_1(a833))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(3089,plain,
% 1.68/1.89 ($false),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3088, 1222, 1683, 570, 615, 276, 277, 613, 618, 288, 1684])).
% 1.68/1.89 tff(3090,plain,((~hskp21) | (~c1_1(a833)) | (~c0_1(a796)) | c2_1(a833) | c3_1(a833) | (~c2_1(a796)) | (~c3_1(a796)) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.89 tff(3091,plain,
% 1.68/1.89 (~hskp21),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[3090, 3076, 2815, 276, 3051, 2814, 2813, 288])).
% 1.68/1.89 tff(3092,plain,
% 1.68/1.89 (hskp11),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2442, 3091])).
% 1.68/1.89 tff(3093,plain,
% 1.68/1.89 (~c1_1(a808)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[770, 3092])).
% 1.68/1.89 tff(3094,plain,
% 1.68/1.89 (c3_1(a808)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[812, 3092])).
% 1.68/1.89 tff(3095,plain,
% 1.68/1.89 (c0_1(a808)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2839, 130, 2811, 2435, 2409, 2401, 3094, 3093, 1413])).
% 1.68/1.89 tff(3096,plain,
% 1.68/1.89 (hskp3),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[2523, 3076, 276, 288, 3051])).
% 1.68/1.89 tff(3097,plain,
% 1.68/1.89 (~c3_1(a798)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[492, 3096])).
% 1.68/1.89 tff(3098,plain,
% 1.68/1.89 (~c2_1(a808)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[776, 3092])).
% 1.68/1.89 tff(3099,plain,
% 1.68/1.89 (c2_1(a798)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[506, 3096])).
% 1.68/1.89 tff(3100,plain,
% 1.68/1.89 (c0_1(a798)),
% 1.68/1.89 inference(unit_resolution,[status(thm)],[514, 3096])).
% 1.68/1.89 tff(3101,plain,
% 1.68/1.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a833) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a833) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)) | c3_1(a833) | (~c1_1(a833)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3102,plain,
% 1.68/1.90 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (c2_1(a833) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)) | c3_1(a833) | (~c1_1(a833)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3103,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a833) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)) | c3_1(a833) | (~c1_1(a833))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[3102])).
% 1.68/1.90 tff(3104,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a833) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)) | c3_1(a833) | (~c1_1(a833)))),
% 1.68/1.90 inference(transitivity,[status(thm)],[3103, 3101])).
% 1.68/1.90 tff(3105,plain,
% 1.68/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | (~c3_1(a808)) | (~c0_1(a808)) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(3106,plain,
% 1.68/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a833) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a808)) | (~c0_1(a808)) | c3_1(a833) | (~c1_1(a833))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[3105, 3104])).
% 1.68/1.90 tff(3107,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3106, 130, 3051, 3094, 3100, 3099, 276, 3098, 3097, 299, 3076, 3095])).
% 1.68/1.90 tff(3108,plain,(c1_1(a832) | c2_1(a833) | c0_1(a833) | c2_1(a832) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(3109,plain,
% 1.68/1.90 (c1_1(a832)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3108, 1362, 288, 276, 22])).
% 1.68/1.90 tff(3110,assumption,(c1_1(a832)), introduced(assumption)).
% 1.68/1.90 tff(3111,assumption,(~c0_1(a797)), introduced(assumption)).
% 1.68/1.90 tff(3112,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3113,plain,
% 1.68/1.90 (((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797))) <=> (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3114,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[3113])).
% 1.68/1.90 tff(3115,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))),
% 1.68/1.90 inference(transitivity,[status(thm)],[3114, 3112])).
% 1.68/1.90 tff(3116,plain,
% 1.68/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a832)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(3117,plain,
% 1.68/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[3116, 3115])).
% 1.68/1.90 tff(3118,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3117, 130, 2435, 2409, 1362, 3110, 22, 84, 408, 3111])).
% 1.68/1.90 tff(3119,plain,(c0_1(a797) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~c0_1(a832))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(3120,plain,
% 1.68/1.90 (c0_1(a797)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3119, 408, 3110, 22, 1362])).
% 1.68/1.90 tff(3121,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3122,plain,
% 1.68/1.90 ((hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832))) <=> (hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3123,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[3122])).
% 1.68/1.90 tff(3124,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)))),
% 1.68/1.90 inference(transitivity,[status(thm)],[3123, 3121])).
% 1.68/1.90 tff(3125,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(3126,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a832) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[3125, 3124])).
% 1.68/1.90 tff(3127,plain,
% 1.68/1.90 (hskp12 | c2_1(a832) | (~c1_1(a832)) | (~c0_1(a797))),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3126, 130, 2435, 2401, 22, 95])).
% 1.68/1.90 tff(3128,plain,
% 1.68/1.90 (hskp12),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3127, 3120, 1362, 3110])).
% 1.68/1.90 tff(3129,plain,
% 1.68/1.90 (~c0_1(a809)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[143, 3128])).
% 1.68/1.90 tff(3130,plain,
% 1.68/1.90 (c2_1(a809)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[152, 3128])).
% 1.68/1.90 tff(3131,plain,
% 1.68/1.90 (c1_1(a809)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[160, 3128])).
% 1.68/1.90 tff(3132,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2877, 130, 1362, 3131, 3130, 3110, 22, 3129, 84, 408])).
% 1.68/1.90 tff(3133,plain,((~c0_1(a832)) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(3134,plain,
% 1.68/1.90 (~c0_1(a832)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3133, 1362, 3110, 22])).
% 1.68/1.90 tff(3135,plain,
% 1.68/1.90 (hskp3),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2885, 3134, 3110])).
% 1.68/1.90 tff(3136,assumption,(hskp3), introduced(assumption)).
% 1.68/1.90 tff(3137,plain,
% 1.68/1.90 (~c3_1(a798)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[492, 3136])).
% 1.68/1.90 tff(3138,plain,
% 1.68/1.90 (c2_1(a798)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[506, 3136])).
% 1.68/1.90 tff(3139,plain,
% 1.68/1.90 (c0_1(a798)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[514, 3136])).
% 1.68/1.90 tff(3140,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3141,plain,
% 1.68/1.90 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832))) <=> (c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3142,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[3141])).
% 1.68/1.90 tff(3143,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.68/1.90 inference(transitivity,[status(thm)],[3142, 3140])).
% 1.68/1.90 tff(3144,plain,
% 1.68/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a832) | c3_1(a832) | (~c1_1(a832)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(3145,plain,
% 1.68/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c3_1(a838)) | (~c0_1(a838))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[3144, 3143])).
% 1.68/1.90 tff(3146,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3145, 130, 432, 431, 1362, 3139, 3138, 422, 3110, 22, 3137, 299])).
% 1.68/1.90 tff(3147,plain,((~hskp3) | (~c0_1(a838)) | (~c3_1(a838)) | c2_1(a832) | c2_1(a838) | (~c1_1(a832)) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(3148,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3147, 1222, 1683, 1362, 3110, 3135, 1684, 22])).
% 1.68/1.90 tff(3149,plain,((~hskp21) | c2_1(a832) | (~c1_1(a832)) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(3150,plain,
% 1.68/1.90 (~hskp21),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3149, 1362, 3109, 22])).
% 1.68/1.90 tff(3151,plain,
% 1.68/1.90 (hskp11),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2442, 3150])).
% 1.68/1.90 tff(3152,plain,
% 1.68/1.90 (c3_1(a808)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[812, 3151])).
% 1.68/1.90 tff(3153,plain,
% 1.68/1.90 (~c2_1(a808)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[776, 3151])).
% 1.68/1.90 tff(3154,plain,
% 1.68/1.90 (hskp21 | hskp18 | c1_1(a808) | (~c3_1(a808))),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[1095, 130, 796, 1088])).
% 1.68/1.90 tff(3155,plain,
% 1.68/1.90 (c1_1(a808)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3154, 629, 941, 2246])).
% 1.68/1.90 tff(3156,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[770, 3155, 2443])).
% 1.68/1.90 tff(3157,plain,(hskp21 | (~c3_1(a808)) | hskp18 | c2_1(a808)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(3158,plain,
% 1.68/1.90 (hskp18),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3157, 3152, 3150, 3153])).
% 1.68/1.90 tff(3159,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2554, 2252, 2253, 570, 276, 1501, 288, 796, 941, 2251])).
% 1.68/1.90 tff(3160,plain,((~hskp18) | (~c1_1(a833)) | c2_1(a833) | hskp19 | c0_1(a833) | c2_1(a808) | (~c3_1(a808))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(3161,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3160, 3158, 3153, 276, 1363, 288, 3051, 3152])).
% 1.68/1.90 tff(3162,plain,(c2_1(a832) | c2_1(a833) | c0_1(a833) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(3163,plain,
% 1.68/1.90 (c2_1(a832)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3162, 22, 288, 276])).
% 1.68/1.90 tff(3164,plain,
% 1.68/1.90 (hskp12),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[997, 979, 3163, 288, 276, 22, 669])).
% 1.68/1.90 tff(3165,plain,
% 1.68/1.90 (~c0_1(a809)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[143, 3164])).
% 1.68/1.90 tff(3166,plain,
% 1.68/1.90 (c2_1(a809)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[152, 3164])).
% 1.68/1.90 tff(3167,plain,
% 1.68/1.90 (c1_1(a809)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[160, 3164])).
% 1.68/1.90 tff(3168,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[1007, 130, 3163, 3167, 3166, 289, 22, 3165, 977, 979])).
% 1.68/1.90 tff(3169,plain,(c0_1(a832) | c1_1(a832) | c3_1(a832) | c0_1(a833) | c2_1(a833) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(3170,plain,
% 1.68/1.90 (c0_1(a832)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3169, 3068, 22, 288, 276, 289])).
% 1.68/1.90 tff(3171,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2763, 130, 2435, 2409, 3163, 288, 276, 22, 2503, 408, 669, 3111])).
% 1.68/1.90 tff(3172,plain,(c0_1(a797) | c0_1(a833) | c2_1(a833) | c3_1(a832) | (~c0_1(a832)) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(3173,plain,
% 1.68/1.90 (c0_1(a797)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3172, 3170, 276, 22, 288, 3068])).
% 1.68/1.90 tff(3174,plain,
% 1.68/1.90 (((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3175,plain,
% 1.68/1.90 ((hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797))) <=> (hskp26 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3176,plain,
% 1.68/1.90 (((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[3175])).
% 1.68/1.90 tff(3177,plain,
% 1.68/1.90 (((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))) <=> ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)))),
% 1.68/1.90 inference(transitivity,[status(thm)],[3176, 3174])).
% 1.68/1.90 tff(3178,plain,
% 1.68/1.90 ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(3179,plain,
% 1.68/1.90 ((~![U: $i] : (hskp26 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp26 | hskp11 | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[3178, 3177])).
% 1.68/1.90 tff(3180,plain,
% 1.68/1.90 (hskp26 | hskp11 | (~c0_1(a797))),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3179, 130, 2409, 2401, 640])).
% 1.68/1.90 tff(3181,plain,
% 1.68/1.90 (hskp26),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3180, 3173, 630])).
% 1.68/1.90 tff(3182,plain,
% 1.68/1.90 (~c0_1(a869)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[700, 3181])).
% 1.68/1.90 tff(3183,plain,
% 1.68/1.90 (c3_1(a869)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[652, 3181])).
% 1.68/1.90 tff(3184,plain,
% 1.68/1.90 (c2_1(a869)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[660, 3181])).
% 1.68/1.90 tff(3185,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a869) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a869)) | (~c3_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a869) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a869)) | (~c3_1(a869)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3186,plain,
% 1.68/1.90 (((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869))) <=> (c0_1(a869) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a869)) | (~c3_1(a869)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3187,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a869) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a869)) | (~c3_1(a869))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[3186])).
% 1.68/1.90 tff(3188,plain,
% 1.68/1.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a869) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a869)) | (~c3_1(a869)))),
% 1.68/1.90 inference(transitivity,[status(thm)],[3187, 3185])).
% 1.68/1.90 tff(3189,plain,
% 1.68/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a869) | (~c3_1(a869)) | (~c2_1(a869)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(3190,plain,
% 1.68/1.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a869) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a869)) | (~c3_1(a869))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[3189, 3188])).
% 1.68/1.90 tff(3191,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3190, 130, 2435, 2409, 2401, 3184, 3183, 3182, 180, 3173])).
% 1.68/1.90 tff(3192,plain,(hskp11 | c2_1(a833) | c3_1(a832) | c0_1(a833) | c1_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(3193,plain,
% 1.68/1.90 (hskp11),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3192, 289, 22, 288, 276])).
% 1.68/1.90 tff(3194,plain,
% 1.68/1.90 (~c2_1(a808)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[776, 3193])).
% 1.68/1.90 tff(3195,plain,
% 1.68/1.90 (c2_1(a798)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[506, 3052])).
% 1.68/1.90 tff(3196,plain,
% 1.68/1.90 (c0_1(a798)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[514, 3052])).
% 1.68/1.90 tff(3197,plain,
% 1.68/1.90 (c3_1(a808)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[812, 3193])).
% 1.68/1.90 tff(3198,plain,
% 1.68/1.90 (~c0_1(a808)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3106, 130, 3051, 3197, 3196, 3195, 276, 3194, 3053, 299, 277])).
% 1.68/1.90 tff(3199,plain,
% 1.68/1.90 (~c1_1(a808)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[770, 3193])).
% 1.68/1.90 tff(3200,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a808) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a808) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c0_1(a808))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3201,plain,
% 1.68/1.90 ((hskp0 | (~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | c1_1(a808) | c0_1(a808)) <=> (hskp0 | c1_1(a808) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c0_1(a808))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3202,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | c1_1(a808) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a808) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c0_1(a808)))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[3201])).
% 1.68/1.90 tff(3203,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | c1_1(a808) | c0_1(a808))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a808) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c0_1(a808))),
% 1.68/1.90 inference(transitivity,[status(thm)],[3202, 3200])).
% 1.68/1.90 tff(3204,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a808) | c1_1(a808) | c0_1(a808))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(3205,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a808) | c2_1(a808) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c0_1(a808)),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[3204, 3203])).
% 1.68/1.90 tff(3206,plain,
% 1.68/1.90 (hskp0),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3205, 130, 3196, 3195, 3199, 3194, 3053, 1338, 3198])).
% 1.68/1.90 tff(3207,plain,
% 1.68/1.90 (~c1_1(a793)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[603, 3206])).
% 1.68/1.90 tff(3208,plain,
% 1.68/1.90 ((~c0_1(a832)) | c3_1(a833)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2580, 130, 3197, 288, 276, 289, 22, 3199, 3194, 795])).
% 1.68/1.90 tff(3209,plain,
% 1.68/1.90 (~c0_1(a832)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3208, 277])).
% 1.68/1.90 tff(3210,plain,
% 1.68/1.90 (hskp15 | (~c2_1(a832)) | c0_1(a832)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2571, 130, 2435, 2409, 2401, 22, 1210])).
% 1.68/1.90 tff(3211,plain,
% 1.68/1.90 (hskp15),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3210, 3209, 3163])).
% 1.68/1.90 tff(3212,plain,
% 1.68/1.90 (~c1_1(a817)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[1252, 3211])).
% 1.68/1.90 tff(3213,plain,
% 1.68/1.90 (c3_1(a817)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[1260, 3211])).
% 1.68/1.90 tff(3214,plain,
% 1.68/1.90 (c2_1(a817)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[1268, 3211])).
% 1.68/1.90 tff(3215,plain,
% 1.68/1.90 (c0_1(a793)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[611, 3206])).
% 1.68/1.90 tff(3216,plain,
% 1.68/1.90 (c2_1(a793)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[597, 3206])).
% 1.68/1.90 tff(3217,plain,
% 1.68/1.90 ($false),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[2716, 3216, 3215, 3051, 277, 3214, 3213, 288, 3212, 3197, 276, 3199, 3194, 3207])).
% 1.68/1.90 tff(3218,plain,(c3_1(a833) | c0_1(a833) | c2_1(a833) | c3_1(a832) | c1_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.90 tff(3219,plain,
% 1.68/1.90 (c3_1(a833)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3218, 289, 276, 22, 288])).
% 1.68/1.90 tff(3220,plain,
% 1.68/1.90 (c0_1(a832)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3169, 3219, 22, 288, 276, 289])).
% 1.68/1.90 tff(3221,plain,
% 1.68/1.90 (c0_1(a797)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3172, 3220, 276, 22, 288, 3219])).
% 1.68/1.90 tff(3222,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3223,plain,
% 1.68/1.90 ((hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832))) <=> (hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3224,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832))))),
% 1.68/1.90 inference(monotonicity,[status(thm)],[3223])).
% 1.68/1.90 tff(3225,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.68/1.90 inference(transitivity,[status(thm)],[3224, 3222])).
% 1.68/1.90 tff(3226,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))),
% 1.68/1.90 inference(quant_inst,[status(thm)],[])).
% 1.68/1.90 tff(3227,plain,
% 1.68/1.90 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832))),
% 1.68/1.90 inference(modus_ponens,[status(thm)],[3226, 3225])).
% 1.68/1.90 tff(3228,plain,
% 1.68/1.90 (hskp5 | (~c0_1(a797)) | (~c2_1(a832)) | (~c0_1(a832))),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3227, 130, 2435, 2401, 22, 190])).
% 1.68/1.90 tff(3229,plain,
% 1.68/1.90 (hskp5),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[3228, 3221, 3163, 3220])).
% 1.68/1.90 tff(3230,plain,
% 1.68/1.90 (~c1_1(a800)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[233, 3229])).
% 1.68/1.90 tff(3231,plain,
% 1.68/1.90 (~c0_1(a800)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[202, 3229])).
% 1.68/1.90 tff(3232,plain,
% 1.68/1.90 (c3_1(a800)),
% 1.68/1.90 inference(unit_resolution,[status(thm)],[210, 3229])).
% 1.68/1.90 tff(3233,plain,
% 1.68/1.90 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a833) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.90 inference(rewrite,[status(thm)],[])).
% 1.68/1.90 tff(3234,plain,
% 1.68/1.90 ((hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (hskp6 | c2_1(a833) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3235,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a833) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[3234])).
% 1.68/1.91 tff(3236,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.91 inference(transitivity,[status(thm)],[3235, 3233])).
% 1.68/1.91 tff(3237,plain,
% 1.68/1.91 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(3238,plain,
% 1.68/1.91 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[3237, 3236])).
% 1.68/1.91 tff(3239,plain,
% 1.68/1.91 (hskp6),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3238, 130, 3051, 3232, 276, 3231, 3230, 1853, 3219])).
% 1.68/1.91 tff(3240,plain,
% 1.68/1.91 (~c0_1(a802)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1873, 3239])).
% 1.68/1.91 tff(3241,plain,
% 1.68/1.91 (c2_1(a802)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1881, 3239])).
% 1.68/1.91 tff(3242,plain,
% 1.68/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c3_1(a802)) | (~c2_1(a802)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3243,plain,
% 1.68/1.91 (((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802))) <=> (c0_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c3_1(a802)) | (~c2_1(a802)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3244,plain,
% 1.68/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c3_1(a802)) | (~c2_1(a802))))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[3243])).
% 1.68/1.91 tff(3245,plain,
% 1.68/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c3_1(a802)) | (~c2_1(a802)))),
% 1.68/1.91 inference(transitivity,[status(thm)],[3244, 3242])).
% 1.68/1.91 tff(3246,plain,
% 1.68/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c2_1(a797)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(3247,plain,
% 1.68/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c3_1(a802)) | (~c2_1(a802))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[3246, 3245])).
% 1.68/1.91 tff(3248,plain,
% 1.68/1.91 (~c3_1(a802)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3247, 130, 2435, 2409, 2401, 3241, 3240, 180, 3221])).
% 1.68/1.91 tff(3249,plain,
% 1.68/1.91 (hskp12),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2681, 130, 3241, 288, 276, 3240, 989, 3219, 3248])).
% 1.68/1.91 tff(3250,plain,
% 1.68/1.91 (~c0_1(a809)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[143, 3249])).
% 1.68/1.91 tff(3251,plain,
% 1.68/1.91 (c2_1(a809)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[152, 3249])).
% 1.68/1.91 tff(3252,plain,
% 1.68/1.91 (c1_1(a809)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[160, 3249])).
% 1.68/1.91 tff(3253,plain,
% 1.68/1.91 ($false),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2740, 130, 3163, 3252, 3251, 288, 276, 22, 3250, 2503, 3220, 3219])).
% 1.68/1.91 tff(3254,plain,(c1_1(a832) | c0_1(a833) | c2_1(a833) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.91 tff(3255,plain,
% 1.68/1.91 (c1_1(a832)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3254, 22, 276, 288])).
% 1.68/1.91 tff(3256,plain,
% 1.68/1.91 (~hskp19),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[352, 3255])).
% 1.68/1.91 tff(3257,plain,
% 1.68/1.91 (hskp27),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2464, 3256])).
% 1.68/1.91 tff(3258,plain,
% 1.68/1.91 (c3_1(a796)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[531, 3257])).
% 1.68/1.91 tff(3259,plain,
% 1.68/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3260,plain,
% 1.68/1.91 (((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3261,plain,
% 1.68/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[3260])).
% 1.68/1.91 tff(3262,plain,
% 1.68/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.68/1.91 inference(transitivity,[status(thm)],[3261, 3259])).
% 1.68/1.91 tff(3263,plain,
% 1.68/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(3264,plain,
% 1.68/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[3263, 3262])).
% 1.68/1.91 tff(3265,plain,
% 1.68/1.91 ((~c1_1(a832)) | (~c2_1(a832)) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3264, 130, 288, 276, 22, 1961])).
% 1.68/1.91 tff(3266,plain,
% 1.68/1.91 (~c3_1(a833)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3265, 3255, 3051, 3163])).
% 1.68/1.91 tff(3267,plain,
% 1.68/1.91 (c0_1(a796)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[547, 3257])).
% 1.68/1.91 tff(3268,plain,
% 1.68/1.91 (c2_1(a796)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[539, 3257])).
% 1.68/1.91 tff(3269,plain,
% 1.68/1.91 (~hskp21),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3090, 3268, 3267, 276, 3051, 3266, 3258, 288])).
% 1.68/1.91 tff(3270,plain,
% 1.68/1.91 (hskp11),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2442, 3269])).
% 1.68/1.91 tff(3271,plain,
% 1.68/1.91 (c3_1(a808)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[812, 3270])).
% 1.68/1.91 tff(3272,plain,
% 1.68/1.91 (~c2_1(a808)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[776, 3270])).
% 1.68/1.91 tff(3273,plain,
% 1.68/1.91 (hskp18),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3157, 3271, 3269, 3272])).
% 1.68/1.91 tff(3274,plain,
% 1.68/1.91 ($false),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3160, 3273, 3272, 276, 3256, 288, 3051, 3271])).
% 1.68/1.91 tff(3275,plain,(c3_1(a832) | c2_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.91 tff(3276,plain,
% 1.68/1.91 (c3_1(a832)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3275, 288, 276])).
% 1.68/1.91 tff(3277,plain,
% 1.68/1.91 (~hskp19),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[346, 3276])).
% 1.68/1.91 tff(3278,plain,
% 1.68/1.91 (hskp27),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2464, 3277])).
% 1.68/1.91 tff(3279,plain,
% 1.68/1.91 (c3_1(a796)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[531, 3278])).
% 1.68/1.91 tff(3280,plain,
% 1.68/1.91 (~hskp21),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2807, 2805, 308])).
% 1.68/1.91 tff(3281,plain,
% 1.68/1.91 (hskp11),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2442, 3280])).
% 1.68/1.91 tff(3282,plain,
% 1.68/1.91 (~c2_1(a808)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[776, 3281])).
% 1.68/1.91 tff(3283,plain,
% 1.68/1.91 (c3_1(a808)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[812, 3281])).
% 1.68/1.91 tff(3284,plain,
% 1.68/1.91 (~c0_1(a808)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1431, 130, 308, 2805, 3283, 3282, 21])).
% 1.68/1.91 tff(3285,plain,
% 1.68/1.91 (c2_1(a867)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2918, 130, 308, 2805, 2770, 2768, 21])).
% 1.68/1.91 tff(3286,plain,
% 1.68/1.91 (~c1_1(a808)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[770, 3281])).
% 1.68/1.91 tff(3287,plain,
% 1.68/1.91 (hskp7 | c0_1(a808)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1422, 130, 2769, 2768, 3283, 3286, 1413, 3285])).
% 1.68/1.91 tff(3288,plain,
% 1.68/1.91 (hskp7),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3287, 3284])).
% 1.68/1.91 tff(3289,plain,
% 1.68/1.91 (~c2_1(a803)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1377, 3288])).
% 1.68/1.91 tff(3290,plain,
% 1.68/1.91 (hskp18),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3157, 3283, 3280, 3282])).
% 1.68/1.91 tff(3291,plain,
% 1.68/1.91 (~c3_1(a828)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1107, 3290])).
% 1.68/1.91 tff(3292,plain,
% 1.68/1.91 (~c2_1(a828)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1101, 3290])).
% 1.68/1.91 tff(3293,plain,
% 1.68/1.91 (~c1_1(a828)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1113, 3290])).
% 1.68/1.91 tff(3294,plain,
% 1.68/1.91 (c3_1(a803)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1385, 3288])).
% 1.68/1.91 tff(3295,plain,
% 1.68/1.91 (c1_1(a803)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1393, 3288])).
% 1.68/1.91 tff(3296,plain,
% 1.68/1.91 ($false),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1707, 130, 3277, 3295, 3294, 3293, 3292, 3291, 3289, 10])).
% 1.68/1.91 tff(3297,plain,(c1_1(a833) | c2_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.91 tff(3298,plain,
% 1.68/1.91 (c1_1(a833)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3297, 288, 276])).
% 1.68/1.91 tff(3299,plain,
% 1.68/1.91 (c2_1(a796)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[539, 3278])).
% 1.68/1.91 tff(3300,plain,
% 1.68/1.91 (c0_1(a796)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[547, 3278])).
% 1.68/1.91 tff(3301,plain,
% 1.68/1.91 (hskp18),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3157, 2446, 629, 2444])).
% 1.68/1.91 tff(3302,plain,
% 1.68/1.91 ($false),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3160, 3301, 2444, 276, 3277, 288, 3298, 2446])).
% 1.68/1.91 tff(3303,plain,(hskp21 | c2_1(a833) | c0_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.68/1.91 tff(3304,plain,
% 1.68/1.91 (hskp21),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3303, 288, 276])).
% 1.68/1.91 tff(3305,plain,
% 1.68/1.91 (c3_1(a833)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3090, 3304, 3300, 276, 3299, 3298, 3279, 288])).
% 1.68/1.91 tff(3306,plain,
% 1.68/1.91 (c0_1(a838)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[406, 3304])).
% 1.68/1.91 tff(3307,plain,
% 1.68/1.91 (~c2_1(a838)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[389, 3304])).
% 1.68/1.91 tff(3308,plain,
% 1.68/1.91 (c3_1(a838)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[398, 3304])).
% 1.68/1.91 tff(3309,assumption,(c0_1(a797)), introduced(assumption)).
% 1.68/1.91 tff(3310,assumption,(hskp26), introduced(assumption)).
% 1.68/1.91 tff(3311,plain,
% 1.68/1.91 (~c0_1(a869)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[700, 3310])).
% 1.68/1.91 tff(3312,plain,
% 1.68/1.91 (c3_1(a869)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[652, 3310])).
% 1.68/1.91 tff(3313,plain,
% 1.68/1.91 (c2_1(a869)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[660, 3310])).
% 1.68/1.91 tff(3314,plain,
% 1.68/1.91 ($false),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3190, 130, 2435, 2409, 2401, 3313, 3312, 3311, 180, 3309])).
% 1.68/1.91 tff(3315,plain,((~hskp26) | (~c0_1(a797))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.91 tff(3316,plain,
% 1.68/1.91 (~hskp26),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3315, 3309])).
% 1.68/1.91 tff(3317,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a798) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c0_1(a798)) | (~c2_1(a798)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a798) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c0_1(a798)) | (~c2_1(a798)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3318,plain,
% 1.68/1.91 ((hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a798) | (~c0_1(a798)) | (~c2_1(a798))) <=> (hskp5 | c3_1(a798) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c0_1(a798)) | (~c2_1(a798)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3319,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a798) | (~c0_1(a798)) | (~c2_1(a798)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a798) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c0_1(a798)) | (~c2_1(a798))))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[3318])).
% 1.68/1.91 tff(3320,plain,
% 1.68/1.91 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a798) | (~c0_1(a798)) | (~c2_1(a798)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a798) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c0_1(a798)) | (~c2_1(a798)))),
% 1.68/1.91 inference(transitivity,[status(thm)],[3319, 3317])).
% 1.68/1.91 tff(3321,plain,
% 1.68/1.91 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a798) | (~c0_1(a798)) | (~c2_1(a798)))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(3322,plain,
% 1.68/1.91 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a798) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | (~c0_1(a798)) | (~c2_1(a798))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[3321, 3320])).
% 1.68/1.91 tff(3323,plain,
% 1.68/1.91 (hskp5),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3322, 130, 2435, 2401, 3139, 3138, 3137, 190, 3309])).
% 1.68/1.91 tff(3324,plain,
% 1.68/1.91 (~c1_1(a800)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[233, 3323])).
% 1.68/1.91 tff(3325,plain,
% 1.68/1.91 (~c0_1(a800)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[202, 3323])).
% 1.68/1.91 tff(3326,plain,
% 1.68/1.91 (c3_1(a800)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[210, 3323])).
% 1.68/1.91 tff(3327,plain,
% 1.68/1.91 (hskp6),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3238, 130, 3298, 3326, 276, 3325, 3324, 1853, 3305])).
% 1.68/1.91 tff(3328,plain,
% 1.68/1.91 (~c0_1(a802)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1873, 3327])).
% 1.68/1.91 tff(3329,plain,
% 1.68/1.91 (c2_1(a802)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[1881, 3327])).
% 1.68/1.91 tff(3330,plain,
% 1.68/1.91 (~c3_1(a802)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3247, 130, 2435, 2409, 2401, 3329, 3328, 180, 3309])).
% 1.68/1.91 tff(3331,plain,
% 1.68/1.91 (hskp12),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[2681, 130, 3329, 288, 276, 3328, 989, 3305, 3330])).
% 1.68/1.91 tff(3332,plain,
% 1.68/1.91 (~c0_1(a809)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[143, 3331])).
% 1.68/1.91 tff(3333,plain,
% 1.68/1.91 (c2_1(a809)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[152, 3331])).
% 1.68/1.91 tff(3334,plain,
% 1.68/1.91 (c1_1(a809)),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[160, 3331])).
% 1.68/1.91 tff(3335,plain,
% 1.68/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c0_1(a809) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c0_1(a809) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a833)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3336,plain,
% 1.68/1.91 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | c0_1(a809) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a833)))),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3337,plain,
% 1.68/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c0_1(a809) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a833))))),
% 1.68/1.91 inference(monotonicity,[status(thm)],[3336])).
% 1.68/1.91 tff(3338,plain,
% 1.68/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c0_1(a809) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a833)))),
% 1.68/1.91 inference(transitivity,[status(thm)],[3337, 3335])).
% 1.68/1.91 tff(3339,plain,
% 1.68/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c0_1(a809) | (~c1_1(a809)) | (~c2_1(a809)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.68/1.91 inference(quant_inst,[status(thm)],[])).
% 1.68/1.91 tff(3340,plain,
% 1.68/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c0_1(a809) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | (~c2_1(a809)) | (~c1_1(a809)) | (~c3_1(a833))),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[3339, 3338])).
% 1.68/1.91 tff(3341,plain,
% 1.68/1.91 ($false),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3340, 130, 3334, 3333, 3139, 3138, 288, 276, 3332, 3137, 2503, 3305])).
% 1.68/1.91 tff(3342,plain,((~hskp3) | c0_1(a833) | c2_1(a833) | (~c0_1(a797))), inference(lemma,lemma(discharge,[]))).
% 1.68/1.91 tff(3343,plain,
% 1.68/1.91 (~hskp3),
% 1.68/1.91 inference(unit_resolution,[status(thm)],[3342, 3309, 276, 288])).
% 1.68/1.91 tff(3344,plain,
% 1.68/1.91 ((hskp26 | hskp9 | hskp3) <=> (hskp26 | hskp9 | hskp3)),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3345,plain,
% 1.68/1.91 (((hskp9 | hskp3) | hskp26) <=> (hskp26 | hskp9 | hskp3)),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3346,plain,
% 1.68/1.91 ((hskp9 | hskp3) <=> (hskp9 | hskp3)),
% 1.68/1.91 inference(rewrite,[status(thm)],[])).
% 1.68/1.91 tff(3347,plain,
% 1.68/1.91 (((hskp9 | hskp3) | hskp26) <=> ((hskp9 | hskp3) | hskp26)),
% 1.68/1.91 inference(monotonicity,[status(thm)],[3346])).
% 1.68/1.91 tff(3348,plain,
% 1.68/1.91 (((hskp9 | hskp3) | hskp26) <=> (hskp26 | hskp9 | hskp3)),
% 1.68/1.91 inference(transitivity,[status(thm)],[3347, 3345])).
% 1.68/1.91 tff(3349,axiom,((hskp9 | hskp3) | hskp26), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 1.68/1.91 tff(3350,plain,
% 1.68/1.91 (hskp26 | hskp9 | hskp3),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[3349, 3348])).
% 1.68/1.91 tff(3351,plain,
% 1.68/1.91 (hskp26 | hskp9 | hskp3),
% 1.68/1.91 inference(modus_ponens,[status(thm)],[3350, 3344])).
% 1.68/1.91 tff(3352,plain,
% 1.75/1.91 (hskp26 | hskp9 | hskp3),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[3351, 3344])).
% 1.75/1.91 tff(3353,plain,
% 1.75/1.91 (hskp26 | hskp9 | hskp3),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[3352, 3344])).
% 1.75/1.91 tff(3354,plain,
% 1.75/1.91 (hskp26 | hskp9 | hskp3),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[3353, 3344])).
% 1.75/1.91 tff(3355,plain,
% 1.75/1.91 (hskp9),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[3354, 3343, 3316])).
% 1.75/1.91 tff(3356,plain,
% 1.75/1.91 (~c3_1(a806)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[63, 3355])).
% 1.75/1.91 tff(3357,plain,
% 1.75/1.91 (c1_1(a806)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[72, 3355])).
% 1.75/1.91 tff(3358,plain,
% 1.75/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(3359,plain,
% 1.75/1.91 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(3360,plain,
% 1.75/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[3359])).
% 1.75/1.91 tff(3361,plain,
% 1.75/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.91 inference(transitivity,[status(thm)],[3360, 3358])).
% 1.75/1.91 tff(3362,plain,
% 1.75/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(3363,plain,
% 1.75/1.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c1_1(a806)) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[3362, 3361])).
% 1.75/1.91 tff(3364,plain,
% 1.75/1.91 (~c2_1(a806)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[3363, 130, 3298, 3357, 288, 276, 3356, 1961, 3305])).
% 1.75/1.91 tff(3365,plain,
% 1.75/1.91 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c2_1(a806) | (~c1_1(a806)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(3366,plain,
% 1.75/1.91 ((hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806))) <=> (hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c2_1(a806) | (~c1_1(a806)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(3367,plain,
% 1.75/1.91 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c2_1(a806) | (~c1_1(a806))))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[3366])).
% 1.75/1.91 tff(3368,plain,
% 1.75/1.91 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c2_1(a806) | (~c1_1(a806)))),
% 1.75/1.91 inference(transitivity,[status(thm)],[3367, 3365])).
% 1.75/1.91 tff(3369,plain,
% 1.75/1.91 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(3370,plain,
% 1.75/1.91 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c0_1(a797)) | c2_1(a806) | (~c1_1(a806))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[3369, 3368])).
% 1.75/1.91 tff(3371,plain,
% 1.75/1.91 (hskp12),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[3370, 130, 2435, 2401, 3357, 3356, 95, 3364, 3309])).
% 1.75/1.91 tff(3372,plain,
% 1.75/1.91 (~c0_1(a809)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[143, 3371])).
% 1.75/1.91 tff(3373,plain,
% 1.75/1.91 (c0_1(a806)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[55, 3355])).
% 1.75/1.91 tff(3374,plain,
% 1.75/1.91 (c2_1(a809)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[152, 3371])).
% 1.75/1.91 tff(3375,plain,
% 1.75/1.91 (c1_1(a809)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[160, 3371])).
% 1.75/1.91 tff(3376,plain,
% 1.75/1.91 ($false),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[167, 130, 3375, 3374, 3373, 3357, 3372, 3356, 84, 3364])).
% 1.75/1.91 tff(3377,plain,((~c0_1(a797)) | c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.91 tff(3378,plain,
% 1.75/1.91 (~c0_1(a797)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[3377, 288, 276])).
% 1.75/1.91 tff(3379,assumption,(hskp6), introduced(assumption)).
% 1.75/1.91 tff(3380,plain,
% 1.75/1.91 (~c1_1(a802)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[2687, 3379])).
% 1.75/1.91 tff(3381,plain,
% 1.75/1.91 (~c0_1(a802)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[1873, 3379])).
% 1.75/1.91 tff(3382,plain,
% 1.75/1.91 (c2_1(a802)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[1881, 3379])).
% 1.75/1.91 tff(3383,plain,
% 1.75/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a802) | c1_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c3_1(a802) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a802) | c1_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c3_1(a802) | (~c2_1(a802)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(3384,plain,
% 1.75/1.91 (((~ndr1_0) | c1_1(a802) | c3_1(a802) | (~c2_1(a802)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a802) | c0_1(a802) | c3_1(a802)) <=> (c0_1(a802) | c1_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c3_1(a802) | (~c2_1(a802)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(3385,plain,
% 1.75/1.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a802) | c3_1(a802) | (~c2_1(a802)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a802) | c0_1(a802) | c3_1(a802))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a802) | c1_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c3_1(a802) | (~c2_1(a802))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[3384])).
% 1.75/1.92 tff(3386,plain,
% 1.75/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a802) | c3_1(a802) | (~c2_1(a802)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a802) | c0_1(a802) | c3_1(a802))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a802) | c1_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c3_1(a802) | (~c2_1(a802)))),
% 1.75/1.92 inference(transitivity,[status(thm)],[3385, 3383])).
% 1.75/1.92 tff(3387,plain,
% 1.75/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a802) | c3_1(a802) | (~c2_1(a802)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a802) | c0_1(a802) | c3_1(a802))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(3388,plain,
% 1.75/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a802) | c1_1(a802) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c3_1(a802) | (~c2_1(a802))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3387, 3386])).
% 1.75/1.92 tff(3389,plain,
% 1.75/1.92 (c3_1(a802)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3388, 130, 2435, 2409, 3382, 3381, 3380, 977, 3111])).
% 1.75/1.92 tff(3390,plain,
% 1.75/1.92 (hskp8),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[2697, 130, 570, 3382, 288, 3380, 687, 669, 3389])).
% 1.75/1.92 tff(3391,plain,
% 1.75/1.92 (~c3_1(a805)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[414, 3390])).
% 1.75/1.92 tff(3392,plain,
% 1.75/1.92 (~c2_1(a805)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[420, 3390])).
% 1.75/1.92 tff(3393,plain,
% 1.75/1.92 (c1_1(a805)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[429, 3390])).
% 1.75/1.92 tff(3394,plain,
% 1.75/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a805)) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a805)) | (~c1_1(a805)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3395,plain,
% 1.75/1.92 (((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797))) <=> (c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a805)) | (~c1_1(a805)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3396,plain,
% 1.75/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a805)) | (~c1_1(a805))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[3395])).
% 1.75/1.92 tff(3397,plain,
% 1.75/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a805)) | (~c1_1(a805)))),
% 1.75/1.92 inference(transitivity,[status(thm)],[3396, 3394])).
% 1.75/1.92 tff(3398,plain,
% 1.75/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a805) | (~c1_1(a805)) | (~c0_1(a805)) | c3_1(a805) | c2_1(a805) | (~c1_1(a805)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(3399,plain,
% 1.75/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a805) | c3_1(a805) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a805)) | (~c1_1(a805))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3398, 3397])).
% 1.75/1.92 tff(3400,plain,
% 1.75/1.92 (~c0_1(a805)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3399, 130, 2435, 2409, 3393, 3392, 3391, 84, 3111])).
% 1.75/1.92 tff(3401,plain,
% 1.75/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a805) | c1_1(a802) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | c1_1(a802) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | (~c1_1(a805)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3402,plain,
% 1.75/1.92 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805))) <=> (c3_1(a805) | c1_1(a802) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | (~c1_1(a805)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3403,plain,
% 1.75/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c3_1(a805) | c1_1(a802) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | (~c1_1(a805))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[3402])).
% 1.75/1.92 tff(3404,plain,
% 1.75/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | c1_1(a802) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | (~c1_1(a805)))),
% 1.75/1.92 inference(transitivity,[status(thm)],[3403, 3401])).
% 1.75/1.92 tff(3405,plain,
% 1.75/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a802) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | c3_1(a805) | (~c1_1(a805)))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(3406,plain,
% 1.75/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c3_1(a805) | c1_1(a802) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c3_1(a802)) | (~c2_1(a802)) | c0_1(a805) | (~c1_1(a805))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3405, 3404])).
% 1.75/1.92 tff(3407,plain,
% 1.75/1.92 ($false),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3406, 130, 615, 613, 618, 3393, 3382, 3391, 3380, 719, 3389, 3400])).
% 1.75/1.92 tff(3408,plain,((~hskp6) | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796)) | c0_1(a797) | (~c1_1(a833)) | c0_1(a833) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.92 tff(3409,plain,
% 1.75/1.92 (~hskp6),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3408, 3378, 3299, 3279, 3300, 3298, 288, 3305])).
% 1.75/1.92 tff(3410,plain,
% 1.75/1.92 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a833) | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3411,plain,
% 1.75/1.92 ((hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a832) | c0_1(a832) | (~c3_1(a832))) <=> (hskp6 | c2_1(a833) | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3412,plain,
% 1.75/1.92 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a832) | c0_1(a832) | (~c3_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a833) | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[3411])).
% 1.75/1.92 tff(3413,plain,
% 1.75/1.92 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a832) | c0_1(a832) | (~c3_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.92 inference(transitivity,[status(thm)],[3412, 3410])).
% 1.75/1.92 tff(3414,plain,
% 1.75/1.92 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c1_1(a832) | c0_1(a832) | (~c3_1(a832)))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(3415,plain,
% 1.75/1.92 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a833) | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3414, 3413])).
% 1.75/1.92 tff(3416,plain,
% 1.75/1.92 (c0_1(a832)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3415, 130, 3409, 3298, 276, 289, 3276, 1853, 3305])).
% 1.75/1.92 tff(3417,plain,
% 1.75/1.92 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.75/1.92 inference(bind,[status(th)],[])).
% 1.75/1.92 tff(3418,plain,
% 1.75/1.92 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.75/1.92 inference(quant_intro,[status(thm)],[3417])).
% 1.75/1.92 tff(3419,plain,
% 1.75/1.92 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3420,plain,
% 1.75/1.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.75/1.92 inference(bind,[status(th)],[])).
% 1.75/1.92 tff(3421,plain,
% 1.75/1.92 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.75/1.92 inference(quant_intro,[status(thm)],[3420])).
% 1.75/1.92 tff(3422,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.75/1.92 tff(3423,plain,
% 1.75/1.92 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3422, 3421])).
% 1.75/1.92 tff(3424,plain,
% 1.75/1.92 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3423, 3419])).
% 1.75/1.92 tff(3425,plain,(
% 1.75/1.92 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.75/1.92 inference(skolemize,[status(sab)],[3424])).
% 1.75/1.92 tff(3426,plain,
% 1.75/1.92 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3425, 3418])).
% 1.75/1.92 tff(3427,assumption,(c3_1(a832)), introduced(assumption)).
% 1.75/1.92 tff(3428,assumption,(~hskp13), introduced(assumption)).
% 1.75/1.92 tff(3429,plain,
% 1.75/1.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3430,plain,
% 1.75/1.92 ((hskp13 | (~ndr1_0) | c1_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797))) <=> (hskp13 | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3431,plain,
% 1.75/1.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[3430])).
% 1.75/1.92 tff(3432,plain,
% 1.75/1.92 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832)))),
% 1.75/1.92 inference(transitivity,[status(thm)],[3431, 3429])).
% 1.75/1.92 tff(3433,plain,
% 1.75/1.92 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(3434,plain,
% 1.75/1.92 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | c1_1(a832) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c0_1(a832))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3433, 3432])).
% 1.75/1.92 tff(3435,plain,
% 1.75/1.92 ($false),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3434, 130, 3428, 2435, 2409, 289, 3427, 3426, 408, 3111])).
% 1.75/1.92 tff(3436,plain,(c0_1(a797) | hskp13 | c1_1(a832) | (~c3_1(a832)) | (~c0_1(a832))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.92 tff(3437,plain,
% 1.75/1.92 (hskp13),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3436, 3416, 3378, 3276, 289])).
% 1.75/1.92 tff(3438,plain,
% 1.75/1.92 (((~hskp13) | (~c3_1(a814))) <=> ((~hskp13) | (~c3_1(a814)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3439,plain,
% 1.75/1.92 (((~c3_1(a814)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a814)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3440,axiom,((~c3_1(a814)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.75/1.92 tff(3441,plain,
% 1.75/1.92 ((~hskp13) | (~c3_1(a814))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3440, 3439])).
% 1.75/1.92 tff(3442,plain,
% 1.75/1.92 ((~hskp13) | (~c3_1(a814))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3441, 3438])).
% 1.75/1.92 tff(3443,plain,
% 1.75/1.92 (~c3_1(a814)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3442, 3437])).
% 1.75/1.92 tff(3444,plain,
% 1.75/1.92 (((~hskp13) | (~c0_1(a814))) <=> ((~hskp13) | (~c0_1(a814)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3445,plain,
% 1.75/1.92 (((~c0_1(a814)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a814)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3446,axiom,((~c0_1(a814)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.75/1.92 tff(3447,plain,
% 1.75/1.92 ((~hskp13) | (~c0_1(a814))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3446, 3445])).
% 1.75/1.92 tff(3448,plain,
% 1.75/1.92 ((~hskp13) | (~c0_1(a814))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3447, 3444])).
% 1.75/1.92 tff(3449,plain,
% 1.75/1.92 (~c0_1(a814)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3448, 3437])).
% 1.75/1.92 tff(3450,plain,
% 1.75/1.92 (((~hskp13) | c1_1(a814)) <=> ((~hskp13) | c1_1(a814))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3451,axiom,((~hskp13) | c1_1(a814)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.75/1.92 tff(3452,plain,
% 1.75/1.92 ((~hskp13) | c1_1(a814)),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3451, 3450])).
% 1.75/1.92 tff(3453,plain,
% 1.75/1.92 ((~hskp13) | c1_1(a814)),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3452, 3450])).
% 1.75/1.92 tff(3454,plain,
% 1.75/1.92 ((~hskp13) | c1_1(a814)),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3453, 3450])).
% 1.75/1.92 tff(3455,plain,
% 1.75/1.92 ((~hskp13) | c1_1(a814)),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3454, 3450])).
% 1.75/1.92 tff(3456,plain,
% 1.75/1.92 ((~hskp13) | c1_1(a814)),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3455, 3450])).
% 1.75/1.92 tff(3457,plain,
% 1.75/1.92 (c1_1(a814)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3456, 3437])).
% 1.75/1.92 tff(3458,assumption,(hskp13), introduced(assumption)).
% 1.75/1.92 tff(3459,plain,
% 1.75/1.92 (~c3_1(a814)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3442, 3458])).
% 1.75/1.92 tff(3460,plain,
% 1.75/1.92 (c1_1(a814)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3456, 3458])).
% 1.75/1.92 tff(3461,plain,
% 1.75/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3462,plain,
% 1.75/1.92 (((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833))) <=> (c0_1(a833) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3463,plain,
% 1.75/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a833) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[3462])).
% 1.75/1.92 tff(3464,plain,
% 1.75/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.92 inference(transitivity,[status(thm)],[3463, 3461])).
% 1.75/1.92 tff(3465,plain,
% 1.75/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a833) | c0_1(a833) | (~c3_1(a833)))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(3466,plain,
% 1.75/1.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a833) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3465, 3464])).
% 1.75/1.92 tff(3467,plain,
% 1.75/1.92 (~c2_1(a814)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3466, 130, 3298, 3460, 288, 276, 3459, 1961, 3305])).
% 1.75/1.92 tff(3468,plain,
% 1.75/1.92 (~c0_1(a814)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3448, 3458])).
% 1.75/1.92 tff(3469,plain,
% 1.75/1.92 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a814) | c3_1(a814) | (~ndr1_0) | c2_1(a814) | (~c1_1(a814)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a814) | c3_1(a814) | (~ndr1_0) | c2_1(a814) | (~c1_1(a814)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3470,plain,
% 1.75/1.92 ((hskp3 | (~ndr1_0) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)) | c3_1(a814) | c0_1(a814) | (~c1_1(a814))) <=> (hskp3 | c0_1(a814) | c3_1(a814) | (~ndr1_0) | c2_1(a814) | (~c1_1(a814)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3471,plain,
% 1.75/1.92 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)) | c3_1(a814) | c0_1(a814) | (~c1_1(a814)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | c0_1(a814) | c3_1(a814) | (~ndr1_0) | c2_1(a814) | (~c1_1(a814))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[3470])).
% 1.75/1.92 tff(3472,plain,
% 1.75/1.92 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)) | c3_1(a814) | c0_1(a814) | (~c1_1(a814)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a814) | c3_1(a814) | (~ndr1_0) | c2_1(a814) | (~c1_1(a814)))),
% 1.75/1.92 inference(transitivity,[status(thm)],[3471, 3469])).
% 1.75/1.92 tff(3473,plain,
% 1.75/1.92 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)) | c3_1(a814) | c0_1(a814) | (~c1_1(a814)))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(3474,plain,
% 1.75/1.92 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp3 | c0_1(a814) | c3_1(a814) | (~ndr1_0) | c2_1(a814) | (~c1_1(a814))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[3473, 3472])).
% 1.75/1.92 tff(3475,plain,
% 1.75/1.92 (hskp3),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[3474, 130, 3460, 3468, 3459, 2514, 3467])).
% 1.75/1.92 tff(3476,plain,
% 1.75/1.92 (~c3_1(a798)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[492, 3475])).
% 1.75/1.92 tff(3477,plain,
% 1.75/1.92 (c2_1(a798)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[506, 3475])).
% 1.75/1.92 tff(3478,plain,
% 1.75/1.92 (c0_1(a798)),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[514, 3475])).
% 1.75/1.92 tff(3479,plain,
% 1.75/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a832) | (~c3_1(a832)) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | (~c3_1(a832)) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c0_1(a832)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3480,plain,
% 1.75/1.92 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814))) <=> (c2_1(a832) | (~c3_1(a832)) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c0_1(a832)))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(3481,plain,
% 1.75/1.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a832) | (~c3_1(a832)) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c0_1(a832))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[3480])).
% 1.75/1.93 tff(3482,plain,
% 1.75/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | (~c3_1(a832)) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c0_1(a832)))),
% 1.75/1.93 inference(transitivity,[status(thm)],[3481, 3479])).
% 1.75/1.93 tff(3483,plain,
% 1.75/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a832) | (~c3_1(a832)) | (~c0_1(a832)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(3484,plain,
% 1.75/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a832) | (~c3_1(a832)) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c0_1(a832))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[3483, 3482])).
% 1.75/1.93 tff(3485,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3484, 130, 1362, 3460, 3478, 3477, 3276, 3459, 3476, 299, 408, 3467])).
% 1.75/1.93 tff(3486,plain,((~hskp13) | c2_1(a832) | (~c0_1(a832)) | c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(3487,plain,
% 1.75/1.93 (c2_1(a832)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3486, 3437, 3416, 288, 276])).
% 1.75/1.93 tff(3488,plain,
% 1.75/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a832) | (~c3_1(a832)) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a814)) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a832) | (~c3_1(a832)) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a814)) | (~c2_1(a832)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3489,plain,
% 1.75/1.93 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a832) | (~c3_1(a832)) | (~c2_1(a832)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814))) <=> (c1_1(a832) | (~c3_1(a832)) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a814)) | (~c2_1(a832)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3490,plain,
% 1.75/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a832) | (~c3_1(a832)) | (~c2_1(a832)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a832) | (~c3_1(a832)) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a814)) | (~c2_1(a832))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[3489])).
% 1.75/1.93 tff(3491,plain,
% 1.75/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a832) | (~c3_1(a832)) | (~c2_1(a832)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a832) | (~c3_1(a832)) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a814)) | (~c2_1(a832)))),
% 1.75/1.93 inference(transitivity,[status(thm)],[3490, 3488])).
% 1.75/1.93 tff(3492,plain,
% 1.75/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a832) | (~c3_1(a832)) | (~c2_1(a832)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814)))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(3493,plain,
% 1.75/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a832) | (~c3_1(a832)) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a814)) | (~c2_1(a832))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[3492, 3491])).
% 1.75/1.93 tff(3494,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3493, 130, 3300, 3299, 3279, 3487, 3457, 289, 3276, 3449, 3443, 719])).
% 1.75/1.93 tff(3495,plain,(c1_1(a832) | c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(3496,plain,
% 1.75/1.93 (c1_1(a832)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3495, 288, 276])).
% 1.75/1.93 tff(3497,plain,
% 1.75/1.93 (~hskp19),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[346, 3427])).
% 1.75/1.93 tff(3498,plain,
% 1.75/1.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3499,plain,
% 1.75/1.93 ((hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3500,plain,
% 1.75/1.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0)))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[3499])).
% 1.75/1.93 tff(3501,plain,
% 1.75/1.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0))),
% 1.75/1.93 inference(transitivity,[status(thm)],[3500, 3498])).
% 1.75/1.93 tff(3502,plain,
% 1.75/1.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(3503,plain,
% 1.75/1.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a828) | c2_1(a828) | c3_1(a828) | (~ndr1_0)),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[3502, 3501])).
% 1.75/1.93 tff(3504,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3503, 130, 3497, 1362, 3110, 3427, 2253, 2252, 2251, 10])).
% 1.75/1.93 tff(3505,plain,((~hskp18) | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(3506,plain,
% 1.75/1.93 (~hskp18),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3505, 1362, 3496, 3276])).
% 1.75/1.93 tff(3507,plain,
% 1.75/1.93 (^[U: $i] : refl((hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.75/1.93 inference(bind,[status(th)],[])).
% 1.75/1.93 tff(3508,plain,
% 1.75/1.93 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.75/1.93 inference(quant_intro,[status(thm)],[3507])).
% 1.75/1.93 tff(3509,plain,
% 1.75/1.93 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3510,plain,
% 1.75/1.93 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp18) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp18) <=> (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.75/1.93 inference(bind,[status(th)],[])).
% 1.75/1.93 tff(3511,plain,
% 1.75/1.93 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp18) <=> ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.75/1.93 inference(quant_intro,[status(thm)],[3510])).
% 1.75/1.93 tff(3512,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 1.75/1.93 tff(3513,plain,
% 1.75/1.93 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[3512, 3511])).
% 1.75/1.93 tff(3514,plain,
% 1.75/1.93 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[3513, 3509])).
% 1.75/1.93 tff(3515,plain,(
% 1.75/1.93 ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.75/1.93 inference(skolemize,[status(sab)],[3514])).
% 1.75/1.93 tff(3516,plain,
% 1.75/1.93 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[3515, 3508])).
% 1.75/1.93 tff(3517,plain,
% 1.75/1.93 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3518,plain,
% 1.75/1.93 ((hskp18 | hskp14 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833))) <=> (hskp18 | hskp14 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3519,plain,
% 1.75/1.93 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[3518])).
% 1.75/1.93 tff(3520,plain,
% 1.75/1.93 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.93 inference(transitivity,[status(thm)],[3519, 3517])).
% 1.75/1.93 tff(3521,plain,
% 1.75/1.93 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(3522,plain,
% 1.75/1.93 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c0_1(a833) | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[3521, 3520])).
% 1.75/1.93 tff(3523,plain,
% 1.75/1.93 (hskp18 | hskp14 | (~c3_1(a833)) | (~c1_1(a833))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3522, 130, 288, 3516])).
% 1.75/1.93 tff(3524,plain,
% 1.75/1.93 (hskp14),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3523, 3506, 3298, 3305])).
% 1.75/1.93 tff(3525,assumption,(hskp14), introduced(assumption)).
% 1.75/1.93 tff(3526,plain,
% 1.75/1.93 (~c1_1(a816)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[2993, 3525])).
% 1.75/1.93 tff(3527,plain,
% 1.75/1.93 (~c2_1(a816)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3014, 3525])).
% 1.75/1.93 tff(3528,assumption,(~c3_1(a816)), introduced(assumption)).
% 1.75/1.93 tff(3529,assumption,(~c2_1(a816)), introduced(assumption)).
% 1.75/1.93 tff(3530,assumption,(~c1_1(a816)), introduced(assumption)).
% 1.75/1.93 tff(3531,plain,
% 1.75/1.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3532,plain,
% 1.75/1.93 ((hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a816) | c2_1(a816) | c1_1(a816)) <=> (hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3533,plain,
% 1.75/1.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a816) | c2_1(a816) | c1_1(a816))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816)))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[3532])).
% 1.75/1.93 tff(3534,plain,
% 1.75/1.93 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a816) | c2_1(a816) | c1_1(a816))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816))),
% 1.75/1.93 inference(transitivity,[status(thm)],[3533, 3531])).
% 1.75/1.93 tff(3535,plain,
% 1.75/1.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a832) | (~c3_1(a832)) | (~c1_1(a832)) | c3_1(a816) | c2_1(a816) | c1_1(a816))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(3536,plain,
% 1.75/1.93 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816)),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[3535, 3534])).
% 1.75/1.93 tff(3537,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3536, 130, 3497, 1362, 3110, 3427, 3530, 3529, 10, 3528])).
% 1.75/1.93 tff(3538,plain,(c3_1(a816) | c2_1(a832) | (~c1_1(a832)) | (~c3_1(a832)) | c1_1(a816) | c2_1(a816)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(3539,plain,
% 1.75/1.93 (c3_1(a816)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3538, 3527, 3110, 3427, 3526, 1362])).
% 1.75/1.93 tff(3540,plain,
% 1.75/1.93 (c0_1(a816)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3001, 3525])).
% 1.75/1.93 tff(3541,plain,
% 1.75/1.93 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | c1_1(a816) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | c1_1(a816) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a816)) | (~c0_1(a816)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3542,plain,
% 1.75/1.93 ((hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797))) <=> (hskp13 | c1_1(a816) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a816)) | (~c0_1(a816)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3543,plain,
% 1.75/1.93 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | c1_1(a816) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a816)) | (~c0_1(a816))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[3542])).
% 1.75/1.93 tff(3544,plain,
% 1.75/1.93 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | c1_1(a816) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a816)) | (~c0_1(a816)))),
% 1.75/1.93 inference(transitivity,[status(thm)],[3543, 3541])).
% 1.75/1.93 tff(3545,plain,
% 1.75/1.93 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(3546,plain,
% 1.75/1.93 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | c1_1(a816) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c3_1(a816)) | (~c0_1(a816))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[3545, 3544])).
% 1.75/1.93 tff(3547,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3546, 130, 3428, 2435, 2409, 3540, 3526, 3426, 3111, 3539])).
% 1.75/1.93 tff(3548,plain,((~hskp14) | hskp13 | c0_1(a797) | (~c1_1(a832)) | (~c3_1(a832)) | c2_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(3549,plain,
% 1.75/1.93 (hskp13),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3548, 3524, 3378, 3496, 3276, 1362])).
% 1.75/1.93 tff(3550,plain,
% 1.75/1.93 (~c0_1(a832)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3486, 3549, 1362, 288, 276])).
% 1.75/1.93 tff(3551,plain,
% 1.75/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3552,plain,
% 1.75/1.93 (((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a832) | c0_1(a832) | (~c3_1(a832))) <=> (c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3553,plain,
% 1.75/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a832) | c0_1(a832) | (~c3_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[3552])).
% 1.75/1.93 tff(3554,plain,
% 1.75/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a832) | c0_1(a832) | (~c3_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.93 inference(transitivity,[status(thm)],[3553, 3551])).
% 1.75/1.93 tff(3555,plain,
% 1.75/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a814) | (~c1_1(a814)) | (~c2_1(a814)) | c0_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c2_1(a832) | c0_1(a832) | (~c3_1(a832)))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(3556,plain,
% 1.75/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c3_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[3555, 3554])).
% 1.75/1.93 tff(3557,plain,
% 1.75/1.93 (~c2_1(a814)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3556, 130, 570, 1362, 3460, 288, 3427, 3459, 1961, 979, 669])).
% 1.75/1.93 tff(3558,plain,
% 1.75/1.93 (hskp3),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3474, 130, 3460, 3468, 3459, 2514, 3557])).
% 1.75/1.93 tff(3559,plain,
% 1.75/1.93 (~c3_1(a798)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[492, 3558])).
% 1.75/1.93 tff(3560,plain,
% 1.75/1.93 (c2_1(a798)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[506, 3558])).
% 1.75/1.93 tff(3561,plain,
% 1.75/1.93 (c0_1(a798)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[514, 3558])).
% 1.75/1.93 tff(3562,plain,
% 1.75/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c3_1(a838)) | (~c0_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3563,plain,
% 1.75/1.93 (((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814))) <=> (c2_1(a838) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(3564,plain,
% 1.75/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a838) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c3_1(a838)) | (~c0_1(a838))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[3563])).
% 1.75/1.93 tff(3565,plain,
% 1.75/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c3_1(a838)) | (~c0_1(a838)))),
% 1.75/1.93 inference(transitivity,[status(thm)],[3564, 3562])).
% 1.75/1.93 tff(3566,plain,
% 1.75/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a798) | (~c2_1(a798)) | (~c0_1(a798)) | c2_1(a838) | (~c3_1(a838)) | (~c0_1(a838)) | c2_1(a814) | c3_1(a814) | (~c1_1(a814)))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(3567,plain,
% 1.75/1.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a838) | c3_1(a814) | c3_1(a798) | (~ndr1_0) | (~c0_1(a798)) | (~c2_1(a798)) | c2_1(a814) | (~c1_1(a814)) | (~c3_1(a838)) | (~c0_1(a838))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[3566, 3565])).
% 1.75/1.93 tff(3568,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3567, 130, 432, 431, 3460, 3561, 3560, 422, 3459, 3559, 299, 3557])).
% 1.75/1.93 tff(3569,plain,((~hskp13) | (~c0_1(a838)) | (~c3_1(a838)) | c2_1(a838) | (~c1_1(a833)) | c2_1(a832) | c0_1(a833) | (~c3_1(a832)) | c0_1(a832) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(3570,plain,
% 1.75/1.93 ($false),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3569, 3550, 3549, 3308, 3307, 3298, 1362, 288, 3276, 3306, 3305])).
% 1.75/1.93 tff(3571,plain,(c2_1(a832) | c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.93 tff(3572,plain,
% 1.75/1.93 (c2_1(a832)),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[3571, 288, 276])).
% 1.75/1.93 tff(3573,plain,
% 1.75/1.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~c1_1(a832)) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~c1_1(a832)) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3574,plain,
% 1.75/1.94 (((~ndr1_0) | (~c3_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c2_1(a832)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797))) <=> ((~c1_1(a832)) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3575,plain,
% 1.75/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c2_1(a832)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~c1_1(a832)) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832))))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[3574])).
% 1.75/1.94 tff(3576,plain,
% 1.75/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c2_1(a832)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~c1_1(a832)) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.75/1.94 inference(transitivity,[status(thm)],[3575, 3573])).
% 1.75/1.94 tff(3577,plain,
% 1.75/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c1_1(a832)) | (~c0_1(a832)) | (~c2_1(a832)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797)))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(3578,plain,
% 1.75/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~c1_1(a832)) | (~c3_1(a832)) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[3577, 3576])).
% 1.75/1.94 tff(3579,plain,
% 1.75/1.94 ((~c2_1(a832)) | (~c0_1(a832))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3578, 130, 2409, 2401, 3496, 3276, 180, 3378])).
% 1.75/1.94 tff(3580,plain,
% 1.75/1.94 (~c0_1(a832)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3579, 3572])).
% 1.75/1.94 tff(3581,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[2084, 130, 1501, 570, 276, 2253, 2252, 2251, 10, 669])).
% 1.75/1.94 tff(3582,plain,((~hskp18) | hskp19 | (~c1_1(a833)) | c2_1(a833) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(3583,plain,
% 1.75/1.94 (~hskp18),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3582, 3277, 3298, 276, 3305])).
% 1.75/1.94 tff(3584,plain,
% 1.75/1.94 (hskp14),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3523, 3583, 3298, 3305])).
% 1.75/1.94 tff(3585,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~c1_1(a832)) | c1_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | (~c1_1(a832)) | c1_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c2_1(a832)) | c0_1(a832))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3586,plain,
% 1.75/1.94 ((hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a832) | (~c1_1(a832)) | (~c2_1(a832))) <=> (hskp13 | (~c1_1(a832)) | c1_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c2_1(a832)) | c0_1(a832))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3587,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a832) | (~c1_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~c1_1(a832)) | c1_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c2_1(a832)) | c0_1(a832)))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[3586])).
% 1.75/1.94 tff(3588,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a832) | (~c1_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | (~c1_1(a832)) | c1_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c2_1(a832)) | c0_1(a832))),
% 1.75/1.94 inference(transitivity,[status(thm)],[3587, 3585])).
% 1.75/1.94 tff(3589,plain,
% 1.75/1.94 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c0_1(a832) | (~c1_1(a832)) | (~c2_1(a832)))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(3590,plain,
% 1.75/1.94 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp13 | (~c1_1(a832)) | c1_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c2_1(a832)) | c0_1(a832)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[3589, 3588])).
% 1.75/1.94 tff(3591,plain,
% 1.75/1.94 (~c3_1(a816)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3590, 130, 3428, 391, 3540, 3110, 3526, 3426, 979])).
% 1.75/1.94 tff(3592,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a833) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a833) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3593,plain,
% 1.75/1.94 ((hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a816) | c2_1(a816) | c1_1(a816)) <=> (hskp19 | c2_1(a833) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3594,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a816) | c2_1(a816) | c1_1(a816))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a833) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[3593])).
% 1.75/1.94 tff(3595,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a816) | c2_1(a816) | c1_1(a816))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a833) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.75/1.94 inference(transitivity,[status(thm)],[3594, 3592])).
% 1.75/1.94 tff(3596,plain,
% 1.75/1.94 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c3_1(a816) | c2_1(a816) | c1_1(a816))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(3597,plain,
% 1.75/1.94 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a833) | c1_1(a816) | c2_1(a816) | (~ndr1_0) | c3_1(a816) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[3596, 3595])).
% 1.75/1.94 tff(3598,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3597, 130, 1501, 570, 276, 3526, 3527, 10, 669, 3591])).
% 1.75/1.94 tff(3599,plain,((~hskp14) | hskp19 | (~c1_1(a833)) | c2_1(a833) | (~c3_1(a833)) | hskp13 | (~c2_1(a832)) | (~c1_1(a832)) | c0_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(3600,plain,
% 1.75/1.94 (hskp13),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3599, 3584, 3298, 276, 3305, 3277, 3572, 3496, 3580])).
% 1.75/1.94 tff(3601,plain,
% 1.75/1.94 (~c3_1(a814)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3442, 3600])).
% 1.75/1.94 tff(3602,plain,
% 1.75/1.94 (c1_1(a814)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3456, 3600])).
% 1.75/1.94 tff(3603,plain,
% 1.75/1.94 (~c2_1(a814)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3466, 130, 3298, 3602, 288, 276, 3601, 1961, 3305])).
% 1.75/1.94 tff(3604,plain,
% 1.75/1.94 (~c0_1(a814)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3448, 3600])).
% 1.75/1.94 tff(3605,plain,
% 1.75/1.94 (hskp3),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3474, 130, 3602, 3604, 3601, 2514, 3603])).
% 1.75/1.94 tff(3606,plain,
% 1.75/1.94 (~c3_1(a798)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[492, 3605])).
% 1.75/1.94 tff(3607,plain,
% 1.75/1.94 (c2_1(a798)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[506, 3605])).
% 1.75/1.94 tff(3608,plain,
% 1.75/1.94 (c0_1(a798)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[514, 3605])).
% 1.75/1.94 tff(3609,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3567, 130, 3306, 3308, 3602, 3608, 3607, 3307, 3601, 3606, 299, 3603])).
% 1.75/1.94 tff(3610,plain,(c0_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(3611,plain,
% 1.75/1.94 (c0_1(a833)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3610, 276])).
% 1.75/1.94 tff(3612,plain,
% 1.75/1.94 (~hskp20),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[563, 3611])).
% 1.75/1.94 tff(3613,plain,
% 1.75/1.94 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3614,plain,
% 1.75/1.94 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833))) <=> (hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3615,plain,
% 1.75/1.94 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0)))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[3614])).
% 1.75/1.94 tff(3616,plain,
% 1.75/1.94 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0))),
% 1.75/1.94 inference(transitivity,[status(thm)],[3615, 3613])).
% 1.75/1.94 tff(3617,plain,
% 1.75/1.94 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(3618,plain,
% 1.75/1.94 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[3617, 3616])).
% 1.75/1.94 tff(3619,plain,
% 1.75/1.94 (hskp20 | hskp1 | c1_1(a833) | (~c0_1(a833))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3618, 130, 276, 1541])).
% 1.75/1.94 tff(3620,plain,
% 1.75/1.94 (hskp1),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3619, 300, 3611, 3612])).
% 1.75/1.94 tff(3621,plain,
% 1.75/1.94 (~c2_1(a794)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[250, 3620])).
% 1.75/1.94 tff(3622,plain,
% 1.75/1.94 (c3_1(a794)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[258, 3620])).
% 1.75/1.94 tff(3623,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3624,plain,
% 1.75/1.94 ((hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833) | c2_1(a833) | c1_1(a833)) <=> (hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3625,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833) | c2_1(a833) | c1_1(a833))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833)))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[3624])).
% 1.75/1.94 tff(3626,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833) | c2_1(a833) | c1_1(a833))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833))),
% 1.75/1.94 inference(transitivity,[status(thm)],[3625, 3623])).
% 1.75/1.94 tff(3627,plain,
% 1.75/1.94 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833) | c2_1(a833) | c1_1(a833))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(3628,plain,
% 1.75/1.94 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | c3_1(a833)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[3627, 3626])).
% 1.75/1.94 tff(3629,plain,
% 1.75/1.94 (hskp19 | (~c1_1(a794))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3628, 130, 300, 3622, 276, 3621, 10, 277])).
% 1.75/1.94 tff(3630,plain,
% 1.75/1.94 (~c1_1(a794)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3629, 1363])).
% 1.75/1.94 tff(3631,plain,
% 1.75/1.94 (~c0_1(a794)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[264, 3620])).
% 1.75/1.94 tff(3632,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3633,plain,
% 1.75/1.94 ((hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3634,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797))))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[3633])).
% 1.75/1.94 tff(3635,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)))),
% 1.75/1.94 inference(transitivity,[status(thm)],[3634, 3632])).
% 1.75/1.94 tff(3636,plain,
% 1.75/1.94 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c1_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(3637,plain,
% 1.75/1.94 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[3636, 3635])).
% 1.75/1.94 tff(3638,plain,
% 1.75/1.94 (hskp7),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3637, 130, 2435, 2409, 2401, 3622, 3631, 1413, 3630])).
% 1.75/1.94 tff(3639,plain,
% 1.75/1.94 (hskp30),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[2456, 2812, 3612])).
% 1.75/1.94 tff(3640,plain,
% 1.75/1.94 (c3_1(a867)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[30, 3639])).
% 1.75/1.94 tff(3641,plain,
% 1.75/1.94 (c0_1(a867)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[46, 3639])).
% 1.75/1.94 tff(3642,plain,
% 1.75/1.94 (c1_1(a867)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[38, 3639])).
% 1.75/1.94 tff(3643,plain,
% 1.75/1.94 (hskp11),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[2830, 3642, 3612, 2814, 2815, 3641, 3640, 2813])).
% 1.75/1.94 tff(3644,plain,
% 1.75/1.94 (~c2_1(a808)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[776, 3643])).
% 1.75/1.94 tff(3645,plain,
% 1.75/1.94 (~c1_1(a808)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[770, 3643])).
% 1.75/1.94 tff(3646,plain,
% 1.75/1.94 (c3_1(a808)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[812, 3643])).
% 1.75/1.94 tff(3647,plain,
% 1.75/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a833) | c2_1(a832) | (~c0_1(a833)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | c2_1(a832) | (~c0_1(a833)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | c3_1(a833))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3648,plain,
% 1.75/1.94 (((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832)) <=> (c1_1(a833) | c2_1(a832) | (~c0_1(a833)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | c3_1(a833))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3649,plain,
% 1.75/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a833) | c2_1(a832) | (~c0_1(a833)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | c3_1(a833)))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[3648])).
% 1.75/1.94 tff(3650,plain,
% 1.75/1.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | c2_1(a832) | (~c0_1(a833)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | c3_1(a833))),
% 1.75/1.94 inference(transitivity,[status(thm)],[3649, 3647])).
% 1.75/1.94 tff(3651,plain,
% 1.75/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a832) | c0_1(a832) | c3_1(a832))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(3652,plain,
% 1.75/1.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | c2_1(a832) | (~c0_1(a833)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a832) | c3_1(a833)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[3651, 3650])).
% 1.75/1.94 tff(3653,plain,
% 1.75/1.94 (c0_1(a832)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3652, 130, 300, 1362, 3646, 3611, 22, 3645, 3644, 795, 277])).
% 1.75/1.94 tff(3654,plain,
% 1.75/1.94 (~c1_1(a832)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3133, 3653, 22, 1362])).
% 1.75/1.94 tff(3655,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1402, 3654, 3638, 22, 1362])).
% 1.75/1.94 tff(3656,plain,(c2_1(a832) | c3_1(a832) | c1_1(a833) | c3_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(3657,plain,
% 1.75/1.94 (c2_1(a832)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3656, 22, 300, 277, 276])).
% 1.75/1.94 tff(3658,plain,
% 1.75/1.94 (((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | c1_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833))) <=> ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp20 | hskp2 | c1_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3659,plain,
% 1.75/1.94 ((hskp20 | hskp2 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | c3_1(a833)) <=> (hskp20 | hskp2 | c1_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3660,plain,
% 1.75/1.94 (((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | c3_1(a833))) <=> ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | c1_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833)))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[3659])).
% 1.75/1.94 tff(3661,plain,
% 1.75/1.94 (((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | c3_1(a833))) <=> ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp20 | hskp2 | c1_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833))),
% 1.75/1.94 inference(transitivity,[status(thm)],[3660, 3658])).
% 1.75/1.94 tff(3662,plain,
% 1.75/1.94 ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp20 | hskp2 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | c3_1(a833))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(3663,plain,
% 1.75/1.94 ((~![U: $i] : (hskp20 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp20 | hskp2 | c1_1(a833) | c2_1(a833) | (~ndr1_0) | c3_1(a833)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[3662, 3661])).
% 1.75/1.94 tff(3664,plain,
% 1.75/1.94 (hskp20 | hskp2 | c1_1(a833) | c3_1(a833)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3663, 130, 276, 1308])).
% 1.75/1.94 tff(3665,plain,
% 1.75/1.94 (hskp2),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[3664, 277, 300, 3612])).
% 1.75/1.94 tff(3666,plain,
% 1.75/1.94 (~c1_1(a795)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1327, 3665])).
% 1.75/1.94 tff(3667,plain,
% 1.75/1.94 (~c3_1(a795)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1321, 3665])).
% 1.75/1.94 tff(3668,plain,
% 1.75/1.94 (~c0_1(a795)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[1353, 3665])).
% 1.75/1.94 tff(3669,plain,
% 1.75/1.94 (~hskp12),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[2308, 289, 1452, 2292, 22, 391, 1453])).
% 1.75/1.94 tff(3670,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a795)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3671,plain,
% 1.75/1.94 ((hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (hskp12 | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a795)))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(3672,plain,
% 1.75/1.94 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a795))))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[3671])).
% 1.75/1.95 tff(3673,plain,
% 1.75/1.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a795)))),
% 1.75/1.95 inference(transitivity,[status(thm)],[3672, 3670])).
% 1.75/1.95 tff(3674,plain,
% 1.75/1.95 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(3675,plain,
% 1.75/1.95 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a795))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[3674, 3673])).
% 1.75/1.95 tff(3676,plain,
% 1.75/1.95 (hskp12 | (~c2_1(a795))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3675, 130, 1743, 1452, 1453, 1753, 1742, 989])).
% 1.75/1.95 tff(3677,plain,
% 1.75/1.95 (~c2_1(a795)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3676, 3669])).
% 1.75/1.95 tff(3678,assumption,(c0_1(a833)), introduced(assumption)).
% 1.75/1.95 tff(3679,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | c2_1(a795) | c3_1(a833))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | c2_1(a795) | c3_1(a833))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3680,plain,
% 1.75/1.95 (((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a794) | c1_1(a794) | (~c3_1(a794)) | c2_1(a795) | c0_1(a795) | c3_1(a795)) <=> (c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | c2_1(a795) | c3_1(a833))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3681,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a794) | c1_1(a794) | (~c3_1(a794)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | c2_1(a795) | c3_1(a833)))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[3680])).
% 1.75/1.95 tff(3682,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a794) | c1_1(a794) | (~c3_1(a794)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | c2_1(a795) | c3_1(a833))),
% 1.75/1.95 inference(transitivity,[status(thm)],[3681, 3679])).
% 1.75/1.95 tff(3683,plain,
% 1.75/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a794) | c1_1(a794) | (~c3_1(a794)) | c2_1(a795) | c0_1(a795) | c3_1(a795))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(3684,plain,
% 1.75/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | c1_1(a794) | c2_1(a795) | c3_1(a833)),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[3683, 3682])).
% 1.75/1.95 tff(3685,plain,
% 1.75/1.95 (c1_1(a794)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3684, 130, 300, 1743, 3678, 1452, 1453, 1742, 795, 3677, 277])).
% 1.75/1.95 tff(3686,plain,
% 1.75/1.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a832)) | c0_1(a832))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a832)) | c0_1(a832))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3687,plain,
% 1.75/1.95 ((hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (hskp12 | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a832)) | c0_1(a832))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3688,plain,
% 1.75/1.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a832)) | c0_1(a832)))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[3687])).
% 1.75/1.95 tff(3689,plain,
% 1.75/1.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a832)) | c0_1(a832))),
% 1.75/1.95 inference(transitivity,[status(thm)],[3688, 3686])).
% 1.75/1.95 tff(3690,plain,
% 1.75/1.95 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(3691,plain,
% 1.75/1.95 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a832)) | c0_1(a832)),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[3690, 3689])).
% 1.75/1.95 tff(3692,plain,
% 1.75/1.95 ($false),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3691, 130, 730, 391, 1743, 22, 1753, 1742, 989, 979])).
% 1.75/1.95 tff(3693,plain,(c0_1(a832) | hskp12 | (~c2_1(a832)) | (~c3_1(a794)) | c3_1(a832) | c0_1(a794) | c2_1(a794)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.95 tff(3694,plain,
% 1.75/1.95 (c0_1(a832)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3693, 3669, 391, 1743, 22, 1753, 1742])).
% 1.75/1.95 tff(3695,plain,
% 1.75/1.95 (~hskp11),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1461, 3694, 22, 1452, 3677, 1453, 289])).
% 1.75/1.95 tff(3696,plain,
% 1.75/1.95 (hskp21),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[2442, 3695])).
% 1.75/1.95 tff(3697,plain,
% 1.75/1.95 (~c2_1(a838)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[389, 3696])).
% 1.75/1.95 tff(3698,plain,
% 1.75/1.95 (c3_1(a838)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[398, 3696])).
% 1.75/1.95 tff(3699,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a833) | c2_1(a838) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | c2_1(a838) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3700,plain,
% 1.75/1.95 (((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a795) | c0_1(a795) | c3_1(a795)) <=> (c1_1(a833) | c2_1(a838) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3701,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a833) | c2_1(a838) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838)))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[3700])).
% 1.75/1.95 tff(3702,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a795) | c0_1(a795) | c3_1(a795))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | c2_1(a838) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838))),
% 1.75/1.95 inference(transitivity,[status(thm)],[3701, 3699])).
% 1.75/1.95 tff(3703,plain,
% 1.75/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a833) | c3_1(a833) | (~c0_1(a833)) | c2_1(a838) | c1_1(a838) | (~c3_1(a838)) | c2_1(a795) | c0_1(a795) | c3_1(a795))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(3704,plain,
% 1.75/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a833) | c2_1(a838) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | c3_1(a833) | (~c3_1(a838)) | c1_1(a838)),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[3703, 3702])).
% 1.75/1.95 tff(3705,plain,
% 1.75/1.95 (c1_1(a838)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3704, 130, 3698, 300, 3697, 3678, 1452, 1453, 795, 3677, 277])).
% 1.75/1.95 tff(3706,plain,
% 1.75/1.95 (~hskp20),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[563, 3678])).
% 1.75/1.95 tff(3707,plain,
% 1.75/1.95 (hskp9),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[2807, 3696, 3706])).
% 1.75/1.95 tff(3708,plain,
% 1.75/1.95 (~c3_1(a806)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[63, 3707])).
% 1.75/1.95 tff(3709,plain,
% 1.75/1.95 (c1_1(a806)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[72, 3707])).
% 1.75/1.95 tff(3710,plain,
% 1.75/1.95 (c0_1(a838)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[406, 3696])).
% 1.75/1.95 tff(3711,plain,
% 1.75/1.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3712,plain,
% 1.75/1.95 ((hskp12 | (~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806))) <=> (hskp12 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3713,plain,
% 1.75/1.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[3712])).
% 1.75/1.95 tff(3714,plain,
% 1.75/1.95 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 1.75/1.95 inference(transitivity,[status(thm)],[3713, 3711])).
% 1.75/1.95 tff(3715,plain,
% 1.75/1.95 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(3716,plain,
% 1.75/1.95 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c3_1(a806) | (~ndr1_0) | c2_1(a806) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[3715, 3714])).
% 1.75/1.95 tff(3717,plain,
% 1.75/1.95 (c2_1(a806)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3716, 130, 3669, 3710, 3698, 3709, 3708, 95, 3705])).
% 1.75/1.95 tff(3718,plain,
% 1.75/1.95 ($false),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[2219, 130, 3709, 1743, 3708, 1753, 1742, 1961, 3717, 3685])).
% 1.75/1.95 tff(3719,plain,(c1_1(a832) | (~c3_1(a794)) | c0_1(a794) | c2_1(a794) | c1_1(a833) | (~c0_1(a833)) | c0_1(a795) | c3_1(a795) | c3_1(a833) | c3_1(a832) | (~c2_1(a832)) | c1_1(a795)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.95 tff(3720,plain,
% 1.75/1.95 (c1_1(a832)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3719, 22, 3631, 3621, 300, 3611, 3668, 3667, 277, 3622, 3657, 3666])).
% 1.75/1.95 tff(3721,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a832)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a832)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a832)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3722,plain,
% 1.75/1.95 (((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> ((~c1_1(a832)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a832)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3723,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a832)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a832))))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[3722])).
% 1.75/1.95 tff(3724,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a832)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a832)))),
% 1.75/1.95 inference(transitivity,[status(thm)],[3723, 3721])).
% 1.75/1.95 tff(3725,plain,
% 1.75/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a794) | (~c3_1(a794)) | (~c1_1(a794)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(3726,plain,
% 1.75/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a832)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a794)) | (~c2_1(a832))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[3725, 3724])).
% 1.75/1.95 tff(3727,plain,
% 1.75/1.95 ((~c1_1(a832)) | (~c1_1(a794)) | (~c2_1(a832))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3726, 130, 3622, 22, 3631, 3621, 1961])).
% 1.75/1.95 tff(3728,plain,
% 1.75/1.95 (~c1_1(a794)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3727, 3720, 3657])).
% 1.75/1.95 tff(3729,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~c1_1(a832)) | c3_1(a832) | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | c2_1(a795) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a832)) | c3_1(a832) | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | c2_1(a795) | (~c2_1(a832)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3730,plain,
% 1.75/1.95 (((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a794) | c1_1(a794) | c0_1(a794)) <=> ((~c1_1(a832)) | c3_1(a832) | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | c2_1(a795) | (~c2_1(a832)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3731,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a794) | c1_1(a794) | c0_1(a794))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~c1_1(a832)) | c3_1(a832) | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | c2_1(a795) | (~c2_1(a832))))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[3730])).
% 1.75/1.95 tff(3732,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a794) | c1_1(a794) | c0_1(a794))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a832)) | c3_1(a832) | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | c2_1(a795) | (~c2_1(a832)))),
% 1.75/1.95 inference(transitivity,[status(thm)],[3731, 3729])).
% 1.75/1.95 tff(3733,plain,
% 1.75/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c3_1(a795) | c2_1(a795) | c0_1(a795) | c2_1(a794) | c1_1(a794) | c0_1(a794))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(3734,plain,
% 1.75/1.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (~c1_1(a832)) | c3_1(a832) | c0_1(a795) | c3_1(a795) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | c2_1(a795) | (~c2_1(a832))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[3733, 3732])).
% 1.75/1.95 tff(3735,plain,
% 1.75/1.95 ((~c1_1(a832)) | c1_1(a794) | c2_1(a795) | (~c2_1(a832))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3734, 130, 22, 3668, 3667, 3631, 3621, 228])).
% 1.75/1.95 tff(3736,plain,
% 1.75/1.95 (c2_1(a795)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3735, 3720, 3657, 3728])).
% 1.75/1.95 tff(3737,plain,
% 1.75/1.95 (hskp12 | (~c2_1(a795))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3675, 130, 3622, 3668, 3667, 3631, 3621, 989])).
% 1.75/1.95 tff(3738,plain,
% 1.75/1.95 (hskp12),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3737, 3736])).
% 1.75/1.95 tff(3739,plain,
% 1.75/1.95 (~c0_1(a809)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[143, 3738])).
% 1.75/1.95 tff(3740,plain,
% 1.75/1.95 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a795)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3741,plain,
% 1.75/1.95 ((hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795))) <=> (hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a795)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(3742,plain,
% 1.75/1.95 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a795))))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[3741])).
% 1.75/1.95 tff(3743,plain,
% 1.75/1.95 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a795)))),
% 1.75/1.95 inference(transitivity,[status(thm)],[3742, 3740])).
% 1.75/1.95 tff(3744,plain,
% 1.75/1.95 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a797)) | c3_1(a795) | c0_1(a795) | (~c2_1(a795)))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(3745,plain,
% 1.75/1.95 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp15 | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c1_1(a797)) | (~c2_1(a795))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[3744, 3743])).
% 1.75/1.95 tff(3746,plain,
% 1.75/1.95 (hskp15 | (~c2_1(a795))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3745, 130, 2435, 2409, 2401, 3668, 3667, 1210])).
% 1.75/1.95 tff(3747,plain,
% 1.75/1.95 (hskp15),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[3746, 3736])).
% 1.75/1.95 tff(3748,plain,
% 1.75/1.95 (~c1_1(a817)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1252, 3747])).
% 1.75/1.95 tff(3749,plain,
% 1.75/1.95 (c1_1(a809)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[160, 3738])).
% 1.75/1.95 tff(3750,plain,
% 1.75/1.95 (c3_1(a817)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1260, 3747])).
% 1.75/1.95 tff(3751,plain,
% 1.75/1.95 (c2_1(a817)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[1268, 3747])).
% 1.75/1.95 tff(3752,plain,
% 1.75/1.95 (~hskp19),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[352, 3720])).
% 1.75/1.95 tff(3753,plain,
% 1.75/1.95 (hskp27),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[2464, 3752])).
% 1.75/1.95 tff(3754,plain,
% 1.75/1.95 (c3_1(a796)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[531, 3753])).
% 1.75/1.95 tff(3755,plain,
% 1.75/1.95 (c2_1(a796)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[539, 3753])).
% 1.75/1.95 tff(3756,plain,
% 1.75/1.95 (c0_1(a796)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[547, 3753])).
% 1.75/1.95 tff(3757,plain,
% 1.75/1.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a817) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a809)) | c3_1(a809) | (~c2_1(a817)) | (~c3_1(a817)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a817) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a809)) | c3_1(a809) | (~c2_1(a817)) | (~c3_1(a817)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3758,plain,
% 1.75/1.96 (((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809))) <=> (c1_1(a817) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a809)) | c3_1(a809) | (~c2_1(a817)) | (~c3_1(a817)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3759,plain,
% 1.75/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a817) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a809)) | c3_1(a809) | (~c2_1(a817)) | (~c3_1(a817))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[3758])).
% 1.75/1.96 tff(3760,plain,
% 1.75/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a817) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a809)) | c3_1(a809) | (~c2_1(a817)) | (~c3_1(a817)))),
% 1.75/1.96 inference(transitivity,[status(thm)],[3759, 3757])).
% 1.75/1.96 tff(3761,plain,
% 1.75/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a809) | c3_1(a809) | (~c1_1(a809)))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(3762,plain,
% 1.75/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a817) | c0_1(a809) | (~ndr1_0) | (~c3_1(a796)) | (~c2_1(a796)) | (~c0_1(a796)) | (~c1_1(a809)) | c3_1(a809) | (~c2_1(a817)) | (~c3_1(a817))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[3761, 3760])).
% 1.75/1.96 tff(3763,plain,
% 1.75/1.96 (c3_1(a809)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3762, 130, 3756, 3755, 3754, 3751, 3750, 3749, 3748, 3739, 719])).
% 1.75/1.96 tff(3764,plain,
% 1.75/1.96 (c2_1(a809)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[152, 3738])).
% 1.75/1.96 tff(3765,plain,
% 1.75/1.96 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | c3_1(a833))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp29 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | c3_1(a833))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3766,plain,
% 1.75/1.96 ((hskp29 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | c1_1(a833)) <=> (hskp29 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | c3_1(a833))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3767,plain,
% 1.75/1.96 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | c1_1(a833))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | c3_1(a833)))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[3766])).
% 1.75/1.96 tff(3768,plain,
% 1.75/1.96 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | c1_1(a833))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp29 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | c3_1(a833))),
% 1.75/1.96 inference(transitivity,[status(thm)],[3767, 3765])).
% 1.75/1.96 tff(3769,plain,
% 1.75/1.96 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp29 | (~ndr1_0) | c2_1(a833) | c1_1(a833) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | c1_1(a833))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(3770,plain,
% 1.75/1.96 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp29 | c1_1(a833) | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | c3_1(a833)),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[3769, 3768])).
% 1.75/1.96 tff(3771,plain,
% 1.75/1.96 (hskp29),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3770, 130, 300, 3611, 276, 2600, 277])).
% 1.75/1.96 tff(3772,plain,
% 1.75/1.96 (c2_1(a829)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[2623, 3771])).
% 1.75/1.96 tff(3773,plain,
% 1.75/1.96 (c1_1(a829)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[2631, 3771])).
% 1.75/1.96 tff(3774,plain,
% 1.75/1.96 (c0_1(a829)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[2615, 3771])).
% 1.75/1.96 tff(3775,plain,
% 1.75/1.96 (hskp30),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[2456, 3753, 3612])).
% 1.75/1.96 tff(3776,plain,
% 1.75/1.96 (c3_1(a867)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[30, 3775])).
% 1.75/1.96 tff(3777,plain,
% 1.75/1.96 (c1_1(a867)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[38, 3775])).
% 1.75/1.96 tff(3778,plain,
% 1.75/1.96 (c0_1(a867)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[46, 3775])).
% 1.75/1.96 tff(3779,plain,
% 1.75/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a809) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a809)) | (~c3_1(a809)) | (~c0_1(a829)) | (~c2_1(a829)) | (~c1_1(a829)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a809) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a809)) | (~c3_1(a809)) | (~c0_1(a829)) | (~c2_1(a829)) | (~c1_1(a829)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3780,plain,
% 1.75/1.96 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a829)) | (~c0_1(a829)) | (~c2_1(a829)) | c0_1(a809) | (~c3_1(a809)) | (~c2_1(a809))) <=> (c0_1(a809) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a809)) | (~c3_1(a809)) | (~c0_1(a829)) | (~c2_1(a829)) | (~c1_1(a829)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3781,plain,
% 1.75/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a829)) | (~c0_1(a829)) | (~c2_1(a829)) | c0_1(a809) | (~c3_1(a809)) | (~c2_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a809) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a809)) | (~c3_1(a809)) | (~c0_1(a829)) | (~c2_1(a829)) | (~c1_1(a829))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[3780])).
% 1.75/1.96 tff(3782,plain,
% 1.75/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a829)) | (~c0_1(a829)) | (~c2_1(a829)) | c0_1(a809) | (~c3_1(a809)) | (~c2_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a809) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a809)) | (~c3_1(a809)) | (~c0_1(a829)) | (~c2_1(a829)) | (~c1_1(a829)))),
% 1.75/1.96 inference(transitivity,[status(thm)],[3781, 3779])).
% 1.75/1.96 tff(3783,plain,
% 1.75/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a829)) | (~c0_1(a829)) | (~c2_1(a829)) | c0_1(a809) | (~c3_1(a809)) | (~c2_1(a809)))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(3784,plain,
% 1.75/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a809) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a809)) | (~c3_1(a809)) | (~c0_1(a829)) | (~c2_1(a829)) | (~c1_1(a829))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[3783, 3782])).
% 1.75/1.96 tff(3785,plain,
% 1.75/1.96 ($false),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3784, 130, 3778, 3777, 3776, 3774, 3773, 3772, 3764, 3739, 180, 3763])).
% 1.75/1.96 tff(3786,plain,(c3_1(a832) | c1_1(a833) | c3_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.96 tff(3787,plain,
% 1.75/1.96 (c3_1(a832)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3786, 277, 300, 276])).
% 1.75/1.96 tff(3788,plain,
% 1.75/1.96 (~hskp19),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[346, 3787])).
% 1.75/1.96 tff(3789,plain,
% 1.75/1.96 (~c1_1(a794)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3629, 3788])).
% 1.75/1.96 tff(3790,plain,
% 1.75/1.96 (hskp7),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3637, 130, 2435, 2409, 2401, 3622, 3631, 1413, 3789])).
% 1.75/1.96 tff(3791,plain,
% 1.75/1.96 (~c2_1(a803)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1377, 3790])).
% 1.75/1.96 tff(3792,plain,
% 1.75/1.96 (c3_1(a803)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1385, 3790])).
% 1.75/1.96 tff(3793,plain,
% 1.75/1.96 (c1_1(a803)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1393, 3790])).
% 1.75/1.96 tff(3794,plain,
% 1.75/1.96 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3795,plain,
% 1.75/1.96 ((hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833) | c2_1(a833) | c1_1(a833)) <=> (hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3796,plain,
% 1.75/1.96 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833) | c2_1(a833) | c1_1(a833))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833)))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[3795])).
% 1.75/1.96 tff(3797,plain,
% 1.75/1.96 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833) | c2_1(a833) | c1_1(a833))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833))),
% 1.75/1.96 inference(transitivity,[status(thm)],[3796, 3794])).
% 1.75/1.96 tff(3798,plain,
% 1.75/1.96 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833) | c2_1(a833) | c1_1(a833))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(3799,plain,
% 1.75/1.96 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c1_1(a833) | c2_1(a833) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a833)),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[3798, 3797])).
% 1.75/1.96 tff(3800,plain,
% 1.75/1.96 ($false),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3799, 130, 3788, 300, 3793, 3792, 276, 3791, 10, 277])).
% 1.75/1.96 tff(3801,plain,(c3_1(a833) | c1_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.96 tff(3802,plain,
% 1.75/1.96 (c3_1(a833)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3801, 300, 276])).
% 1.75/1.96 tff(3803,plain,
% 1.75/1.96 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | (~c3_1(a833)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | (~c3_1(a833)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3804,plain,
% 1.75/1.96 ((hskp20 | hskp9 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c0_1(a833))) <=> (hskp20 | hskp9 | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | (~c3_1(a833)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3805,plain,
% 1.75/1.96 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c0_1(a833)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | (~c3_1(a833))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[3804])).
% 1.75/1.96 tff(3806,plain,
% 1.75/1.96 (((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c0_1(a833)))) <=> ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | (~c3_1(a833)))),
% 1.75/1.96 inference(transitivity,[status(thm)],[3805, 3803])).
% 1.75/1.96 tff(3807,plain,
% 1.75/1.96 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp20 | hskp9 | (~ndr1_0) | c2_1(a833) | (~c3_1(a833)) | (~c0_1(a833)))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(3808,plain,
% 1.75/1.96 ((~![U: $i] : (hskp20 | hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp20 | hskp9 | (~c0_1(a833)) | c2_1(a833) | (~ndr1_0) | (~c3_1(a833))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[3807, 3806])).
% 1.75/1.96 tff(3809,plain,
% 1.75/1.96 (hskp20 | hskp9 | (~c0_1(a833)) | (~c3_1(a833))),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3808, 130, 276, 21])).
% 1.75/1.96 tff(3810,plain,
% 1.75/1.96 (hskp9),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3809, 3802, 3612, 3611])).
% 1.75/1.96 tff(3811,plain,
% 1.75/1.96 (c0_1(a806)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[55, 3810])).
% 1.75/1.96 tff(3812,plain,
% 1.75/1.96 (c1_1(a806)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[72, 3810])).
% 1.75/1.96 tff(3813,plain,
% 1.75/1.96 (~c3_1(a806)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[63, 3810])).
% 1.75/1.96 tff(3814,plain,
% 1.75/1.96 (hskp30),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[2456, 2812, 310])).
% 1.75/1.96 tff(3815,plain,
% 1.75/1.96 (c1_1(a867)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[38, 3814])).
% 1.75/1.96 tff(3816,plain,
% 1.75/1.96 (c0_1(a867)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[46, 3814])).
% 1.75/1.96 tff(3817,plain,
% 1.75/1.96 (c3_1(a867)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[30, 3814])).
% 1.75/1.96 tff(3818,plain,
% 1.75/1.96 (c2_1(a806)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[169, 3817, 96, 85, 3816, 3815, 145])).
% 1.75/1.96 tff(3819,plain,
% 1.75/1.96 ((~c1_1(a794)) | (~c2_1(a806))),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[2219, 130, 96, 1743, 85, 1753, 1742, 1961])).
% 1.75/1.96 tff(3820,plain,
% 1.75/1.96 (~c1_1(a794)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3819, 3818])).
% 1.75/1.96 tff(3821,plain,
% 1.75/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a832) | c3_1(a832) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a832) | c3_1(a832) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3822,plain,
% 1.75/1.96 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a832) | c2_1(a832) | c0_1(a832) | c2_1(a794) | c1_1(a794) | c0_1(a794)) <=> (c2_1(a832) | c3_1(a832) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3823,plain,
% 1.75/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a832) | c2_1(a832) | c0_1(a832) | c2_1(a794) | c1_1(a794) | c0_1(a794))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a832) | c3_1(a832) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832)))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[3822])).
% 1.75/1.96 tff(3824,plain,
% 1.75/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a832) | c2_1(a832) | c0_1(a832) | c2_1(a794) | c1_1(a794) | c0_1(a794))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a832) | c3_1(a832) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832))),
% 1.75/1.96 inference(transitivity,[status(thm)],[3823, 3821])).
% 1.75/1.96 tff(3825,plain,
% 1.75/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c2_1(a806)) | c3_1(a832) | c2_1(a832) | c0_1(a832) | c2_1(a794) | c1_1(a794) | c0_1(a794))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(3826,plain,
% 1.75/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a832) | c3_1(a832) | c3_1(a806) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | c1_1(a794) | (~c2_1(a806)) | (~c1_1(a806)) | c0_1(a832)),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[3825, 3824])).
% 1.75/1.96 tff(3827,plain,
% 1.75/1.96 (c2_1(a832) | c1_1(a794) | (~c2_1(a806)) | c0_1(a832)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3826, 130, 96, 22, 85, 1753, 1742, 228])).
% 1.75/1.96 tff(3828,plain,
% 1.75/1.96 (c0_1(a832)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3827, 3818, 1362, 3820])).
% 1.75/1.96 tff(3829,plain,
% 1.75/1.96 (~c1_1(a832)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3133, 3828, 22, 1362])).
% 1.75/1.96 tff(3830,plain,
% 1.75/1.96 (~hskp7),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1402, 3829, 22, 1362])).
% 1.75/1.96 tff(3831,plain,
% 1.75/1.96 ($false),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3637, 130, 3830, 2435, 2409, 2401, 1743, 1753, 1413, 3820])).
% 1.75/1.96 tff(3832,plain,(c2_1(a832) | (~c3_1(a794)) | c0_1(a794) | c3_1(a832) | (~c1_1(a806)) | c3_1(a806) | c2_1(a794) | (~c0_1(a806)) | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.75/1.96 tff(3833,plain,
% 1.75/1.96 (c2_1(a832)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3832, 22, 1753, 1743, 96, 85, 1742, 145, 310])).
% 1.75/1.96 tff(3834,plain,
% 1.75/1.96 (hskp12),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3693, 979, 391, 1743, 22, 1753, 1742])).
% 1.75/1.96 tff(3835,plain,
% 1.75/1.96 (~c0_1(a809)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[143, 3834])).
% 1.75/1.96 tff(3836,plain,
% 1.75/1.96 (c2_1(a809)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[152, 3834])).
% 1.75/1.96 tff(3837,plain,
% 1.75/1.96 (c1_1(a809)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[160, 3834])).
% 1.75/1.96 tff(3838,plain,
% 1.75/1.96 ($false),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1007, 130, 391, 3837, 3836, 289, 22, 3835, 977, 979])).
% 1.75/1.96 tff(3839,plain,(c0_1(a832) | (~c2_1(a832)) | c1_1(a832) | c3_1(a832) | (~c3_1(a794)) | c0_1(a794) | c2_1(a794)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.96 tff(3840,plain,
% 1.75/1.96 (c0_1(a832)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3839, 289, 391, 22, 1743, 1753, 1742])).
% 1.75/1.96 tff(3841,plain,
% 1.75/1.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3842,plain,
% 1.75/1.96 ((hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832))) <=> (hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3843,plain,
% 1.75/1.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | (~c0_1(a832))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[3842])).
% 1.75/1.96 tff(3844,plain,
% 1.75/1.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.75/1.96 inference(transitivity,[status(thm)],[3843, 3841])).
% 1.75/1.96 tff(3845,plain,
% 1.75/1.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(3846,plain,
% 1.75/1.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c2_1(a832)) | (~c0_1(a832))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[3845, 3844])).
% 1.75/1.96 tff(3847,plain,
% 1.75/1.96 (hskp5),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3846, 130, 47, 39, 31, 391, 22, 190, 3840])).
% 1.75/1.96 tff(3848,plain,
% 1.75/1.96 (~c1_1(a800)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[233, 3847])).
% 1.75/1.96 tff(3849,plain,
% 1.75/1.96 (~c0_1(a800)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[202, 3847])).
% 1.75/1.96 tff(3850,plain,
% 1.75/1.96 (c2_1(a806)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[169, 31, 96, 85, 47, 39, 145])).
% 1.75/1.96 tff(3851,plain,
% 1.75/1.96 (~c1_1(a794)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3819, 3850])).
% 1.75/1.96 tff(3852,plain,
% 1.75/1.96 (hskp7),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3637, 130, 2435, 2409, 2401, 1743, 1753, 1413, 3851])).
% 1.75/1.96 tff(3853,plain,
% 1.75/1.96 (~c2_1(a803)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1377, 3852])).
% 1.75/1.96 tff(3854,plain,
% 1.75/1.96 (c3_1(a800)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[210, 3847])).
% 1.75/1.96 tff(3855,plain,
% 1.75/1.96 (c1_1(a803)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[1393, 3852])).
% 1.75/1.96 tff(3856,plain,
% 1.75/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a832) | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a832) | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3857,plain,
% 1.75/1.96 (((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (c1_1(a832) | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3858,plain,
% 1.75/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a832) | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a832)) | (~c0_1(a832))))),
% 1.75/1.96 inference(monotonicity,[status(thm)],[3857])).
% 1.75/1.96 tff(3859,plain,
% 1.75/1.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a832) | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.75/1.96 inference(transitivity,[status(thm)],[3858, 3856])).
% 1.75/1.96 tff(3860,plain,
% 1.75/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a803) | (~c1_1(a803)) | (~c0_1(a803)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(3861,plain,
% 1.75/1.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a832) | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c0_1(a803)) | (~c1_1(a803)) | (~c2_1(a832)) | (~c0_1(a832))),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[3860, 3859])).
% 1.75/1.96 tff(3862,plain,
% 1.75/1.96 (~c0_1(a803)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[3861, 130, 391, 3855, 3854, 289, 3853, 3849, 3848, 287, 3840])).
% 1.75/1.96 tff(3863,plain,
% 1.75/1.96 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a832)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3864,plain,
% 1.75/1.96 ((hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c1_1(a832) | (~c0_1(a832))) <=> (hskp22 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a832)))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(3865,plain,
% 1.75/1.96 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c1_1(a832) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a832))))),
% 1.75/1.97 inference(monotonicity,[status(thm)],[3864])).
% 1.75/1.97 tff(3866,plain,
% 1.75/1.97 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c1_1(a832) | (~c0_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a832)))),
% 1.75/1.97 inference(transitivity,[status(thm)],[3865, 3863])).
% 1.75/1.97 tff(3867,plain,
% 1.75/1.97 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a832) | c1_1(a832) | (~c0_1(a832)))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(3868,plain,
% 1.75/1.97 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp22 | c1_1(a832) | c3_1(a832) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c0_1(a832))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[3867, 3866])).
% 1.75/1.97 tff(3869,plain,
% 1.75/1.97 (hskp22),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3868, 130, 47, 39, 31, 289, 22, 1813, 3840])).
% 1.75/1.97 tff(3870,plain,
% 1.75/1.97 (~c0_1(a840)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1826, 3869])).
% 1.75/1.97 tff(3871,plain,
% 1.75/1.97 (c3_1(a803)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1385, 3852])).
% 1.75/1.97 tff(3872,plain,
% 1.75/1.97 (c3_1(a840)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1834, 3869])).
% 1.75/1.97 tff(3873,plain,
% 1.75/1.97 (c1_1(a840)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1860, 3869])).
% 1.75/1.97 tff(3874,plain,
% 1.75/1.97 ($false),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1988, 130, 3873, 3872, 96, 3871, 3870, 85, 3853, 1961, 3850, 3862])).
% 1.75/1.97 tff(3875,plain,((~hskp30) | (~c1_1(a806)) | c3_1(a806) | (~c2_1(a832)) | c1_1(a832) | (~c3_1(a794)) | c0_1(a794) | c3_1(a832) | c2_1(a794) | (~c0_1(a806))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.97 tff(3876,plain,
% 1.75/1.97 (~hskp30),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3875, 289, 85, 3833, 96, 1743, 1753, 22, 1742, 145])).
% 1.75/1.97 tff(3877,plain,
% 1.75/1.97 (~c0_1(a797)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[2416, 3876, 310])).
% 1.75/1.97 tff(3878,plain,
% 1.75/1.97 (c0_1(a832)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3839, 289, 3833, 22, 1743, 1753, 1742])).
% 1.75/1.97 tff(3879,plain,
% 1.75/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(3880,plain,
% 1.75/1.97 (((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(3881,plain,
% 1.75/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832))))),
% 1.75/1.97 inference(monotonicity,[status(thm)],[3880])).
% 1.75/1.97 tff(3882,plain,
% 1.75/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832)))),
% 1.75/1.97 inference(transitivity,[status(thm)],[3881, 3879])).
% 1.75/1.97 tff(3883,plain,
% 1.75/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c2_1(a832)) | (~c0_1(a832)) | c0_1(a797) | (~c1_1(a797)) | (~c2_1(a797)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(3884,plain,
% 1.75/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a832) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | (~c2_1(a832)) | (~c0_1(a832))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[3883, 3882])).
% 1.75/1.97 tff(3885,plain,
% 1.75/1.97 ($false),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3884, 130, 2435, 2409, 3833, 1743, 22, 1753, 1742, 2503, 3878, 3877])).
% 1.75/1.97 tff(3886,plain,(c1_1(a832) | (~c3_1(a794)) | c3_1(a832) | c0_1(a794) | c2_1(a794) | hskp20 | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.97 tff(3887,plain,
% 1.75/1.97 (c1_1(a832)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3886, 22, 1743, 1753, 1742, 310, 85, 96, 145])).
% 1.75/1.97 tff(3888,plain,
% 1.75/1.97 ((~c1_1(a832)) | (~c1_1(a794)) | (~c2_1(a832))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3726, 130, 1743, 22, 1753, 1742, 1961])).
% 1.75/1.97 tff(3889,plain,
% 1.75/1.97 (~c1_1(a794)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3888, 3887, 3833])).
% 1.75/1.97 tff(3890,plain,
% 1.75/1.97 (~hskp19),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[352, 3887])).
% 1.75/1.97 tff(3891,plain,
% 1.75/1.97 (hskp27),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[2464, 3890])).
% 1.75/1.97 tff(3892,plain,
% 1.75/1.97 (hskp30),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[2456, 3891, 310])).
% 1.75/1.97 tff(3893,plain,
% 1.75/1.97 (c1_1(a867)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[38, 3892])).
% 1.75/1.97 tff(3894,plain,
% 1.75/1.97 (c0_1(a867)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[46, 3892])).
% 1.75/1.97 tff(3895,plain,
% 1.75/1.97 (c3_1(a867)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[30, 3892])).
% 1.75/1.97 tff(3896,plain,
% 1.75/1.97 (c2_1(a806)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[169, 3895, 96, 85, 3894, 3893, 145])).
% 1.75/1.97 tff(3897,plain,
% 1.75/1.97 (hskp0 | c1_1(a794) | (~c2_1(a806))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1583, 130, 145, 85, 1753, 1742, 1338])).
% 1.75/1.97 tff(3898,plain,
% 1.75/1.97 (hskp0),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3897, 3896, 3889])).
% 1.75/1.97 tff(3899,plain,
% 1.75/1.97 (~c1_1(a793)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[603, 3898])).
% 1.75/1.97 tff(3900,plain,
% 1.75/1.97 (hskp5),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[196, 130, 3894, 3893, 3895, 145, 85, 190, 3896])).
% 1.75/1.97 tff(3901,plain,
% 1.75/1.97 (~c1_1(a800)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[233, 3900])).
% 1.75/1.97 tff(3902,plain,
% 1.75/1.97 (~c0_1(a800)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[202, 3900])).
% 1.75/1.97 tff(3903,plain,
% 1.75/1.97 (hskp7),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3637, 130, 2435, 2409, 2401, 1743, 1753, 1413, 3889])).
% 1.75/1.97 tff(3904,plain,
% 1.75/1.97 (~c2_1(a803)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1377, 3903])).
% 1.75/1.97 tff(3905,plain,
% 1.75/1.97 (c2_1(a793)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[597, 3898])).
% 1.75/1.97 tff(3906,plain,
% 1.75/1.97 (c0_1(a793)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[611, 3898])).
% 1.75/1.97 tff(3907,plain,
% 1.75/1.97 (c3_1(a800)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[210, 3900])).
% 1.75/1.97 tff(3908,plain,
% 1.75/1.97 (c1_1(a803)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1393, 3903])).
% 1.75/1.97 tff(3909,plain,
% 1.75/1.97 (~c0_1(a803)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[2794, 130, 3908, 3907, 3906, 3905, 3904, 3902, 3901, 3899, 287])).
% 1.75/1.97 tff(3910,plain,
% 1.75/1.97 (c3_1(a803)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1385, 3903])).
% 1.75/1.97 tff(3911,plain,
% 1.75/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a832)) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a832)) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(3912,plain,
% 1.75/1.97 (((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803))) <=> ((~c1_1(a832)) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(3913,plain,
% 1.75/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a832)) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832))))),
% 1.75/1.97 inference(monotonicity,[status(thm)],[3912])).
% 1.75/1.97 tff(3914,plain,
% 1.75/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a832)) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832)))),
% 1.75/1.97 inference(transitivity,[status(thm)],[3913, 3911])).
% 1.75/1.97 tff(3915,plain,
% 1.75/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a832) | (~c1_1(a832)) | (~c2_1(a832)) | c0_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c2_1(a803) | c0_1(a803) | (~c3_1(a803)))),
% 1.75/1.97 inference(quant_inst,[status(thm)],[])).
% 1.75/1.97 tff(3916,plain,
% 1.75/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a832)) | c3_1(a832) | c2_1(a803) | (~ndr1_0) | (~c3_1(a803)) | c0_1(a803) | (~c1_1(a803)) | (~c2_1(a832))),
% 1.75/1.97 inference(modus_ponens,[status(thm)],[3915, 3914])).
% 1.75/1.97 tff(3917,plain,
% 1.75/1.97 ($false),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3916, 130, 3833, 3908, 3910, 3887, 22, 3904, 1961, 3909])).
% 1.75/1.97 tff(3918,plain,(c3_1(a832) | (~c0_1(a806)) | c3_1(a806) | (~c3_1(a794)) | c0_1(a794) | c2_1(a794) | (~c1_1(a806)) | hskp20), inference(lemma,lemma(discharge,[]))).
% 1.75/1.97 tff(3919,plain,
% 1.75/1.97 (c3_1(a832)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3918, 3811, 3813, 3622, 3631, 3621, 3812, 3612])).
% 1.75/1.97 tff(3920,plain,
% 1.75/1.97 (~hskp19),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[346, 3919])).
% 1.75/1.97 tff(3921,plain,
% 1.75/1.97 (hskp27),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[2464, 3920])).
% 1.75/1.97 tff(3922,plain,
% 1.75/1.97 (hskp30),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[2456, 3921, 3612])).
% 1.75/1.97 tff(3923,plain,
% 1.75/1.97 (c1_1(a867)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[38, 3922])).
% 1.75/1.97 tff(3924,plain,
% 1.75/1.97 (c0_1(a867)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[46, 3922])).
% 1.75/1.97 tff(3925,plain,
% 1.75/1.97 (c3_1(a867)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[30, 3922])).
% 1.75/1.97 tff(3926,plain,
% 1.75/1.97 (c2_1(a806)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[169, 3925, 3812, 3813, 3924, 3923, 3811])).
% 1.75/1.97 tff(3927,plain,
% 1.75/1.97 ((~c1_1(a794)) | (~c2_1(a806))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[2219, 130, 3812, 3622, 3813, 3631, 3621, 1961])).
% 1.75/1.97 tff(3928,plain,
% 1.75/1.97 (~c1_1(a794)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3927, 3926])).
% 1.75/1.97 tff(3929,plain,
% 1.75/1.97 (hskp0 | c1_1(a794) | (~c2_1(a806))),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1583, 130, 3811, 3813, 3631, 3621, 1338])).
% 1.75/1.97 tff(3930,plain,
% 1.75/1.97 (hskp0),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3929, 3926, 3928])).
% 1.75/1.97 tff(3931,plain,
% 1.75/1.97 (~c1_1(a793)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[603, 3930])).
% 1.75/1.97 tff(3932,plain,
% 1.75/1.97 (hskp5),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[196, 130, 3924, 3923, 3925, 3811, 3813, 190, 3926])).
% 1.75/1.97 tff(3933,plain,
% 1.75/1.97 (~c1_1(a800)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[233, 3932])).
% 1.75/1.97 tff(3934,plain,
% 1.75/1.97 (~c0_1(a800)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[202, 3932])).
% 1.75/1.97 tff(3935,plain,
% 1.75/1.97 (hskp7),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3637, 130, 2435, 2409, 2401, 3622, 3631, 1413, 3928])).
% 1.75/1.97 tff(3936,plain,
% 1.75/1.97 (~c2_1(a803)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1377, 3935])).
% 1.75/1.97 tff(3937,plain,
% 1.75/1.97 (c2_1(a793)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[597, 3930])).
% 1.75/1.97 tff(3938,plain,
% 1.75/1.97 (c0_1(a793)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[611, 3930])).
% 1.75/1.97 tff(3939,plain,
% 1.75/1.97 (c3_1(a800)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[210, 3932])).
% 1.75/1.97 tff(3940,plain,
% 1.75/1.97 (c1_1(a803)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1393, 3935])).
% 1.75/1.97 tff(3941,plain,
% 1.75/1.97 (~c0_1(a803)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[2794, 130, 3940, 3939, 3938, 3937, 3936, 3934, 3933, 3931, 287])).
% 1.75/1.97 tff(3942,plain,
% 1.75/1.97 (c3_1(a803)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[1385, 3935])).
% 1.75/1.97 tff(3943,plain,
% 1.75/1.97 ($false),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[2802, 130, 3812, 3940, 3942, 3813, 3936, 1961, 3926, 3941])).
% 1.75/1.97 tff(3944,plain,(c1_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.97 tff(3945,plain,
% 1.75/1.97 (c1_1(a833)),
% 1.75/1.97 inference(unit_resolution,[status(thm)],[3944, 276])).
% 1.75/1.97 tff(3946,plain,
% 1.75/1.97 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.75/1.97 inference(bind,[status(th)],[])).
% 1.75/1.97 tff(3947,plain,
% 1.75/1.97 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.75/1.97 inference(quant_intro,[status(thm)],[3946])).
% 1.75/1.97 tff(3948,plain,
% 1.75/1.97 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.75/1.97 inference(rewrite,[status(thm)],[])).
% 1.75/1.97 tff(3949,plain,
% 1.75/1.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.81/1.97 inference(bind,[status(th)],[])).
% 1.81/1.97 tff(3950,plain,
% 1.81/1.97 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.81/1.97 inference(quant_intro,[status(thm)],[3949])).
% 1.81/1.97 tff(3951,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 1.81/1.97 tff(3952,plain,
% 1.81/1.97 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.81/1.97 inference(modus_ponens,[status(thm)],[3951, 3950])).
% 1.81/1.97 tff(3953,plain,
% 1.81/1.97 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.81/1.97 inference(modus_ponens,[status(thm)],[3952, 3948])).
% 1.81/1.97 tff(3954,plain,(
% 1.81/1.97 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.81/1.97 inference(skolemize,[status(sab)],[3953])).
% 1.81/1.97 tff(3955,plain,
% 1.81/1.97 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.81/1.97 inference(modus_ponens,[status(thm)],[3954, 3947])).
% 1.81/1.97 tff(3956,plain,
% 1.81/1.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~c0_1(a833)) | c2_1(a833) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | (~c0_1(a833)) | c2_1(a833) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a833)))),
% 1.81/1.97 inference(rewrite,[status(thm)],[])).
% 1.81/1.97 tff(3957,plain,
% 1.81/1.97 ((hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794))) <=> (hskp9 | (~c0_1(a833)) | c2_1(a833) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a833)))),
% 1.81/1.97 inference(rewrite,[status(thm)],[])).
% 1.81/1.97 tff(3958,plain,
% 1.81/1.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~c0_1(a833)) | c2_1(a833) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a833))))),
% 1.81/1.97 inference(monotonicity,[status(thm)],[3957])).
% 1.81/1.97 tff(3959,plain,
% 1.81/1.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | (~c0_1(a833)) | c2_1(a833) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a833)))),
% 1.81/1.97 inference(transitivity,[status(thm)],[3958, 3956])).
% 1.81/1.97 tff(3960,plain,
% 1.81/1.97 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a794) | c0_1(a794) | (~c3_1(a794)))),
% 1.81/1.97 inference(quant_inst,[status(thm)],[])).
% 1.81/1.97 tff(3961,plain,
% 1.81/1.97 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | (~c0_1(a833)) | c2_1(a833) | c0_1(a794) | c2_1(a794) | (~ndr1_0) | (~c3_1(a794)) | (~c1_1(a833))),
% 1.81/1.97 inference(modus_ponens,[status(thm)],[3960, 3959])).
% 1.81/1.97 tff(3962,plain,
% 1.81/1.97 (hskp9),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[3961, 130, 3945, 259, 3611, 276, 265, 251, 3955])).
% 1.81/1.97 tff(3963,plain,
% 1.81/1.97 (c1_1(a806)),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[72, 3962])).
% 1.81/1.97 tff(3964,plain,
% 1.81/1.97 (c0_1(a806)),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[55, 3962])).
% 1.81/1.97 tff(3965,plain,
% 1.81/1.97 (~c3_1(a806)),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[63, 3962])).
% 1.81/1.97 tff(3966,plain,
% 1.81/1.97 ($false),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[3918, 3965, 3964, 22, 265, 259, 251, 3963, 3612])).
% 1.81/1.97 tff(3967,plain,((~hskp1) | c3_1(a832) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.81/1.97 tff(3968,plain,
% 1.81/1.97 (~hskp1),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[3967, 22, 276])).
% 1.81/1.97 tff(3969,assumption,(~hskp1), introduced(assumption)).
% 1.81/1.97 tff(3970,plain,
% 1.81/1.97 (^[U: $i] : refl((hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.81/1.97 inference(bind,[status(th)],[])).
% 1.81/1.97 tff(3971,plain,
% 1.81/1.97 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.81/1.97 inference(quant_intro,[status(thm)],[3970])).
% 1.81/1.97 tff(3972,plain,
% 1.81/1.97 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.81/1.97 inference(rewrite,[status(thm)],[])).
% 1.81/1.97 tff(3973,plain,
% 1.81/1.97 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1) <=> ((hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp1))), rewrite(((hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp1) <=> (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1) <=> (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.81/1.97 inference(bind,[status(th)],[])).
% 1.81/1.97 tff(3974,plain,
% 1.81/1.97 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.81/1.97 inference(quant_intro,[status(thm)],[3973])).
% 1.81/1.97 tff(3975,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.81/1.97 tff(3976,plain,
% 1.81/1.97 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.81/1.97 inference(modus_ponens,[status(thm)],[3975, 3974])).
% 1.81/1.97 tff(3977,plain,
% 1.81/1.97 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.81/1.97 inference(modus_ponens,[status(thm)],[3976, 3972])).
% 1.81/1.97 tff(3978,plain,(
% 1.81/1.97 ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.81/1.97 inference(skolemize,[status(sab)],[3977])).
% 1.81/1.97 tff(3979,plain,
% 1.81/1.97 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.81/1.97 inference(modus_ponens,[status(thm)],[3978, 3971])).
% 1.81/1.97 tff(3980,plain,
% 1.81/1.97 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp13 | hskp1 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp13 | hskp1 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.97 inference(rewrite,[status(thm)],[])).
% 1.81/1.97 tff(3981,plain,
% 1.81/1.97 ((hskp13 | hskp1 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833))) <=> (hskp13 | hskp1 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.97 inference(rewrite,[status(thm)],[])).
% 1.81/1.97 tff(3982,plain,
% 1.81/1.97 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp13 | hskp1 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))))),
% 1.81/1.97 inference(monotonicity,[status(thm)],[3981])).
% 1.81/1.97 tff(3983,plain,
% 1.81/1.97 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp13 | hskp1 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.97 inference(transitivity,[status(thm)],[3982, 3980])).
% 1.81/1.97 tff(3984,plain,
% 1.81/1.97 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp13 | hskp1 | (~ndr1_0) | c2_1(a833) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.97 inference(quant_inst,[status(thm)],[])).
% 1.81/1.97 tff(3985,plain,
% 1.81/1.97 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp13 | hskp1 | c2_1(a833) | (~ndr1_0) | c3_1(a833) | (~c1_1(a833))),
% 1.81/1.97 inference(modus_ponens,[status(thm)],[3984, 3983])).
% 1.81/1.97 tff(3986,plain,
% 1.81/1.97 (hskp13 | hskp1 | c3_1(a833) | (~c1_1(a833))),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[3985, 130, 276, 3979])).
% 1.81/1.97 tff(3987,plain,
% 1.81/1.97 (hskp13),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[3986, 3969, 3945, 277])).
% 1.81/1.97 tff(3988,plain,
% 1.81/1.97 (~c0_1(a814)),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[3448, 3987])).
% 1.81/1.97 tff(3989,plain,
% 1.81/1.97 (c1_1(a814)),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[3456, 3987])).
% 1.81/1.97 tff(3990,plain,
% 1.81/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c0_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c0_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.97 inference(rewrite,[status(thm)],[])).
% 1.81/1.97 tff(3991,plain,
% 1.81/1.97 (((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a814) | (~c2_1(a814)) | (~c1_1(a814))) <=> ((~c0_1(a833)) | c2_1(a833) | c0_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.97 inference(rewrite,[status(thm)],[])).
% 1.81/1.97 tff(3992,plain,
% 1.81/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a814) | (~c2_1(a814)) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c0_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c3_1(a833) | (~c1_1(a833))))),
% 1.81/1.97 inference(monotonicity,[status(thm)],[3991])).
% 1.81/1.97 tff(3993,plain,
% 1.81/1.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a814) | (~c2_1(a814)) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c0_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.97 inference(transitivity,[status(thm)],[3992, 3990])).
% 1.81/1.97 tff(3994,plain,
% 1.81/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a814) | (~c2_1(a814)) | (~c1_1(a814)))),
% 1.81/1.97 inference(quant_inst,[status(thm)],[])).
% 1.81/1.97 tff(3995,plain,
% 1.81/1.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c0_1(a814) | (~ndr1_0) | (~c2_1(a814)) | (~c1_1(a814)) | c3_1(a833) | (~c1_1(a833))),
% 1.81/1.97 inference(modus_ponens,[status(thm)],[3994, 3993])).
% 1.81/1.97 tff(3996,plain,
% 1.81/1.97 (~c2_1(a814)),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[3995, 130, 3945, 3989, 3611, 276, 3988, 84, 277])).
% 1.81/1.97 tff(3997,assumption,(c0_1(a808)), introduced(assumption)).
% 1.81/1.97 tff(3998,plain,
% 1.81/1.97 (hskp9),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[2005, 3997])).
% 1.81/1.97 tff(3999,plain,
% 1.81/1.97 (c1_1(a806)),
% 1.81/1.97 inference(unit_resolution,[status(thm)],[72, 3998])).
% 1.81/1.97 tff(4000,plain,
% 1.81/1.97 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c0_1(a808)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c0_1(a808)))),
% 1.81/1.97 inference(rewrite,[status(thm)],[])).
% 1.81/1.97 tff(4001,plain,
% 1.81/1.97 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c0_1(a808))) <=> (hskp20 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c0_1(a808)))),
% 1.81/1.97 inference(rewrite,[status(thm)],[])).
% 1.81/1.97 tff(4002,plain,
% 1.81/1.97 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c0_1(a808)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c0_1(a808))))),
% 1.81/1.97 inference(monotonicity,[status(thm)],[4001])).
% 1.81/1.97 tff(4003,plain,
% 1.81/1.97 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c0_1(a808)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c0_1(a808)))),
% 1.81/1.97 inference(transitivity,[status(thm)],[4002, 4000])).
% 1.81/1.97 tff(4004,plain,
% 1.81/1.97 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | (~c0_1(a808)))),
% 1.81/1.97 inference(quant_inst,[status(thm)],[])).
% 1.81/1.97 tff(4005,plain,
% 1.81/1.97 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c0_1(a808))),
% 1.81/1.98 inference(modus_ponens,[status(thm)],[4004, 4003])).
% 1.81/1.98 tff(4006,plain,
% 1.81/1.98 (hskp1 | (~c0_1(a808))),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4005, 130, 310, 797, 796, 1541])).
% 1.81/1.98 tff(4007,plain,
% 1.81/1.98 (hskp1),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4006, 3997])).
% 1.81/1.98 tff(4008,plain,
% 1.81/1.98 (~c2_1(a794)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[250, 4007])).
% 1.81/1.98 tff(4009,plain,
% 1.81/1.98 (~c0_1(a794)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[264, 4007])).
% 1.81/1.98 tff(4010,plain,
% 1.81/1.98 (c3_1(a794)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[258, 4007])).
% 1.81/1.98 tff(4011,plain,
% 1.81/1.98 (c0_1(a806)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[55, 3998])).
% 1.81/1.98 tff(4012,plain,
% 1.81/1.98 (~c3_1(a806)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[63, 3998])).
% 1.81/1.98 tff(4013,plain,
% 1.81/1.98 ($false),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[3918, 4012, 4011, 22, 4010, 4009, 4008, 3999, 310])).
% 1.81/1.98 tff(4014,plain,((~c0_1(a808)) | c3_1(a832) | hskp20 | c1_1(a808) | c2_1(a808) | (~c3_1(a808))), inference(lemma,lemma(discharge,[]))).
% 1.81/1.98 tff(4015,plain,
% 1.81/1.98 (~c0_1(a808)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4014, 3645, 3612, 22, 3644, 3646])).
% 1.81/1.98 tff(4016,plain,
% 1.81/1.98 (hskp7 | c0_1(a808)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[2839, 130, 2435, 2409, 2401, 3646, 3645, 1413])).
% 1.81/1.98 tff(4017,plain,
% 1.81/1.98 (hskp7),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4016, 4015])).
% 1.81/1.98 tff(4018,plain,
% 1.81/1.98 (c1_1(a832)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[1402, 4017, 22, 1362])).
% 1.81/1.98 tff(4019,plain,
% 1.81/1.98 (hskp12 | (~c1_1(a832))),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[2866, 130, 3641, 3642, 3640, 1362, 22, 95])).
% 1.81/1.98 tff(4020,plain,
% 1.81/1.98 (hskp12),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4019, 4018])).
% 1.81/1.98 tff(4021,plain,
% 1.81/1.98 (~c0_1(a809)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[143, 4020])).
% 1.81/1.98 tff(4022,plain,
% 1.81/1.98 (c2_1(a809)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[152, 4020])).
% 1.81/1.98 tff(4023,plain,
% 1.81/1.98 (c1_1(a809)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[160, 4020])).
% 1.81/1.98 tff(4024,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a832) | (~c0_1(a833)) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c0_1(a833)) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c1_1(a833)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4025,plain,
% 1.81/1.98 (((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809))) <=> (c2_1(a832) | (~c0_1(a833)) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c1_1(a833)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4026,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a832) | (~c0_1(a833)) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c1_1(a833))))),
% 1.81/1.98 inference(monotonicity,[status(thm)],[4025])).
% 1.81/1.98 tff(4027,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c0_1(a833)) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c1_1(a833)))),
% 1.81/1.98 inference(transitivity,[status(thm)],[4026, 4024])).
% 1.81/1.98 tff(4028,plain,
% 1.81/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | c2_1(a832) | (~c1_1(a832)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.81/1.98 inference(quant_inst,[status(thm)],[])).
% 1.81/1.98 tff(4029,plain,
% 1.81/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a832) | (~c0_1(a833)) | c2_1(a833) | (~c1_1(a832)) | c3_1(a832) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | (~c1_1(a833))),
% 1.81/1.98 inference(modus_ponens,[status(thm)],[4028, 4027])).
% 1.81/1.98 tff(4030,plain,
% 1.81/1.98 ($false),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4029, 130, 3945, 1362, 4023, 4022, 3611, 276, 4018, 22, 4021, 84])).
% 1.81/1.98 tff(4031,plain,(c2_1(a832) | c2_1(a833) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.81/1.98 tff(4032,plain,
% 1.81/1.98 (c2_1(a832)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4031, 22, 276])).
% 1.81/1.98 tff(4033,plain,
% 1.81/1.98 (hskp15),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[3210, 979, 4032])).
% 1.81/1.98 tff(4034,plain,
% 1.81/1.98 (~c1_1(a817)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[1252, 4033])).
% 1.81/1.98 tff(4035,plain,
% 1.81/1.98 (c3_1(a817)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[1260, 4033])).
% 1.81/1.98 tff(4036,plain,
% 1.81/1.98 (c2_1(a817)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[1268, 4033])).
% 1.81/1.98 tff(4037,plain,
% 1.81/1.98 (~c2_1(a814)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[3995, 130, 3945, 3460, 3611, 276, 3468, 84, 277])).
% 1.81/1.98 tff(4038,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a817) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)) | (~c1_1(a814)) | (~c2_1(a817)) | (~c3_1(a817)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a817) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)) | (~c1_1(a814)) | (~c2_1(a817)) | (~c3_1(a817)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4039,plain,
% 1.81/1.98 (((~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814))) <=> (c1_1(a817) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)) | (~c1_1(a814)) | (~c2_1(a817)) | (~c3_1(a817)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4040,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a817) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)) | (~c1_1(a814)) | (~c2_1(a817)) | (~c3_1(a817))))),
% 1.81/1.98 inference(monotonicity,[status(thm)],[4039])).
% 1.81/1.98 tff(4041,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a817) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)) | (~c1_1(a814)) | (~c2_1(a817)) | (~c3_1(a817)))),
% 1.81/1.98 inference(transitivity,[status(thm)],[4040, 4038])).
% 1.81/1.98 tff(4042,plain,
% 1.81/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a797)) | (~c2_1(a797)) | (~c0_1(a797)) | c1_1(a817) | (~c3_1(a817)) | (~c2_1(a817)) | c0_1(a814) | c3_1(a814) | (~c1_1(a814)))),
% 1.81/1.98 inference(quant_inst,[status(thm)],[])).
% 1.81/1.98 tff(4043,plain,
% 1.81/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a817) | c0_1(a814) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | (~c0_1(a797)) | (~c1_1(a814)) | (~c2_1(a817)) | (~c3_1(a817))),
% 1.81/1.98 inference(modus_ponens,[status(thm)],[4042, 4041])).
% 1.81/1.98 tff(4044,plain,
% 1.81/1.98 (~c0_1(a797)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4043, 130, 2409, 2401, 2708, 2707, 3460, 2706, 3468, 3459, 719])).
% 1.81/1.98 tff(4045,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a814) | (~c1_1(a814)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a814) | (~c1_1(a814)) | (~c1_1(a833)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4046,plain,
% 1.81/1.98 (((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a814) | c2_1(a814) | (~c1_1(a814)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797))) <=> ((~c0_1(a833)) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a814) | (~c1_1(a814)) | (~c1_1(a833)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4047,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a814) | c2_1(a814) | (~c1_1(a814)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a814) | (~c1_1(a814)) | (~c1_1(a833))))),
% 1.81/1.98 inference(monotonicity,[status(thm)],[4046])).
% 1.81/1.98 tff(4048,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a814) | c2_1(a814) | (~c1_1(a814)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a814) | (~c1_1(a814)) | (~c1_1(a833)))),
% 1.81/1.98 inference(transitivity,[status(thm)],[4047, 4045])).
% 1.81/1.98 tff(4049,plain,
% 1.81/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a814) | c2_1(a814) | (~c1_1(a814)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))),
% 1.81/1.98 inference(quant_inst,[status(thm)],[])).
% 1.81/1.98 tff(4050,plain,
% 1.81/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c3_1(a814) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a814) | (~c1_1(a814)) | (~c1_1(a833))),
% 1.81/1.98 inference(modus_ponens,[status(thm)],[4049, 4048])).
% 1.81/1.98 tff(4051,plain,
% 1.81/1.98 ($false),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4050, 130, 2435, 2409, 3945, 3460, 3611, 276, 3459, 84, 4044, 4037])).
% 1.81/1.98 tff(4052,plain,((~hskp13) | c2_1(a833) | c3_1(a833) | (~c2_1(a817)) | (~c3_1(a817)) | c1_1(a817)), inference(lemma,lemma(discharge,[]))).
% 1.81/1.98 tff(4053,plain,
% 1.81/1.98 (~hskp13),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4052, 4036, 277, 276, 4035, 4034])).
% 1.81/1.98 tff(4054,plain,
% 1.81/1.98 (hskp1),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[3986, 4053, 3945, 277])).
% 1.81/1.98 tff(4055,plain,
% 1.81/1.98 (~c0_1(a794)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[264, 4054])).
% 1.81/1.98 tff(4056,plain,
% 1.81/1.98 (c3_1(a794)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[258, 4054])).
% 1.81/1.98 tff(4057,plain,
% 1.81/1.98 (~c2_1(a794)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[250, 4054])).
% 1.81/1.98 tff(4058,plain,
% 1.81/1.98 ($false),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[3839, 4057, 4056, 4032, 22, 289, 979, 4055])).
% 1.81/1.98 tff(4059,plain,(c0_1(a832) | c3_1(a832) | c1_1(a832) | c3_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.81/1.98 tff(4060,plain,
% 1.81/1.98 (c0_1(a832)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4059, 277, 289, 22, 276])).
% 1.81/1.98 tff(4061,plain,
% 1.81/1.98 (~c3_1(a814)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[3442, 3987])).
% 1.81/1.98 tff(4062,assumption,(~c2_1(a814)), introduced(assumption)).
% 1.81/1.98 tff(4063,assumption,(~c3_1(a814)), introduced(assumption)).
% 1.81/1.98 tff(4064,assumption,(~c0_1(a814)), introduced(assumption)).
% 1.81/1.98 tff(4065,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c2_1(a814) | (~c0_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c2_1(a814) | (~c0_1(a832)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4066,plain,
% 1.81/1.98 (((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a814) | c0_1(a814) | c3_1(a814)) <=> (c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c2_1(a814) | (~c0_1(a832)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4067,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a814) | c0_1(a814) | c3_1(a814))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c2_1(a814) | (~c0_1(a832))))),
% 1.81/1.98 inference(monotonicity,[status(thm)],[4066])).
% 1.81/1.98 tff(4068,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a814) | c0_1(a814) | c3_1(a814))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c2_1(a814) | (~c0_1(a832)))),
% 1.81/1.98 inference(transitivity,[status(thm)],[4067, 4065])).
% 1.81/1.98 tff(4069,plain,
% 1.81/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a832) | c3_1(a832) | (~c0_1(a832)) | c2_1(a808) | c1_1(a808) | (~c3_1(a808)) | c2_1(a814) | c0_1(a814) | c3_1(a814))),
% 1.81/1.98 inference(quant_inst,[status(thm)],[])).
% 1.81/1.98 tff(4070,plain,
% 1.81/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | c1_1(a808) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c2_1(a814) | (~c0_1(a832))),
% 1.81/1.98 inference(modus_ponens,[status(thm)],[4069, 4068])).
% 1.81/1.98 tff(4071,plain,
% 1.81/1.98 ($false),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4070, 130, 1416, 289, 22, 4064, 4063, 1415, 1425, 795, 408, 4062])).
% 1.81/1.98 tff(4072,plain,((~hskp11) | c1_1(a832) | c3_1(a832) | c0_1(a814) | c3_1(a814) | (~c0_1(a832)) | c2_1(a814)), inference(lemma,lemma(discharge,[]))).
% 1.81/1.98 tff(4073,plain,
% 1.81/1.98 (~hskp11),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4072, 3988, 22, 289, 4061, 4060, 3996])).
% 1.81/1.98 tff(4074,plain,
% 1.81/1.98 (hskp21),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[2442, 4073])).
% 1.81/1.98 tff(4075,plain,
% 1.81/1.98 (hskp9),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[2807, 4074, 3612])).
% 1.81/1.98 tff(4076,plain,
% 1.81/1.98 (~c3_1(a806)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[63, 4075])).
% 1.81/1.98 tff(4077,plain,
% 1.81/1.98 ((hskp22 | hskp11 | hskp1) <=> (hskp22 | hskp11 | hskp1)),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4078,plain,
% 1.81/1.98 (((hskp22 | hskp1) | hskp11) <=> (hskp22 | hskp11 | hskp1)),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4079,plain,
% 1.81/1.98 ((hskp22 | hskp1) <=> (hskp22 | hskp1)),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4080,plain,
% 1.81/1.98 (((hskp22 | hskp1) | hskp11) <=> ((hskp22 | hskp1) | hskp11)),
% 1.81/1.98 inference(monotonicity,[status(thm)],[4079])).
% 1.81/1.98 tff(4081,plain,
% 1.81/1.98 (((hskp22 | hskp1) | hskp11) <=> (hskp22 | hskp11 | hskp1)),
% 1.81/1.98 inference(transitivity,[status(thm)],[4080, 4078])).
% 1.81/1.98 tff(4082,axiom,((hskp22 | hskp1) | hskp11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 1.81/1.98 tff(4083,plain,
% 1.81/1.98 (hskp22 | hskp11 | hskp1),
% 1.81/1.98 inference(modus_ponens,[status(thm)],[4082, 4081])).
% 1.81/1.98 tff(4084,plain,
% 1.81/1.98 (hskp22 | hskp11 | hskp1),
% 1.81/1.98 inference(modus_ponens,[status(thm)],[4083, 4077])).
% 1.81/1.98 tff(4085,plain,
% 1.81/1.98 (hskp22 | hskp11 | hskp1),
% 1.81/1.98 inference(modus_ponens,[status(thm)],[4084, 4077])).
% 1.81/1.98 tff(4086,plain,
% 1.81/1.98 (hskp22 | hskp11 | hskp1),
% 1.81/1.98 inference(modus_ponens,[status(thm)],[4085, 4077])).
% 1.81/1.98 tff(4087,plain,
% 1.81/1.98 (hskp22 | hskp11 | hskp1),
% 1.81/1.98 inference(modus_ponens,[status(thm)],[4086, 4077])).
% 1.81/1.98 tff(4088,plain,
% 1.81/1.98 (hskp22),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4087, 4073, 3969])).
% 1.81/1.98 tff(4089,plain,
% 1.81/1.98 (~c0_1(a840)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[1826, 4088])).
% 1.81/1.98 tff(4090,plain,
% 1.81/1.98 (c1_1(a806)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[72, 4075])).
% 1.81/1.98 tff(4091,plain,
% 1.81/1.98 (c0_1(a806)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[55, 4075])).
% 1.81/1.98 tff(4092,plain,
% 1.81/1.98 (c3_1(a840)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[1834, 4088])).
% 1.81/1.98 tff(4093,plain,
% 1.81/1.98 (c1_1(a840)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[1860, 4088])).
% 1.81/1.98 tff(4094,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a840) | c0_1(a814) | c3_1(a814) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | c2_1(a814) | (~c1_1(a840)) | (~c3_1(a840)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a840) | c0_1(a814) | c3_1(a814) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | c2_1(a814) | (~c1_1(a840)) | (~c3_1(a840)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4095,plain,
% 1.81/1.98 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a814) | c0_1(a814) | c3_1(a814)) <=> (c0_1(a840) | c0_1(a814) | c3_1(a814) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | c2_1(a814) | (~c1_1(a840)) | (~c3_1(a840)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4096,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a814) | c0_1(a814) | c3_1(a814))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a840) | c0_1(a814) | c3_1(a814) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | c2_1(a814) | (~c1_1(a840)) | (~c3_1(a840))))),
% 1.81/1.98 inference(monotonicity,[status(thm)],[4095])).
% 1.81/1.98 tff(4097,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a814) | c0_1(a814) | c3_1(a814))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a840) | c0_1(a814) | c3_1(a814) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | c2_1(a814) | (~c1_1(a840)) | (~c3_1(a840)))),
% 1.81/1.98 inference(transitivity,[status(thm)],[4096, 4094])).
% 1.81/1.98 tff(4098,plain,
% 1.81/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c0_1(a840) | (~c3_1(a840)) | (~c1_1(a840)) | c2_1(a814) | c0_1(a814) | c3_1(a814))),
% 1.81/1.98 inference(quant_inst,[status(thm)],[])).
% 1.81/1.98 tff(4099,plain,
% 1.81/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a840) | c0_1(a814) | c3_1(a814) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | c2_1(a814) | (~c1_1(a840)) | (~c3_1(a840))),
% 1.81/1.98 inference(modus_ponens,[status(thm)],[4098, 4097])).
% 1.81/1.98 tff(4100,plain,
% 1.81/1.98 ($false),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4099, 130, 4093, 4092, 4091, 4090, 4089, 3988, 4061, 4076, 2427, 3996])).
% 1.81/1.98 tff(4101,plain,(hskp1 | c3_1(a832) | c1_1(a832) | c2_1(a833) | c3_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.81/1.98 tff(4102,plain,
% 1.81/1.98 (c3_1(a833)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4101, 289, 3968, 276, 22])).
% 1.81/1.98 tff(4103,plain,
% 1.81/1.98 (hskp9),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[3809, 669, 3612, 3611])).
% 1.81/1.98 tff(4104,plain,
% 1.81/1.98 (~c3_1(a806)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[63, 4103])).
% 1.81/1.98 tff(4105,plain,
% 1.81/1.98 (c1_1(a806)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[72, 4103])).
% 1.81/1.98 tff(4106,plain,
% 1.81/1.98 (c0_1(a806)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[55, 4103])).
% 1.81/1.98 tff(4107,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a833) | c3_1(a832) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a833) | c3_1(a832) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4108,plain,
% 1.81/1.98 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c0_1(a832) | c3_1(a832) | (~c2_1(a832))) <=> (c2_1(a833) | c3_1(a832) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4109,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a833) | c3_1(a832) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.81/1.98 inference(monotonicity,[status(thm)],[4108])).
% 1.81/1.98 tff(4110,plain,
% 1.81/1.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a833) | c3_1(a832) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.81/1.98 inference(transitivity,[status(thm)],[4109, 4107])).
% 1.81/1.98 tff(4111,plain,
% 1.81/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a833) | (~c3_1(a833)) | (~c1_1(a833)) | c0_1(a832) | c3_1(a832) | (~c2_1(a832)))),
% 1.81/1.98 inference(quant_inst,[status(thm)],[])).
% 1.81/1.98 tff(4112,plain,
% 1.81/1.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a833) | c3_1(a832) | c3_1(a806) | (~ndr1_0) | (~c0_1(a806)) | (~c1_1(a806)) | (~c2_1(a832)) | c0_1(a832) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.81/1.98 inference(modus_ponens,[status(thm)],[4111, 4110])).
% 1.81/1.98 tff(4113,plain,
% 1.81/1.98 ($false),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4112, 130, 3945, 4032, 4106, 4105, 276, 22, 4104, 275, 979, 669])).
% 1.81/1.98 tff(4114,plain,(c0_1(a832) | c2_1(a833) | c3_1(a832) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 1.81/1.98 tff(4115,plain,
% 1.81/1.98 (c0_1(a832)),
% 1.81/1.98 inference(unit_resolution,[status(thm)],[4114, 4102, 22, 276])).
% 1.81/1.98 tff(4116,plain,
% 1.81/1.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~c0_1(a833)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~c0_1(a833)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4117,plain,
% 1.81/1.98 ((hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832))) <=> (hskp5 | (~c0_1(a833)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.81/1.98 inference(rewrite,[status(thm)],[])).
% 1.81/1.98 tff(4118,plain,
% 1.81/1.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~c0_1(a833)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.81/1.98 inference(monotonicity,[status(thm)],[4117])).
% 1.81/1.98 tff(4119,plain,
% 1.81/1.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~c0_1(a833)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.81/1.98 inference(transitivity,[status(thm)],[4118, 4116])).
% 1.81/1.98 tff(4120,plain,
% 1.81/1.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a832) | (~c0_1(a832)) | (~c2_1(a832)))),
% 1.81/1.98 inference(quant_inst,[status(thm)],[])).
% 1.81/1.98 tff(4121,plain,
% 1.81/1.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~c0_1(a833)) | c3_1(a832) | (~ndr1_0) | (~c2_1(a832)) | (~c0_1(a832)) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.81/1.99 inference(modus_ponens,[status(thm)],[4120, 4119])).
% 1.81/1.99 tff(4122,plain,
% 1.81/1.99 (hskp5 | (~c0_1(a832))),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4121, 130, 3945, 4032, 3611, 22, 190, 4102])).
% 1.81/1.99 tff(4123,plain,
% 1.81/1.99 (hskp5),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4122, 4115])).
% 1.81/1.99 tff(4124,plain,
% 1.81/1.99 (~c1_1(a800)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[233, 4123])).
% 1.81/1.99 tff(4125,plain,
% 1.81/1.99 (~c0_1(a800)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[202, 4123])).
% 1.81/1.99 tff(4126,plain,
% 1.81/1.99 (c3_1(a800)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[210, 4123])).
% 1.81/1.99 tff(4127,plain,
% 1.81/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c1_1(a832) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c1_1(a832) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c1_1(a833)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4128,plain,
% 1.81/1.99 (((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> ((~c0_1(a833)) | c2_1(a833) | c1_1(a832) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c1_1(a833)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4129,plain,
% 1.81/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c1_1(a832) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c1_1(a833))))),
% 1.81/1.99 inference(monotonicity,[status(thm)],[4128])).
% 1.81/1.99 tff(4130,plain,
% 1.81/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c1_1(a832) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c1_1(a833)))),
% 1.81/1.99 inference(transitivity,[status(thm)],[4129, 4127])).
% 1.81/1.99 tff(4131,plain,
% 1.81/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c1_1(a832) | (~c0_1(a832)) | (~c2_1(a832)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 1.81/1.99 inference(quant_inst,[status(thm)],[])).
% 1.81/1.99 tff(4132,plain,
% 1.81/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c1_1(a832) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c2_1(a832)) | (~c0_1(a832)) | (~c1_1(a833))),
% 1.81/1.99 inference(modus_ponens,[status(thm)],[4131, 4130])).
% 1.81/1.99 tff(4133,plain,
% 1.81/1.99 ($false),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4132, 130, 3945, 4032, 4126, 3611, 276, 289, 4125, 4124, 287, 4115])).
% 1.81/1.99 tff(4134,plain,(c1_1(a832) | c2_1(a833) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.81/1.99 tff(4135,plain,
% 1.81/1.99 (c1_1(a832)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4134, 22, 276])).
% 1.81/1.99 tff(4136,plain,
% 1.81/1.99 (~hskp19),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[352, 4135])).
% 1.81/1.99 tff(4137,plain,
% 1.81/1.99 (hskp27),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[2464, 4136])).
% 1.81/1.99 tff(4138,plain,
% 1.81/1.99 (c3_1(a796)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[531, 4137])).
% 1.81/1.99 tff(4139,plain,
% 1.81/1.99 (hskp30),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[2456, 4137, 3612])).
% 1.81/1.99 tff(4140,plain,
% 1.81/1.99 (c3_1(a867)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[30, 4139])).
% 1.81/1.99 tff(4141,plain,
% 1.81/1.99 (c0_1(a867)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[46, 4139])).
% 1.81/1.99 tff(4142,plain,
% 1.81/1.99 (c0_1(a796)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[547, 4137])).
% 1.81/1.99 tff(4143,plain,
% 1.81/1.99 (c2_1(a796)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[539, 4137])).
% 1.81/1.99 tff(4144,plain,
% 1.81/1.99 (c1_1(a867)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[38, 4139])).
% 1.81/1.99 tff(4145,plain,
% 1.81/1.99 (hskp11),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[2830, 4144, 3612, 4143, 4142, 4141, 4140, 4138])).
% 1.81/1.99 tff(4146,plain,
% 1.81/1.99 (~c2_1(a808)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[776, 4145])).
% 1.81/1.99 tff(4147,plain,
% 1.81/1.99 (~c1_1(a808)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[770, 4145])).
% 1.81/1.99 tff(4148,plain,
% 1.81/1.99 (c3_1(a808)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[812, 4145])).
% 1.81/1.99 tff(4149,plain,
% 1.81/1.99 (~c0_1(a808)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4014, 4148, 3612, 4147, 4146, 22])).
% 1.81/1.99 tff(4150,plain,
% 1.81/1.99 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | c0_1(a808))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | c0_1(a808))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4151,plain,
% 1.81/1.99 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | c0_1(a808)) <=> (hskp2 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | c0_1(a808))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4152,plain,
% 1.81/1.99 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | c0_1(a808))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | c0_1(a808)))),
% 1.81/1.99 inference(monotonicity,[status(thm)],[4151])).
% 1.81/1.99 tff(4153,plain,
% 1.81/1.99 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | c0_1(a808))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | c0_1(a808))),
% 1.81/1.99 inference(transitivity,[status(thm)],[4152, 4150])).
% 1.81/1.99 tff(4154,plain,
% 1.81/1.99 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a808) | c1_1(a808) | c0_1(a808))),
% 1.81/1.99 inference(quant_inst,[status(thm)],[])).
% 1.81/1.99 tff(4155,plain,
% 1.81/1.99 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a808) | c2_1(a808) | (~ndr1_0) | c0_1(a808)),
% 1.81/1.99 inference(modus_ponens,[status(thm)],[4154, 4153])).
% 1.81/1.99 tff(4156,plain,
% 1.81/1.99 (hskp2),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4155, 130, 3968, 4147, 4146, 2328, 4149])).
% 1.81/1.99 tff(4157,plain,
% 1.81/1.99 (~c3_1(a795)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[1321, 4156])).
% 1.81/1.99 tff(4158,plain,
% 1.81/1.99 (~c0_1(a795)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[1353, 4156])).
% 1.81/1.99 tff(4159,plain,
% 1.81/1.99 (hskp7),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[2839, 130, 2435, 2409, 2401, 4148, 4147, 1413, 4149])).
% 1.81/1.99 tff(4160,plain,
% 1.81/1.99 (~c2_1(a803)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[1377, 4159])).
% 1.81/1.99 tff(4161,plain,
% 1.81/1.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~c0_1(a833)) | c2_1(a833) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | (~c0_1(a833)) | c2_1(a833) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c1_1(a833)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4162,plain,
% 1.81/1.99 ((hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808))) <=> (hskp9 | (~c0_1(a833)) | c2_1(a833) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c1_1(a833)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4163,plain,
% 1.81/1.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~c0_1(a833)) | c2_1(a833) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c1_1(a833))))),
% 1.81/1.99 inference(monotonicity,[status(thm)],[4162])).
% 1.81/1.99 tff(4164,plain,
% 1.81/1.99 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | (~c0_1(a833)) | c2_1(a833) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c1_1(a833)))),
% 1.81/1.99 inference(transitivity,[status(thm)],[4163, 4161])).
% 1.81/1.99 tff(4165,plain,
% 1.81/1.99 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a808) | c0_1(a808) | (~c3_1(a808)))),
% 1.81/1.99 inference(quant_inst,[status(thm)],[])).
% 1.81/1.99 tff(4166,plain,
% 1.81/1.99 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | (~c0_1(a833)) | c2_1(a833) | c2_1(a808) | (~ndr1_0) | (~c3_1(a808)) | c0_1(a808) | (~c1_1(a833))),
% 1.81/1.99 inference(modus_ponens,[status(thm)],[4165, 4164])).
% 1.81/1.99 tff(4167,plain,
% 1.81/1.99 (hskp9),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4166, 130, 3945, 4148, 3611, 276, 4146, 3955, 4149])).
% 1.81/1.99 tff(4168,plain,
% 1.81/1.99 (~c3_1(a806)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[63, 4167])).
% 1.81/1.99 tff(4169,plain,
% 1.81/1.99 (c3_1(a803)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[1385, 4159])).
% 1.81/1.99 tff(4170,plain,
% 1.81/1.99 (c1_1(a803)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[1393, 4159])).
% 1.81/1.99 tff(4171,plain,
% 1.81/1.99 (c1_1(a806)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[72, 4167])).
% 1.81/1.99 tff(4172,plain,
% 1.81/1.99 (c0_1(a806)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[55, 4167])).
% 1.81/1.99 tff(4173,plain,
% 1.81/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a806) | c2_1(a803) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a806) | c2_1(a803) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4174,plain,
% 1.81/1.99 (((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a795) | c3_1(a795) | (~c2_1(a795))) <=> (c3_1(a806) | c2_1(a803) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4175,plain,
% 1.81/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a806) | c2_1(a803) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806))))),
% 1.81/1.99 inference(monotonicity,[status(thm)],[4174])).
% 1.81/1.99 tff(4176,plain,
% 1.81/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a806) | c2_1(a803) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 1.81/1.99 inference(transitivity,[status(thm)],[4175, 4173])).
% 1.81/1.99 tff(4177,plain,
% 1.81/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a806) | (~c1_1(a806)) | (~c0_1(a806)) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c0_1(a795) | c3_1(a795) | (~c2_1(a795)))),
% 1.81/1.99 inference(quant_inst,[status(thm)],[])).
% 1.81/1.99 tff(4178,plain,
% 1.81/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a806) | c2_1(a803) | c0_1(a795) | c3_1(a795) | (~ndr1_0) | (~c2_1(a795)) | (~c3_1(a803)) | (~c1_1(a803)) | (~c0_1(a806)) | (~c1_1(a806))),
% 1.81/1.99 inference(modus_ponens,[status(thm)],[4177, 4176])).
% 1.81/1.99 tff(4179,plain,
% 1.81/1.99 (~c2_1(a795)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4178, 130, 4172, 4171, 4170, 4169, 4168, 4160, 4158, 4157, 275])).
% 1.81/1.99 tff(4180,plain,
% 1.81/1.99 (~c1_1(a795)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[1327, 4156])).
% 1.81/1.99 tff(4181,plain,
% 1.81/1.99 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a803) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a803)) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a803) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4182,plain,
% 1.81/1.99 ((hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a795) | c2_1(a795) | c1_1(a795)) <=> (hskp19 | c2_1(a803) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4183,plain,
% 1.81/1.99 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a795) | c2_1(a795) | c1_1(a795))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | c2_1(a803) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a803)) | (~c1_1(a803))))),
% 1.81/1.99 inference(monotonicity,[status(thm)],[4182])).
% 1.81/1.99 tff(4184,plain,
% 1.81/1.99 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a795) | c2_1(a795) | c1_1(a795))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a803) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.81/1.99 inference(transitivity,[status(thm)],[4183, 4181])).
% 1.81/1.99 tff(4185,plain,
% 1.81/1.99 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp19 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c3_1(a795) | c2_1(a795) | c1_1(a795))),
% 1.81/1.99 inference(quant_inst,[status(thm)],[])).
% 1.81/1.99 tff(4186,plain,
% 1.81/1.99 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp19 | c2_1(a803) | c1_1(a795) | c3_1(a795) | (~ndr1_0) | c2_1(a795) | (~c3_1(a803)) | (~c1_1(a803))),
% 1.81/1.99 inference(modus_ponens,[status(thm)],[4185, 4184])).
% 1.81/1.99 tff(4187,plain,
% 1.81/1.99 ($false),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4186, 130, 4136, 4170, 4169, 4160, 4180, 4157, 10, 4179])).
% 1.81/1.99 tff(4188,plain,(c3_1(a832) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.81/1.99 tff(4189,plain,
% 1.81/1.99 (c3_1(a832)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4188, 276])).
% 1.81/1.99 tff(4190,plain,
% 1.81/1.99 (~hskp19),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[346, 4189])).
% 1.81/1.99 tff(4191,plain,
% 1.81/1.99 (hskp27),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[2464, 4190])).
% 1.81/1.99 tff(4192,plain,
% 1.81/1.99 (hskp30),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[2456, 4191, 3612])).
% 1.81/1.99 tff(4193,plain,
% 1.81/1.99 (c3_1(a867)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[30, 4192])).
% 1.81/1.99 tff(4194,plain,
% 1.81/1.99 (c1_1(a867)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[38, 4192])).
% 1.81/1.99 tff(4195,plain,
% 1.81/1.99 (c0_1(a867)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[46, 4192])).
% 1.81/1.99 tff(4196,plain,
% 1.81/1.99 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4197,plain,
% 1.81/1.99 ((hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833))) <=> (hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4198,plain,
% 1.81/1.99 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c3_1(a833) | (~c1_1(a833))))),
% 1.81/1.99 inference(monotonicity,[status(thm)],[4197])).
% 1.81/1.99 tff(4199,plain,
% 1.81/1.99 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.99 inference(transitivity,[status(thm)],[4198, 4196])).
% 1.81/1.99 tff(4200,plain,
% 1.81/1.99 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)))),
% 1.81/1.99 inference(quant_inst,[status(thm)],[])).
% 1.81/1.99 tff(4201,plain,
% 1.81/1.99 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a833) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | c3_1(a833) | (~c1_1(a833))),
% 1.81/1.99 inference(modus_ponens,[status(thm)],[4200, 4199])).
% 1.81/1.99 tff(4202,plain,
% 1.81/1.99 (hskp12),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4201, 130, 4195, 4194, 4193, 3945, 276, 95, 277])).
% 1.81/1.99 tff(4203,plain,
% 1.81/1.99 (~c0_1(a809)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[143, 4202])).
% 1.81/1.99 tff(4204,plain,
% 1.81/1.99 (c2_1(a809)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[152, 4202])).
% 1.81/1.99 tff(4205,plain,
% 1.81/1.99 (c1_1(a809)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[160, 4202])).
% 1.81/1.99 tff(4206,plain,
% 1.81/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | c3_1(a833) | (~c1_1(a833)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4207,plain,
% 1.81/1.99 (((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809))) <=> ((~c0_1(a833)) | c2_1(a833) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4208,plain,
% 1.81/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~c0_1(a833)) | c2_1(a833) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | c3_1(a833) | (~c1_1(a833))))),
% 1.81/1.99 inference(monotonicity,[status(thm)],[4207])).
% 1.81/1.99 tff(4209,plain,
% 1.81/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | c3_1(a833) | (~c1_1(a833)))),
% 1.81/1.99 inference(transitivity,[status(thm)],[4208, 4206])).
% 1.81/1.99 tff(4210,plain,
% 1.81/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a833) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a833) | c2_1(a833) | (~c1_1(a833)) | c0_1(a809) | (~c2_1(a809)) | (~c1_1(a809)))),
% 1.81/1.99 inference(quant_inst,[status(thm)],[])).
% 1.81/1.99 tff(4211,plain,
% 1.81/1.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (~c0_1(a833)) | c2_1(a833) | c0_1(a809) | (~ndr1_0) | (~c2_1(a809)) | (~c1_1(a809)) | c3_1(a833) | (~c1_1(a833))),
% 1.81/1.99 inference(modus_ponens,[status(thm)],[4210, 4209])).
% 1.81/1.99 tff(4212,plain,
% 1.81/1.99 ($false),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4211, 130, 3945, 4205, 4204, 3611, 276, 4203, 84, 277])).
% 1.81/1.99 tff(4213,plain,(c3_1(a833) | c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.81/1.99 tff(4214,plain,
% 1.81/1.99 (c3_1(a833)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4213, 276])).
% 1.81/1.99 tff(4215,plain,
% 1.81/1.99 (hskp9),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[3809, 4214, 3612, 3611])).
% 1.81/1.99 tff(4216,plain,
% 1.81/1.99 (c0_1(a806)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[55, 4215])).
% 1.81/1.99 tff(4217,plain,
% 1.81/1.99 (~c3_1(a806)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[63, 4215])).
% 1.81/1.99 tff(4218,plain,
% 1.81/1.99 (c1_1(a806)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[72, 4215])).
% 1.81/1.99 tff(4219,plain,
% 1.81/1.99 (c2_1(a806)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[169, 4218, 4193, 4217, 4195, 4194, 4216])).
% 1.81/1.99 tff(4220,plain,
% 1.81/1.99 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~c0_1(a833)) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~c0_1(a833)) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4221,plain,
% 1.81/1.99 ((hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806))) <=> (hskp5 | (~c0_1(a833)) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4222,plain,
% 1.81/1.99 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~c0_1(a833)) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)) | (~c3_1(a833)) | (~c1_1(a833))))),
% 1.81/1.99 inference(monotonicity,[status(thm)],[4221])).
% 1.81/1.99 tff(4223,plain,
% 1.81/1.99 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~c0_1(a833)) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)) | (~c3_1(a833)) | (~c1_1(a833)))),
% 1.81/1.99 inference(transitivity,[status(thm)],[4222, 4220])).
% 1.81/1.99 tff(4224,plain,
% 1.81/1.99 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c3_1(a806) | (~c0_1(a806)) | (~c2_1(a806)))),
% 1.81/1.99 inference(quant_inst,[status(thm)],[])).
% 1.81/1.99 tff(4225,plain,
% 1.81/1.99 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp5 | (~c0_1(a833)) | c3_1(a806) | (~ndr1_0) | (~c2_1(a806)) | (~c0_1(a806)) | (~c3_1(a833)) | (~c1_1(a833))),
% 1.81/1.99 inference(modus_ponens,[status(thm)],[4224, 4223])).
% 1.81/1.99 tff(4226,plain,
% 1.81/1.99 (hskp5),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[4225, 130, 3945, 4216, 3611, 4217, 190, 4214, 4219])).
% 1.81/1.99 tff(4227,plain,
% 1.81/1.99 (~c1_1(a800)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[233, 4226])).
% 1.81/1.99 tff(4228,plain,
% 1.81/1.99 (~c0_1(a800)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[202, 4226])).
% 1.81/1.99 tff(4229,plain,
% 1.81/1.99 (c3_1(a800)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[210, 4226])).
% 1.81/1.99 tff(4230,plain,
% 1.81/1.99 (hskp6),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[3238, 130, 3945, 4229, 276, 4228, 4227, 1853, 4214])).
% 1.81/1.99 tff(4231,plain,
% 1.81/1.99 (~c0_1(a802)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[1873, 4230])).
% 1.81/1.99 tff(4232,plain,
% 1.81/1.99 (hskp7),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[2783, 130, 2435, 2409, 2401, 4229, 4228, 4227, 1413])).
% 1.81/1.99 tff(4233,plain,
% 1.81/1.99 (~c2_1(a803)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[1377, 4232])).
% 1.81/1.99 tff(4234,plain,
% 1.81/1.99 (c2_1(a802)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[1881, 4230])).
% 1.81/1.99 tff(4235,plain,
% 1.81/1.99 (c3_1(a803)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[1385, 4232])).
% 1.81/1.99 tff(4236,plain,
% 1.81/1.99 (c1_1(a803)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[1393, 4232])).
% 1.81/1.99 tff(4237,plain,
% 1.81/1.99 (c3_1(a802)),
% 1.81/1.99 inference(unit_resolution,[status(thm)],[1942, 130, 4216, 4218, 4236, 4235, 4234, 4217, 4233, 4231, 275])).
% 1.81/1.99 tff(4238,plain,
% 1.81/1.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 1.81/1.99 inference(rewrite,[status(thm)],[])).
% 1.81/1.99 tff(4239,plain,
% 1.81/1.99 (((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802))) <=> (c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 1.81/2.00 inference(rewrite,[status(thm)],[])).
% 1.81/2.00 tff(4240,plain,
% 1.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806))))),
% 1.81/2.00 inference(monotonicity,[status(thm)],[4239])).
% 1.81/2.00 tff(4241,plain,
% 1.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)))),
% 1.81/2.00 inference(transitivity,[status(thm)],[4240, 4238])).
% 1.81/2.00 tff(4242,plain,
% 1.81/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a867)) | (~c1_1(a867)) | (~c0_1(a867)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a802) | (~c3_1(a802)) | (~c2_1(a802)))),
% 1.81/2.00 inference(quant_inst,[status(thm)],[])).
% 1.81/2.00 tff(4243,plain,
% 1.81/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a802) | (~ndr1_0) | (~c3_1(a867)) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a802)) | (~c2_1(a802)) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806))),
% 1.81/2.00 inference(modus_ponens,[status(thm)],[4242, 4241])).
% 1.81/2.00 tff(4244,plain,
% 1.81/2.00 ($false),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4243, 130, 4195, 4194, 4193, 4216, 4218, 4234, 4231, 180, 4219, 4237])).
% 1.81/2.00 tff(4245,plain,(c2_1(a833)), inference(lemma,lemma(discharge,[]))).
% 1.81/2.00 tff(4246,plain,
% 1.81/2.00 (~hskp20),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[557, 4245])).
% 1.81/2.00 tff(4247,plain,
% 1.81/2.00 (c3_1(a832) | (~c0_1(a806)) | c3_1(a806) | (~c3_1(a794)) | c0_1(a794) | c2_1(a794) | (~c1_1(a806))),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[3918, 4246])).
% 1.81/2.00 tff(4248,plain,
% 1.81/2.00 ($false),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4247, 265, 259, 22, 145, 85, 251, 96])).
% 1.81/2.00 tff(4249,plain,((~hskp1) | c3_1(a832) | (~c0_1(a806)) | c3_1(a806) | (~c1_1(a806))), inference(lemma,lemma(discharge,[]))).
% 1.81/2.00 tff(4250,plain,
% 1.81/2.00 (~hskp1),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4249, 64, 22, 56, 73])).
% 1.81/2.00 tff(4251,plain,
% 1.81/2.00 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | c0_1(a800) | (~ndr1_0) | (~c3_1(a800)) | c2_1(a800))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp1 | c0_1(a800) | (~ndr1_0) | (~c3_1(a800)) | c2_1(a800))),
% 1.81/2.00 inference(rewrite,[status(thm)],[])).
% 1.81/2.00 tff(4252,plain,
% 1.81/2.00 ((hskp10 | hskp1 | (~ndr1_0) | c2_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (hskp10 | hskp1 | c0_1(a800) | (~ndr1_0) | (~c3_1(a800)) | c2_1(a800))),
% 1.81/2.00 inference(rewrite,[status(thm)],[])).
% 1.81/2.00 tff(4253,plain,
% 1.81/2.00 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | c0_1(a800) | (~ndr1_0) | (~c3_1(a800)) | c2_1(a800)))),
% 1.81/2.00 inference(monotonicity,[status(thm)],[4252])).
% 1.81/2.00 tff(4254,plain,
% 1.81/2.00 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp1 | c0_1(a800) | (~ndr1_0) | (~c3_1(a800)) | c2_1(a800))),
% 1.81/2.00 inference(transitivity,[status(thm)],[4253, 4251])).
% 1.81/2.00 tff(4255,plain,
% 1.81/2.00 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c2_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 1.81/2.00 inference(quant_inst,[status(thm)],[])).
% 1.81/2.00 tff(4256,plain,
% 1.81/2.00 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp10 | hskp1 | c0_1(a800) | (~ndr1_0) | (~c3_1(a800)) | c2_1(a800)),
% 1.81/2.00 inference(modus_ponens,[status(thm)],[4255, 4254])).
% 1.81/2.00 tff(4257,plain,
% 1.81/2.00 (hskp10 | c2_1(a800)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4256, 130, 4250, 211, 203, 244])).
% 1.81/2.00 tff(4258,plain,
% 1.81/2.00 (hskp10),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4257, 218])).
% 1.81/2.00 tff(4259,plain,
% 1.81/2.00 (~c3_1(a807)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[455, 4258])).
% 1.81/2.00 tff(4260,plain,
% 1.81/2.00 (~c2_1(a807)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[498, 4258])).
% 1.81/2.00 tff(4261,plain,
% 1.81/2.00 (~c0_1(a807)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[461, 4258])).
% 1.81/2.00 tff(4262,plain,
% 1.81/2.00 (hskp25 | hskp1),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2354, 130, 58, 57, 65, 2348])).
% 1.81/2.00 tff(4263,plain,
% 1.81/2.00 (hskp25),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4262, 4250])).
% 1.81/2.00 tff(4264,plain,
% 1.81/2.00 (~c3_1(a865)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2361, 4263])).
% 1.81/2.00 tff(4265,plain,
% 1.81/2.00 (c2_1(a865)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2369, 4263])).
% 1.81/2.00 tff(4266,plain,
% 1.81/2.00 (c1_1(a865)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2377, 4263])).
% 1.81/2.00 tff(4267,plain,
% 1.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a865) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | c2_1(a800) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a865) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | c2_1(a800) | (~c2_1(a865)) | (~c1_1(a865)))),
% 1.81/2.00 inference(rewrite,[status(thm)],[])).
% 1.81/2.00 tff(4268,plain,
% 1.81/2.00 (((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a807) | c2_1(a807) | c0_1(a807) | c2_1(a800) | c1_1(a800) | c0_1(a800)) <=> (c3_1(a865) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | c2_1(a800) | (~c2_1(a865)) | (~c1_1(a865)))),
% 1.81/2.00 inference(rewrite,[status(thm)],[])).
% 1.81/2.00 tff(4269,plain,
% 1.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a807) | c2_1(a807) | c0_1(a807) | c2_1(a800) | c1_1(a800) | c0_1(a800))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a865) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | c2_1(a800) | (~c2_1(a865)) | (~c1_1(a865))))),
% 1.81/2.00 inference(monotonicity,[status(thm)],[4268])).
% 1.81/2.00 tff(4270,plain,
% 1.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a807) | c2_1(a807) | c0_1(a807) | c2_1(a800) | c1_1(a800) | c0_1(a800))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a865) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | c2_1(a800) | (~c2_1(a865)) | (~c1_1(a865)))),
% 1.81/2.00 inference(transitivity,[status(thm)],[4269, 4267])).
% 1.81/2.00 tff(4271,plain,
% 1.81/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | c3_1(a807) | c2_1(a807) | c0_1(a807) | c2_1(a800) | c1_1(a800) | c0_1(a800))),
% 1.81/2.00 inference(quant_inst,[status(thm)],[])).
% 1.81/2.00 tff(4272,plain,
% 1.81/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a865) | c0_1(a807) | c2_1(a807) | c3_1(a807) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | c2_1(a800) | (~c2_1(a865)) | (~c1_1(a865))),
% 1.81/2.00 inference(modus_ponens,[status(thm)],[4271, 4270])).
% 1.81/2.00 tff(4273,plain,
% 1.81/2.00 ($false),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4272, 130, 4266, 4265, 4264, 4261, 4260, 4259, 203, 234, 228, 218])).
% 1.81/2.00 tff(4274,plain,((~hskp9) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a867)) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.81/2.00 tff(4275,plain,
% 1.81/2.00 (~hskp9),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4274, 47, 39, 31, 22])).
% 1.81/2.00 tff(4276,plain,
% 1.81/2.00 ((~hskp21) | hskp9),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2807, 4246])).
% 1.81/2.00 tff(4277,plain,
% 1.81/2.00 (~hskp21),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4276, 4275])).
% 1.81/2.00 tff(4278,plain,
% 1.81/2.00 (hskp11),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2442, 4277])).
% 1.81/2.00 tff(4279,plain,
% 1.81/2.00 (~c2_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[776, 4278])).
% 1.81/2.00 tff(4280,plain,
% 1.81/2.00 (~c1_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[770, 4278])).
% 1.81/2.00 tff(4281,plain,
% 1.81/2.00 (c3_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[812, 4278])).
% 1.81/2.00 tff(4282,plain,
% 1.81/2.00 ((~c0_1(a808)) | c3_1(a832) | c1_1(a808) | c2_1(a808) | (~c3_1(a808))),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4014, 4246])).
% 1.81/2.00 tff(4283,plain,
% 1.81/2.00 (~c0_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4282, 4281, 4280, 4279, 22])).
% 1.81/2.00 tff(4284,plain,
% 1.81/2.00 (hskp9 | c2_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2918, 130, 4246, 47, 31, 21])).
% 1.81/2.00 tff(4285,plain,
% 1.81/2.00 (c2_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4284, 4275])).
% 1.81/2.00 tff(4286,plain,
% 1.81/2.00 (hskp7),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1422, 130, 39, 31, 4281, 4280, 1413, 4285, 4283])).
% 1.81/2.00 tff(4287,plain,
% 1.81/2.00 (~c2_1(a803)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1377, 4286])).
% 1.81/2.00 tff(4288,plain,
% 1.81/2.00 (hskp18),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2248, 4285, 4277, 39, 31])).
% 1.81/2.00 tff(4289,plain,
% 1.81/2.00 (~c3_1(a828)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1107, 4288])).
% 1.81/2.00 tff(4290,plain,
% 1.81/2.00 (~c2_1(a828)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1101, 4288])).
% 1.81/2.00 tff(4291,plain,
% 1.81/2.00 (~c1_1(a828)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1113, 4288])).
% 1.81/2.00 tff(4292,plain,
% 1.81/2.00 (c3_1(a803)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1385, 4286])).
% 1.81/2.00 tff(4293,plain,
% 1.81/2.00 (c1_1(a803)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1393, 4286])).
% 1.81/2.00 tff(4294,plain,
% 1.81/2.00 (~hskp21),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4276, 11])).
% 1.81/2.00 tff(4295,plain,
% 1.81/2.00 (hskp30),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2743, 4294])).
% 1.81/2.00 tff(4296,plain,
% 1.81/2.00 (c3_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[30, 4295])).
% 1.81/2.00 tff(4297,plain,
% 1.81/2.00 (c1_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[38, 4295])).
% 1.81/2.00 tff(4298,plain,
% 1.81/2.00 (c0_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[46, 4295])).
% 1.81/2.00 tff(4299,plain,
% 1.81/2.00 (hskp11),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2442, 4294])).
% 1.81/2.00 tff(4300,plain,
% 1.81/2.00 (c3_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[812, 4299])).
% 1.81/2.00 tff(4301,plain,
% 1.81/2.00 ((~hskp27) | hskp30),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2456, 4246])).
% 1.81/2.00 tff(4302,plain,
% 1.81/2.00 (hskp30),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4301, 2812])).
% 1.81/2.00 tff(4303,plain,
% 1.81/2.00 (c3_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[30, 4302])).
% 1.81/2.00 tff(4304,plain,
% 1.81/2.00 (c0_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[46, 4302])).
% 1.81/2.00 tff(4305,plain,
% 1.81/2.00 (c1_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[38, 4302])).
% 1.81/2.00 tff(4306,plain,
% 1.81/2.00 (hskp11 | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a867)) | (~c0_1(a796)) | (~c2_1(a796)) | (~c3_1(a796))),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2830, 4246])).
% 1.81/2.00 tff(4307,plain,
% 1.81/2.00 (hskp11),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4306, 4305, 2814, 2815, 4304, 4303, 2813])).
% 1.81/2.00 tff(4308,plain,
% 1.81/2.00 (~c2_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[776, 4307])).
% 1.81/2.00 tff(4309,plain,
% 1.81/2.00 (~c1_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[770, 4307])).
% 1.81/2.00 tff(4310,plain,
% 1.81/2.00 (c3_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[812, 4307])).
% 1.81/2.00 tff(4311,plain,
% 1.81/2.00 (~c0_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4282, 4310, 4309, 4308, 22])).
% 1.81/2.00 tff(4312,plain,
% 1.81/2.00 (~hskp7),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1402, 1362, 22, 289])).
% 1.81/2.00 tff(4313,plain,
% 1.81/2.00 ($false),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2839, 130, 4312, 2435, 2409, 2401, 4310, 4309, 1413, 4311])).
% 1.81/2.00 tff(4314,plain,(c2_1(a832) | c3_1(a832) | c1_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.81/2.00 tff(4315,plain,
% 1.81/2.00 (c2_1(a832)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4314, 289, 22])).
% 1.81/2.00 tff(4316,plain,
% 1.81/2.00 (~c1_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[770, 4299])).
% 1.81/2.00 tff(4317,plain,
% 1.81/2.00 (~c2_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[776, 4299])).
% 1.81/2.00 tff(4318,plain,
% 1.81/2.00 (c1_1(a808) | hskp9 | (~c3_1(a808)) | c2_1(a808) | (~c2_1(a832)) | c3_1(a832) | c1_1(a832) | (~c0_1(a867)) | (~c1_1(a867)) | (~c3_1(a867))),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[3023, 4246])).
% 1.81/2.00 tff(4319,plain,
% 1.81/2.00 ($false),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4318, 4317, 4316, 289, 4315, 11, 22, 4300, 4298, 4297, 4296])).
% 1.81/2.00 tff(4320,plain,(hskp9 | c1_1(a832) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.81/2.00 tff(4321,plain,
% 1.81/2.00 (c1_1(a832)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4320, 4275, 22])).
% 1.81/2.00 tff(4322,plain,
% 1.81/2.00 (~hskp19),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[352, 4321])).
% 1.81/2.00 tff(4323,plain,
% 1.81/2.00 ($false),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1707, 130, 4322, 4293, 4292, 4291, 4290, 4289, 4287, 10])).
% 1.81/2.00 tff(4324,plain,((~hskp30) | c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.81/2.00 tff(4325,plain,
% 1.81/2.00 (~hskp30),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4324, 22])).
% 1.81/2.00 tff(4326,plain,
% 1.81/2.00 (hskp21),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2743, 4325])).
% 1.81/2.00 tff(4327,plain,
% 1.81/2.00 (hskp9),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4276, 4326])).
% 1.81/2.00 tff(4328,plain,
% 1.81/2.00 (c1_1(a806)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[72, 4327])).
% 1.81/2.00 tff(4329,plain,
% 1.81/2.00 (c0_1(a806)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[55, 4327])).
% 1.81/2.00 tff(4330,plain,
% 1.81/2.00 (~c3_1(a806)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[63, 4327])).
% 1.81/2.00 tff(4331,plain,
% 1.81/2.00 (~hskp1),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4249, 4330, 22, 4329, 4328])).
% 1.81/2.00 tff(4332,plain,
% 1.81/2.00 (hskp30 | (~c0_1(a797))),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2416, 4246])).
% 1.81/2.00 tff(4333,plain,
% 1.81/2.00 (~c0_1(a797)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4332, 309])).
% 1.81/2.00 tff(4334,plain,
% 1.81/2.00 (c0_1(a838)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[406, 2744])).
% 1.81/2.00 tff(4335,plain,
% 1.81/2.00 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | c1_1(a838))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | c1_1(a838))),
% 1.81/2.00 inference(rewrite,[status(thm)],[])).
% 1.81/2.00 tff(4336,plain,
% 1.81/2.00 ((hskp20 | hskp1 | (~ndr1_0) | c2_1(a838) | c1_1(a838) | (~c0_1(a838))) <=> (hskp20 | hskp1 | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | c1_1(a838))),
% 1.81/2.00 inference(rewrite,[status(thm)],[])).
% 1.81/2.00 tff(4337,plain,
% 1.81/2.00 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a838) | c1_1(a838) | (~c0_1(a838)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | c1_1(a838)))),
% 1.81/2.00 inference(monotonicity,[status(thm)],[4336])).
% 1.81/2.00 tff(4338,plain,
% 1.81/2.00 (((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a838) | c1_1(a838) | (~c0_1(a838)))) <=> ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | c1_1(a838))),
% 1.81/2.00 inference(transitivity,[status(thm)],[4337, 4335])).
% 1.81/2.00 tff(4339,plain,
% 1.81/2.00 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp20 | hskp1 | (~ndr1_0) | c2_1(a838) | c1_1(a838) | (~c0_1(a838)))),
% 1.81/2.00 inference(quant_inst,[status(thm)],[])).
% 1.81/2.00 tff(4340,plain,
% 1.81/2.00 ((~![U: $i] : (hskp20 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp20 | hskp1 | c2_1(a838) | (~ndr1_0) | (~c0_1(a838)) | c1_1(a838)),
% 1.81/2.00 inference(modus_ponens,[status(thm)],[4339, 4338])).
% 1.81/2.00 tff(4341,plain,
% 1.81/2.00 (c1_1(a838)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4340, 130, 4246, 3969, 4334, 2745, 1541])).
% 1.81/2.00 tff(4342,plain,
% 1.81/2.00 (c3_1(a838)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[398, 2744])).
% 1.81/2.00 tff(4343,plain,
% 1.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 1.81/2.00 inference(rewrite,[status(thm)],[])).
% 1.81/2.00 tff(4344,plain,
% 1.81/2.00 (((~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797))) <=> ((~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 1.81/2.00 inference(rewrite,[status(thm)],[])).
% 1.81/2.00 tff(4345,plain,
% 1.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))))),
% 1.81/2.00 inference(monotonicity,[status(thm)],[4344])).
% 1.81/2.00 tff(4346,plain,
% 1.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 1.81/2.00 inference(transitivity,[status(thm)],[4345, 4343])).
% 1.81/2.00 tff(4347,plain,
% 1.81/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a838)) | (~c1_1(a838)) | (~c0_1(a838)) | (~c1_1(a806)) | (~c0_1(a806)) | (~c2_1(a806)) | c0_1(a797) | (~c3_1(a797)) | (~c2_1(a797)))),
% 1.81/2.00 inference(quant_inst,[status(thm)],[])).
% 1.81/2.00 tff(4348,plain,
% 1.81/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~ndr1_0) | (~c2_1(a797)) | (~c3_1(a797)) | c0_1(a797) | (~c2_1(a806)) | (~c0_1(a806)) | (~c1_1(a806)) | (~c3_1(a838)) | (~c0_1(a838)) | (~c1_1(a838))),
% 1.81/2.00 inference(modus_ponens,[status(thm)],[4347, 4346])).
% 1.81/2.00 tff(4349,plain,
% 1.81/2.00 (~c2_1(a806)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4348, 130, 2409, 2401, 4334, 4342, 145, 96, 180, 4341, 4333])).
% 1.81/2.00 tff(4350,plain,
% 1.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a838) | c3_1(a806) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a838)) | (~c1_1(a838)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a838) | c3_1(a806) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 1.81/2.00 inference(rewrite,[status(thm)],[])).
% 1.81/2.00 tff(4351,plain,
% 1.81/2.00 (((~ndr1_0) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797))) <=> (c2_1(a838) | c3_1(a806) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 1.81/2.00 inference(rewrite,[status(thm)],[])).
% 1.81/2.00 tff(4352,plain,
% 1.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a838) | c3_1(a806) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a838)) | (~c1_1(a838))))),
% 1.81/2.00 inference(monotonicity,[status(thm)],[4351])).
% 1.81/2.00 tff(4353,plain,
% 1.81/2.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a838) | c3_1(a806) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a838)) | (~c1_1(a838)))),
% 1.81/2.00 inference(transitivity,[status(thm)],[4352, 4350])).
% 1.81/2.00 tff(4354,plain,
% 1.81/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a838) | (~c1_1(a838)) | (~c0_1(a838)) | c3_1(a806) | c2_1(a806) | (~c1_1(a806)) | c0_1(a797) | (~c2_1(a797)) | (~c1_1(a797)))),
% 1.81/2.00 inference(quant_inst,[status(thm)],[])).
% 1.81/2.00 tff(4355,plain,
% 1.81/2.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a838) | c3_1(a806) | (~ndr1_0) | (~c2_1(a797)) | (~c1_1(a797)) | c0_1(a797) | c2_1(a806) | (~c1_1(a806)) | (~c0_1(a838)) | (~c1_1(a838))),
% 1.81/2.00 inference(modus_ponens,[status(thm)],[4354, 4353])).
% 1.81/2.00 tff(4356,plain,
% 1.81/2.00 ($false),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4355, 130, 2435, 2409, 4334, 96, 2745, 85, 84, 4341, 4349, 4333])).
% 1.81/2.00 tff(4357,plain,(hskp30 | (~c1_1(a806)) | c3_1(a806) | (~c0_1(a806)) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.81/2.00 tff(4358,plain,
% 1.81/2.00 ($false),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4357, 4331, 4330, 4325, 4329, 4328])).
% 1.81/2.00 tff(4359,plain,(c3_1(a832)), inference(lemma,lemma(discharge,[]))).
% 1.81/2.00 tff(4360,plain,
% 1.81/2.00 (~hskp19),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[346, 4359])).
% 1.81/2.00 tff(4361,plain,
% 1.81/2.00 (hskp27),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2464, 4360])).
% 1.81/2.00 tff(4362,plain,
% 1.81/2.00 (c3_1(a796)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[531, 4361])).
% 1.81/2.00 tff(4363,plain,
% 1.81/2.00 (hskp30),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4301, 4361])).
% 1.81/2.00 tff(4364,plain,
% 1.81/2.00 (c3_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[30, 4363])).
% 1.81/2.00 tff(4365,plain,
% 1.81/2.00 (c0_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[46, 4363])).
% 1.81/2.00 tff(4366,plain,
% 1.81/2.00 (c0_1(a796)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[547, 4361])).
% 1.81/2.00 tff(4367,plain,
% 1.81/2.00 (c2_1(a796)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[539, 4361])).
% 1.81/2.00 tff(4368,plain,
% 1.81/2.00 (c1_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[38, 4363])).
% 1.81/2.00 tff(4369,plain,
% 1.81/2.00 (hskp11),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4306, 4368, 4367, 4366, 4365, 4364, 4362])).
% 1.81/2.00 tff(4370,plain,
% 1.81/2.00 (~c2_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[776, 4369])).
% 1.81/2.00 tff(4371,plain,
% 1.81/2.00 (c3_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[812, 4369])).
% 1.81/2.00 tff(4372,plain,
% 1.81/2.00 (hskp9 | (~c0_1(a808))),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1431, 130, 4246, 4371, 4370, 21])).
% 1.81/2.00 tff(4373,plain,
% 1.81/2.00 (~c0_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4372, 11])).
% 1.81/2.00 tff(4374,plain,
% 1.81/2.00 (hskp9 | c2_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2918, 130, 4246, 4365, 4364, 21])).
% 1.81/2.00 tff(4375,plain,
% 1.81/2.00 (c2_1(a867)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4374, 11])).
% 1.81/2.00 tff(4376,plain,
% 1.81/2.00 (~c1_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[770, 4369])).
% 1.81/2.00 tff(4377,plain,
% 1.81/2.00 (hskp7 | (~c2_1(a867)) | c0_1(a808)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1422, 130, 4368, 4364, 4371, 4376, 1413])).
% 1.81/2.00 tff(4378,plain,
% 1.81/2.00 (hskp7),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[4377, 4375, 4373])).
% 1.81/2.00 tff(4379,plain,
% 1.81/2.00 (~c2_1(a803)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1377, 4378])).
% 1.81/2.00 tff(4380,plain,
% 1.81/2.00 (hskp18),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[3157, 4294, 4371, 4370])).
% 1.81/2.00 tff(4381,plain,
% 1.81/2.00 (~c3_1(a828)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1107, 4380])).
% 1.81/2.00 tff(4382,plain,
% 1.81/2.00 (~c2_1(a828)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1101, 4380])).
% 1.81/2.00 tff(4383,plain,
% 1.81/2.00 (~c1_1(a828)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1113, 4380])).
% 1.81/2.00 tff(4384,plain,
% 1.81/2.00 (c3_1(a803)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1385, 4378])).
% 1.81/2.00 tff(4385,plain,
% 1.81/2.00 (c1_1(a803)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1393, 4378])).
% 1.81/2.00 tff(4386,plain,
% 1.81/2.00 ($false),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1707, 130, 4360, 4385, 4384, 4383, 4382, 4381, 4379, 10])).
% 1.81/2.00 tff(4387,plain,(hskp9), inference(lemma,lemma(discharge,[]))).
% 1.81/2.00 tff(4388,plain,
% 1.81/2.00 (c0_1(a806)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[55, 4387])).
% 1.81/2.00 tff(4389,plain,
% 1.81/2.00 (~c3_1(a806)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[63, 4387])).
% 1.81/2.00 tff(4390,plain,
% 1.81/2.00 (c1_1(a806)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[72, 4387])).
% 1.81/2.00 tff(4391,plain,
% 1.81/2.00 (c2_1(a806)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[169, 4390, 4364, 4389, 4365, 4368, 4388])).
% 1.81/2.00 tff(4392,plain,
% 1.81/2.00 (hskp5),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[196, 130, 4365, 4368, 4364, 4388, 4389, 190, 4391])).
% 1.81/2.00 tff(4393,plain,
% 1.81/2.00 (~c1_1(a800)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[233, 4392])).
% 1.81/2.00 tff(4394,plain,
% 1.81/2.00 (~c0_1(a800)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[202, 4392])).
% 1.81/2.00 tff(4395,plain,
% 1.81/2.00 (c3_1(a800)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[210, 4392])).
% 1.81/2.00 tff(4396,plain,
% 1.81/2.00 (hskp7),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[2783, 130, 2435, 2409, 2401, 4395, 4394, 4393, 1413])).
% 1.81/2.00 tff(4397,plain,
% 1.81/2.00 (~c2_1(a803)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1377, 4396])).
% 1.81/2.00 tff(4398,plain,
% 1.81/2.00 (c3_1(a803)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1385, 4396])).
% 1.81/2.00 tff(4399,plain,
% 1.81/2.00 (c1_1(a803)),
% 1.81/2.00 inference(unit_resolution,[status(thm)],[1393, 4396])).
% 1.81/2.00 tff(4400,plain,
% 1.81/2.00 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a803)) | (~c1_1(a803)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.81/2.00 inference(rewrite,[status(thm)],[])).
% 1.81/2.00 tff(4401,plain,
% 1.81/2.00 ((hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800))) <=> (hskp6 | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.81/2.01 inference(rewrite,[status(thm)],[])).
% 1.81/2.01 tff(4402,plain,
% 1.81/2.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a803)) | (~c1_1(a803))))),
% 1.81/2.01 inference(monotonicity,[status(thm)],[4401])).
% 1.81/2.01 tff(4403,plain,
% 1.81/2.01 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a803)) | (~c1_1(a803)))),
% 1.81/2.01 inference(transitivity,[status(thm)],[4402, 4400])).
% 1.81/2.01 tff(4404,plain,
% 1.81/2.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a803) | (~c3_1(a803)) | (~c1_1(a803)) | c1_1(a800) | c0_1(a800) | (~c3_1(a800)))),
% 1.81/2.01 inference(quant_inst,[status(thm)],[])).
% 1.81/2.01 tff(4405,plain,
% 1.81/2.01 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c2_1(a803) | c0_1(a800) | c1_1(a800) | (~ndr1_0) | (~c3_1(a800)) | (~c3_1(a803)) | (~c1_1(a803))),
% 1.81/2.01 inference(modus_ponens,[status(thm)],[4404, 4403])).
% 1.81/2.01 tff(4406,plain,
% 1.81/2.01 (hskp6),
% 1.81/2.01 inference(unit_resolution,[status(thm)],[4405, 130, 4399, 4398, 4395, 4397, 4394, 4393, 1853])).
% 1.81/2.01 tff(4407,plain,
% 1.81/2.01 (~c0_1(a802)),
% 1.81/2.01 inference(unit_resolution,[status(thm)],[1873, 4406])).
% 1.81/2.01 tff(4408,plain,
% 1.81/2.01 (c2_1(a802)),
% 1.81/2.01 inference(unit_resolution,[status(thm)],[1881, 4406])).
% 1.81/2.01 tff(4409,plain,
% 1.81/2.01 (~c3_1(a802)),
% 1.81/2.01 inference(unit_resolution,[status(thm)],[4243, 130, 4365, 4368, 4364, 4388, 4390, 4408, 4407, 180, 4391])).
% 1.81/2.01 tff(4410,plain,
% 1.81/2.01 ($false),
% 1.81/2.01 inference(unit_resolution,[status(thm)],[1942, 130, 4388, 4390, 4399, 4398, 4408, 4389, 4397, 4407, 275, 4409])).
% 1.81/2.01 % SZS output end Proof
% 1.81/2.01 % E exiting
%------------------------------------------------------------------------------