%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN465-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:39:13 AM UTC 2025
% Result : Unsatisfiable 0.59s 0.83s
% Output : Proof 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN465-1 : TPTP v9.0.0. Released v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:35:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.59/0.83 % SZS status Unsatisfiable
% 0.59/0.83 % SZS output start Proof
% 0.59/0.83 tff(c0_1_type, type, (
% 0.59/0.83 c0_1: $i > $o)).
% 0.59/0.83 tff(a20_type, type, (
% 0.59/0.83 a20: $i)).
% 0.59/0.83 tff(hskp30_type, type, (
% 0.59/0.83 hskp30: $o)).
% 0.59/0.83 tff(c3_1_type, type, (
% 0.59/0.83 c3_1: $i > $o)).
% 0.59/0.83 tff(a15_type, type, (
% 0.59/0.83 a15: $i)).
% 0.59/0.83 tff(hskp9_type, type, (
% 0.59/0.83 hskp9: $o)).
% 0.59/0.83 tff(c2_1_type, type, (
% 0.59/0.83 c2_1: $i > $o)).
% 0.59/0.83 tff(c1_1_type, type, (
% 0.59/0.83 c1_1: $i > $o)).
% 0.59/0.83 tff(ndr1_0_type, type, (
% 0.59/0.83 ndr1_0: $o)).
% 0.59/0.83 tff(hskp25_type, type, (
% 0.59/0.83 hskp25: $o)).
% 0.59/0.83 tff(a8_type, type, (
% 0.59/0.83 a8: $i)).
% 0.59/0.83 tff(hskp29_type, type, (
% 0.59/0.83 hskp29: $o)).
% 0.59/0.83 tff(a6_type, type, (
% 0.59/0.83 a6: $i)).
% 0.59/0.83 tff(hskp8_type, type, (
% 0.59/0.83 hskp8: $o)).
% 0.59/0.83 tff(hskp21_type, type, (
% 0.59/0.83 hskp21: $o)).
% 0.59/0.83 tff(hskp3_type, type, (
% 0.59/0.83 hskp3: $o)).
% 0.59/0.83 tff(a21_type, type, (
% 0.59/0.83 a21: $i)).
% 0.59/0.83 tff(hskp11_type, type, (
% 0.59/0.83 hskp11: $o)).
% 0.59/0.83 tff(a9_type, type, (
% 0.59/0.83 a9: $i)).
% 0.59/0.83 tff(hskp5_type, type, (
% 0.59/0.83 hskp5: $o)).
% 0.59/0.83 tff(a30_type, type, (
% 0.59/0.83 a30: $i)).
% 0.59/0.83 tff(hskp16_type, type, (
% 0.59/0.83 hskp16: $o)).
% 0.59/0.83 tff(a29_type, type, (
% 0.59/0.83 a29: $i)).
% 0.59/0.83 tff(hskp15_type, type, (
% 0.59/0.83 hskp15: $o)).
% 0.59/0.83 tff(a39_type, type, (
% 0.59/0.83 a39: $i)).
% 0.59/0.83 tff(hskp24_type, type, (
% 0.59/0.83 hskp24: $o)).
% 0.59/0.83 tff(hskp31_type, type, (
% 0.59/0.83 hskp31: $o)).
% 0.59/0.83 tff(hskp12_type, type, (
% 0.59/0.83 hskp12: $o)).
% 0.59/0.83 tff(a24_type, type, (
% 0.59/0.83 a24: $i)).
% 0.59/0.83 tff(a13_type, type, (
% 0.59/0.83 a13: $i)).
% 0.59/0.83 tff(a10_type, type, (
% 0.59/0.83 a10: $i)).
% 0.59/0.83 tff(hskp6_type, type, (
% 0.59/0.83 hskp6: $o)).
% 0.59/0.83 tff(a52_type, type, (
% 0.59/0.83 a52: $i)).
% 0.59/0.83 tff(hskp2_type, type, (
% 0.59/0.83 hskp2: $o)).
% 0.59/0.83 tff(a5_type, type, (
% 0.59/0.83 a5: $i)).
% 0.59/0.83 tff(a42_type, type, (
% 0.59/0.83 a42: $i)).
% 0.59/0.83 tff(hskp10_type, type, (
% 0.59/0.83 hskp10: $o)).
% 0.59/0.83 tff(a17_type, type, (
% 0.59/0.83 a17: $i)).
% 0.59/0.83 tff(hskp13_type, type, (
% 0.59/0.83 hskp13: $o)).
% 0.59/0.83 tff(a26_type, type, (
% 0.59/0.83 a26: $i)).
% 0.59/0.83 tff(hskp23_type, type, (
% 0.59/0.83 hskp23: $o)).
% 0.59/0.83 tff(a1_type, type, (
% 0.59/0.83 a1: $i)).
% 0.59/0.83 tff(hskp0_type, type, (
% 0.59/0.83 hskp0: $o)).
% 0.59/0.83 tff(a54_type, type, (
% 0.59/0.83 a54: $i)).
% 0.59/0.83 tff(a28_type, type, (
% 0.59/0.83 a28: $i)).
% 0.59/0.83 tff(hskp14_type, type, (
% 0.59/0.83 hskp14: $o)).
% 0.59/0.83 tff(hskp19_type, type, (
% 0.59/0.83 hskp19: $o)).
% 0.59/0.83 tff(a35_type, type, (
% 0.59/0.83 a35: $i)).
% 0.59/0.83 tff(a12_type, type, (
% 0.59/0.83 a12: $i)).
% 0.59/0.83 tff(hskp7_type, type, (
% 0.59/0.83 hskp7: $o)).
% 0.59/0.83 tff(a40_type, type, (
% 0.59/0.83 a40: $i)).
% 0.59/0.83 tff(hskp22_type, type, (
% 0.59/0.83 hskp22: $o)).
% 0.59/0.83 tff(a76_type, type, (
% 0.59/0.83 a76: $i)).
% 0.59/0.83 tff(1,assumption,(~hskp30), introduced(assumption)).
% 0.59/0.83 tff(2,plain,
% 0.59/0.83 (^[U: $i] : refl((hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))),
% 0.59/0.83 inference(bind,[status(th)],[])).
% 0.59/0.83 tff(3,plain,
% 0.59/0.83 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.59/0.83 inference(quant_intro,[status(thm)],[2])).
% 0.59/0.83 tff(4,plain,
% 0.59/0.83 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(5,plain,
% 0.59/0.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp25))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) <=> (hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp9) <=> ((hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp9))), rewrite(((hskp25 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp9) <=> (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp9) <=> (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(6,plain,
% 0.59/0.84 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp9) <=> ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[5])).
% 0.59/0.84 tff(7,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp25) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.59/0.84 tff(8,plain,
% 0.59/0.84 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.59/0.84 tff(9,plain,
% 0.59/0.84 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.59/0.84 tff(10,plain,(
% 0.59/0.84 ![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.59/0.84 inference(skolemize,[status(sab)],[9])).
% 0.59/0.84 tff(11,plain,
% 0.59/0.84 (![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.59/0.84 tff(12,plain,
% 0.59/0.84 (^[U: $i] : refl((hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(13,plain,
% 0.59/0.84 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[12])).
% 0.59/0.84 tff(14,plain,
% 0.59/0.84 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(15,plain,
% 0.59/0.84 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp21) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp21) <=> (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(16,plain,
% 0.59/0.84 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp21) <=> ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[15])).
% 0.59/0.84 tff(17,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.59/0.84 tff(18,plain,
% 0.59/0.84 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.59/0.84 tff(19,plain,
% 0.59/0.84 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.59/0.84 tff(20,plain,(
% 0.59/0.84 ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(skolemize,[status(sab)],[19])).
% 0.59/0.84 tff(21,plain,
% 0.59/0.84 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.59/0.84 tff(22,plain,
% 0.59/0.84 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(23,plain,
% 0.59/0.84 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[22])).
% 0.59/0.84 tff(24,plain,
% 0.59/0.84 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(25,plain,
% 0.59/0.84 (^[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(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(26,plain,
% 0.59/0.84 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[25])).
% 0.59/0.84 tff(27,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 0.59/0.84 tff(28,plain,
% 0.59/0.84 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.59/0.84 tff(29,plain,
% 0.59/0.84 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.59/0.84 tff(30,plain,(
% 0.59/0.84 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.59/0.84 inference(skolemize,[status(sab)],[29])).
% 0.59/0.84 tff(31,plain,
% 0.59/0.84 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.59/0.84 tff(32,plain,
% 0.59/0.84 (^[U: $i] : refl((hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(33,plain,
% 0.59/0.84 (![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[32])).
% 0.59/0.84 tff(34,plain,
% 0.59/0.84 (![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(35,plain,
% 0.59/0.84 (^[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)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp11) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp11))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp11) <=> (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp11) <=> (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(36,plain,
% 0.59/0.84 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp11) <=> ![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[35])).
% 0.59/0.84 tff(37,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp30) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.59/0.84 tff(38,plain,
% 0.59/0.84 (![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.59/0.84 tff(39,plain,
% 0.59/0.84 (![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.59/0.84 tff(40,plain,(
% 0.59/0.84 ![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.59/0.84 inference(skolemize,[status(sab)],[39])).
% 0.59/0.84 tff(41,plain,
% 0.59/0.84 (![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.59/0.84 tff(42,assumption,(hskp21), introduced(assumption)).
% 0.59/0.84 tff(43,assumption,(~hskp16), introduced(assumption)).
% 0.59/0.84 tff(44,plain,
% 0.59/0.84 (^[U: $i] : refl((hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(45,plain,
% 0.59/0.84 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[44])).
% 0.59/0.84 tff(46,plain,
% 0.59/0.84 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(47,plain,
% 0.59/0.84 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp16))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(48,plain,
% 0.59/0.84 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16) <=> ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[47])).
% 0.59/0.84 tff(49,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.59/0.84 tff(50,plain,
% 0.59/0.84 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.59/0.84 tff(51,plain,
% 0.59/0.84 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.59/0.84 tff(52,plain,(
% 0.59/0.84 ![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.84 inference(skolemize,[status(sab)],[51])).
% 0.59/0.84 tff(53,plain,
% 0.59/0.84 (![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.59/0.84 tff(54,plain,
% 0.59/0.84 (((~hskp21) | (~c3_1(a39))) <=> ((~hskp21) | (~c3_1(a39)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(55,plain,
% 0.59/0.84 (((~c3_1(a39)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a39)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(56,axiom,((~c3_1(a39)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.59/0.84 tff(57,plain,
% 0.59/0.84 ((~hskp21) | (~c3_1(a39))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.59/0.84 tff(58,plain,
% 0.59/0.84 ((~hskp21) | (~c3_1(a39))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.59/0.84 tff(59,plain,
% 0.59/0.84 (~c3_1(a39)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[58, 42])).
% 0.59/0.84 tff(60,plain,
% 0.59/0.84 (((~hskp21) | (~c0_1(a39))) <=> ((~hskp21) | (~c0_1(a39)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(61,plain,
% 0.59/0.84 (((~c0_1(a39)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a39)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(62,axiom,((~c0_1(a39)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.59/0.84 tff(63,plain,
% 0.59/0.84 ((~hskp21) | (~c0_1(a39))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.59/0.84 tff(64,plain,
% 0.59/0.84 ((~hskp21) | (~c0_1(a39))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.59/0.84 tff(65,plain,
% 0.59/0.84 (~c0_1(a39)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[64, 42])).
% 0.59/0.84 tff(66,plain,
% 0.59/0.84 (((~hskp21) | c2_1(a39)) <=> ((~hskp21) | c2_1(a39))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(67,axiom,((~hskp21) | c2_1(a39)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.59/0.84 tff(68,plain,
% 0.59/0.84 ((~hskp21) | c2_1(a39)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.59/0.84 tff(69,plain,
% 0.59/0.84 ((~hskp21) | c2_1(a39)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[68, 66])).
% 0.59/0.84 tff(70,plain,
% 0.59/0.84 ((~hskp21) | c2_1(a39)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.59/0.84 tff(71,plain,
% 0.59/0.84 ((~hskp21) | c2_1(a39)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.59/0.84 tff(72,plain,
% 0.59/0.84 ((~hskp21) | c2_1(a39)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[71, 66])).
% 0.59/0.84 tff(73,plain,
% 0.59/0.84 (c2_1(a39)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[72, 42])).
% 0.59/0.84 tff(74,assumption,(~hskp15), introduced(assumption)).
% 0.59/0.84 tff(75,assumption,(~ndr1_0), introduced(assumption)).
% 0.59/0.84 tff(76,plain,
% 0.59/0.84 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(77,plain,
% 0.59/0.84 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(78,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 0.59/0.84 tff(79,plain,
% 0.59/0.84 (ndr1_0 | (~hskp24)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.59/0.84 tff(80,plain,
% 0.59/0.84 (ndr1_0 | (~hskp24)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.59/0.84 tff(81,plain,
% 0.59/0.84 (~hskp24),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[80, 75])).
% 0.59/0.84 tff(82,plain,
% 0.59/0.84 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(83,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.59/0.84 tff(84,plain,
% 0.59/0.84 ((~hskp31) | ndr1_0),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.59/0.84 tff(85,plain,
% 0.59/0.84 ((~hskp31) | ndr1_0),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[84, 82])).
% 0.59/0.84 tff(86,plain,
% 0.59/0.84 ((~hskp31) | ndr1_0),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.59/0.84 tff(87,plain,
% 0.59/0.84 ((~hskp31) | ndr1_0),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.59/0.84 tff(88,plain,
% 0.59/0.84 ((~hskp31) | ndr1_0),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[87, 82])).
% 0.59/0.84 tff(89,plain,
% 0.59/0.84 (~hskp31),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[88, 75])).
% 0.59/0.84 tff(90,plain,
% 0.59/0.84 ((ndr1_0 | (~hskp12)) <=> (ndr1_0 | (~hskp12))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(91,plain,
% 0.59/0.84 (((~hskp12) | ndr1_0) <=> (ndr1_0 | (~hskp12))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(92,axiom,((~hskp12) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause20')).
% 0.59/0.84 tff(93,plain,
% 0.59/0.84 (ndr1_0 | (~hskp12)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.59/0.84 tff(94,plain,
% 0.59/0.84 (ndr1_0 | (~hskp12)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[93, 90])).
% 0.59/0.84 tff(95,plain,
% 0.59/0.84 (~hskp12),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[94, 75])).
% 0.59/0.84 tff(96,plain,
% 0.59/0.84 ((hskp31 | hskp24 | hskp12) <=> (hskp31 | hskp24 | hskp12)),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(97,plain,
% 0.59/0.84 (((hskp31 | hskp12) | hskp24) <=> (hskp31 | hskp24 | hskp12)),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(98,plain,
% 0.59/0.84 ((hskp31 | hskp12) <=> (hskp31 | hskp12)),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(99,plain,
% 0.59/0.84 (((hskp31 | hskp12) | hskp24) <=> ((hskp31 | hskp12) | hskp24)),
% 0.59/0.84 inference(monotonicity,[status(thm)],[98])).
% 0.59/0.84 tff(100,plain,
% 0.59/0.84 (((hskp31 | hskp12) | hskp24) <=> (hskp31 | hskp24 | hskp12)),
% 0.59/0.84 inference(transitivity,[status(thm)],[99, 97])).
% 0.59/0.84 tff(101,axiom,((hskp31 | hskp12) | hskp24), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.59/0.84 tff(102,plain,
% 0.59/0.84 (hskp31 | hskp24 | hskp12),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.59/0.84 tff(103,plain,
% 0.59/0.84 (hskp31 | hskp24 | hskp12),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[102, 96])).
% 0.59/0.84 tff(104,plain,
% 0.59/0.84 (hskp31 | hskp24 | hskp12),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.59/0.84 tff(105,plain,
% 0.59/0.84 (hskp31 | hskp24 | hskp12),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[104, 96])).
% 0.59/0.84 tff(106,plain,
% 0.59/0.84 (hskp31 | hskp24 | hskp12),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[105, 96])).
% 0.59/0.84 tff(107,plain,
% 0.59/0.84 ($false),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[106, 95, 89, 81])).
% 0.59/0.84 tff(108,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.59/0.84 tff(109,plain,
% 0.59/0.84 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c2_1(a39)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c2_1(a39)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(110,plain,
% 0.59/0.84 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39))) <=> (hskp16 | hskp15 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c2_1(a39)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(111,plain,
% 0.59/0.84 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c2_1(a39))))),
% 0.59/0.84 inference(monotonicity,[status(thm)],[110])).
% 0.59/0.84 tff(112,plain,
% 0.59/0.84 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c2_1(a39)))),
% 0.59/0.84 inference(transitivity,[status(thm)],[111, 109])).
% 0.59/0.84 tff(113,plain,
% 0.59/0.84 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)))),
% 0.59/0.84 inference(quant_inst,[status(thm)],[])).
% 0.59/0.84 tff(114,plain,
% 0.59/0.84 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c2_1(a39))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.59/0.84 tff(115,plain,
% 0.59/0.84 ($false),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[114, 108, 43, 74, 73, 65, 59, 53])).
% 0.59/0.84 tff(116,plain,((~hskp21) | hskp16 | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.59/0.84 tff(117,plain,
% 0.59/0.84 (hskp15),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[116, 43, 42])).
% 0.59/0.84 tff(118,plain,
% 0.59/0.84 (((~hskp15) | c1_1(a29)) <=> ((~hskp15) | c1_1(a29))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(119,axiom,((~hskp15) | c1_1(a29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.59/0.84 tff(120,plain,
% 0.59/0.84 ((~hskp15) | c1_1(a29)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.59/0.84 tff(121,plain,
% 0.59/0.84 ((~hskp15) | c1_1(a29)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[120, 118])).
% 0.59/0.84 tff(122,plain,
% 0.59/0.84 ((~hskp15) | c1_1(a29)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[121, 118])).
% 0.59/0.84 tff(123,plain,
% 0.59/0.84 ((~hskp15) | c1_1(a29)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.59/0.84 tff(124,plain,
% 0.59/0.84 ((~hskp15) | c1_1(a29)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[123, 118])).
% 0.59/0.84 tff(125,plain,
% 0.59/0.84 (c1_1(a29)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[124, 117])).
% 0.59/0.84 tff(126,plain,
% 0.59/0.84 (((~hskp15) | (~c3_1(a29))) <=> ((~hskp15) | (~c3_1(a29)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(127,plain,
% 0.59/0.84 (((~c3_1(a29)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a29)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(128,axiom,((~c3_1(a29)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.59/0.84 tff(129,plain,
% 0.59/0.84 ((~hskp15) | (~c3_1(a29))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.59/0.84 tff(130,plain,
% 0.59/0.84 ((~hskp15) | (~c3_1(a29))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[129, 126])).
% 0.59/0.84 tff(131,plain,
% 0.59/0.84 (~c3_1(a29)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[130, 117])).
% 0.59/0.84 tff(132,plain,
% 0.59/0.84 (((~hskp15) | (~c2_1(a29))) <=> ((~hskp15) | (~c2_1(a29)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(133,plain,
% 0.59/0.84 (((~c2_1(a29)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a29)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(134,axiom,((~c2_1(a29)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.59/0.84 tff(135,plain,
% 0.59/0.84 ((~hskp15) | (~c2_1(a29))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.59/0.84 tff(136,plain,
% 0.59/0.84 ((~hskp15) | (~c2_1(a29))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[135, 132])).
% 0.59/0.84 tff(137,plain,
% 0.59/0.84 (~c2_1(a29)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[136, 117])).
% 0.59/0.84 tff(138,assumption,(c0_1(a29)), introduced(assumption)).
% 0.59/0.84 tff(139,plain,
% 0.59/0.84 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W)))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(140,plain,
% 0.59/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~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)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[139])).
% 0.59/0.84 tff(141,plain,
% 0.59/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~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)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(142,plain,
% 0.59/0.84 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~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(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_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) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_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(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(143,plain,
% 0.68/0.84 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_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)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[142])).
% 0.68/0.84 tff(144,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.68/0.84 tff(145,plain,
% 0.68/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.68/0.84 tff(146,plain,
% 0.68/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.68/0.84 tff(147,plain,(
% 0.68/0.84 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.68/0.84 inference(skolemize,[status(sab)],[146])).
% 0.68/0.84 tff(148,plain,
% 0.68/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.68/0.84 tff(149,assumption,(~c3_1(a29)), introduced(assumption)).
% 0.68/0.84 tff(150,assumption,(~c2_1(a29)), introduced(assumption)).
% 0.68/0.84 tff(151,assumption,(c1_1(a29)), introduced(assumption)).
% 0.68/0.84 tff(152,plain,
% 0.68/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c0_1(a29)) | (~c2_1(a39)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c0_1(a29)) | (~c2_1(a39)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(153,plain,
% 0.68/0.84 (((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a39) | (~c2_1(a39)) | c3_1(a39)) <=> (c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c0_1(a29)) | (~c2_1(a39)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(154,plain,
% 0.68/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a39) | (~c2_1(a39)) | c3_1(a39))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c0_1(a29)) | (~c2_1(a39))))),
% 0.68/0.84 inference(monotonicity,[status(thm)],[153])).
% 0.68/0.84 tff(155,plain,
% 0.68/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a39) | (~c2_1(a39)) | c3_1(a39))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c0_1(a29)) | (~c2_1(a39)))),
% 0.68/0.84 inference(transitivity,[status(thm)],[154, 152])).
% 0.68/0.84 tff(156,plain,
% 0.68/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a39) | (~c2_1(a39)) | c3_1(a39))),
% 0.68/0.84 inference(quant_inst,[status(thm)],[])).
% 0.68/0.84 tff(157,plain,
% 0.68/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c0_1(a29)) | (~c2_1(a39))),
% 0.68/0.84 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.68/0.84 tff(158,plain,
% 0.68/0.84 ($false),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[157, 108, 73, 151, 65, 59, 150, 149, 148, 138])).
% 0.68/0.84 tff(159,plain,((~hskp21) | (~c1_1(a29)) | c2_1(a29) | c3_1(a29) | (~c0_1(a29))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.84 tff(160,plain,
% 0.68/0.84 (~c0_1(a29)),
% 0.68/0.84 inference(unit_resolution,[status(thm)],[159, 137, 42, 131, 125])).
% 0.68/0.84 tff(161,plain,
% 0.68/0.84 (^[U: $i] : refl((hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(162,plain,
% 0.68/0.84 (![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[161])).
% 0.68/0.84 tff(163,plain,
% 0.68/0.84 (![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.84 inference(rewrite,[status(thm)],[])).
% 0.68/0.84 tff(164,plain,
% 0.68/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp12))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.68/0.84 inference(bind,[status(th)],[])).
% 0.68/0.84 tff(165,plain,
% 0.68/0.84 (![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp12) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.84 inference(quant_intro,[status(thm)],[164])).
% 0.68/0.85 tff(166,axiom,(![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.68/0.85 tff(167,plain,
% 0.68/0.85 (![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.68/0.85 tff(168,plain,
% 0.68/0.85 (![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.68/0.85 tff(169,plain,(
% 0.68/0.85 ![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.85 inference(skolemize,[status(sab)],[168])).
% 0.68/0.85 tff(170,plain,
% 0.68/0.85 (![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.68/0.85 tff(171,plain,
% 0.68/0.85 (^[U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(172,plain,
% 0.68/0.85 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[171])).
% 0.68/0.85 tff(173,plain,
% 0.68/0.85 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(174,plain,
% 0.68/0.85 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | 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)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(175,plain,
% 0.68/0.85 (![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16) <=> ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[174])).
% 0.68/0.85 tff(176,axiom,(![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.68/0.85 tff(177,plain,
% 0.68/0.85 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.68/0.85 tff(178,plain,
% 0.68/0.85 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.68/0.85 tff(179,plain,(
% 0.68/0.85 ![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.68/0.85 inference(skolemize,[status(sab)],[178])).
% 0.68/0.85 tff(180,plain,
% 0.68/0.85 (![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.68/0.85 tff(181,assumption,(hskp12), introduced(assumption)).
% 0.68/0.85 tff(182,plain,
% 0.68/0.85 (((~hskp12) | (~c2_1(a24))) <=> ((~hskp12) | (~c2_1(a24)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(183,plain,
% 0.68/0.85 (((~c2_1(a24)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a24)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(184,axiom,((~c2_1(a24)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.68/0.85 tff(185,plain,
% 0.68/0.85 ((~hskp12) | (~c2_1(a24))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.68/0.85 tff(186,plain,
% 0.68/0.85 ((~hskp12) | (~c2_1(a24))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[185, 182])).
% 0.68/0.85 tff(187,plain,
% 0.68/0.85 (~c2_1(a24)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[186, 181])).
% 0.68/0.85 tff(188,plain,
% 0.68/0.85 (((~hskp12) | c3_1(a24)) <=> ((~hskp12) | c3_1(a24))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(189,axiom,((~hskp12) | c3_1(a24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.68/0.85 tff(190,plain,
% 0.68/0.85 ((~hskp12) | c3_1(a24)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.68/0.85 tff(191,plain,
% 0.68/0.85 ((~hskp12) | c3_1(a24)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[190, 188])).
% 0.68/0.85 tff(192,plain,
% 0.68/0.85 ((~hskp12) | c3_1(a24)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[191, 188])).
% 0.68/0.85 tff(193,plain,
% 0.68/0.85 ((~hskp12) | c3_1(a24)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.68/0.85 tff(194,plain,
% 0.68/0.85 ((~hskp12) | c3_1(a24)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[193, 188])).
% 0.68/0.85 tff(195,plain,
% 0.68/0.85 (c3_1(a24)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[194, 181])).
% 0.68/0.85 tff(196,plain,
% 0.68/0.85 (((~hskp12) | c1_1(a24)) <=> ((~hskp12) | c1_1(a24))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(197,axiom,((~hskp12) | c1_1(a24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.68/0.85 tff(198,plain,
% 0.68/0.85 ((~hskp12) | c1_1(a24)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.68/0.85 tff(199,plain,
% 0.68/0.85 ((~hskp12) | c1_1(a24)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[198, 196])).
% 0.68/0.85 tff(200,plain,
% 0.68/0.85 ((~hskp12) | c1_1(a24)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[199, 196])).
% 0.68/0.85 tff(201,plain,
% 0.68/0.85 ((~hskp12) | c1_1(a24)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.68/0.85 tff(202,plain,
% 0.68/0.85 ((~hskp12) | c1_1(a24)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[201, 196])).
% 0.68/0.85 tff(203,plain,
% 0.68/0.85 (c1_1(a24)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[202, 181])).
% 0.68/0.85 tff(204,plain,
% 0.68/0.85 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(205,plain,
% 0.68/0.85 ((hskp16 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24))) <=> (hskp16 | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(206,plain,
% 0.68/0.85 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24))))),
% 0.68/0.85 inference(monotonicity,[status(thm)],[205])).
% 0.68/0.85 tff(207,plain,
% 0.68/0.85 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)))),
% 0.68/0.85 inference(transitivity,[status(thm)],[206, 204])).
% 0.68/0.85 tff(208,plain,
% 0.68/0.85 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(209,plain,
% 0.68/0.85 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.68/0.85 tff(210,plain,
% 0.68/0.85 ($false),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[209, 108, 43, 203, 195, 187, 180])).
% 0.68/0.85 tff(211,plain,((~hskp12) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.68/0.85 tff(212,plain,
% 0.68/0.85 (~hskp12),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[211, 43])).
% 0.68/0.85 tff(213,plain,
% 0.68/0.85 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(214,plain,
% 0.68/0.85 ((hskp12 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29))) <=> (hskp12 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(215,plain,
% 0.68/0.85 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29)))),
% 0.68/0.85 inference(monotonicity,[status(thm)],[214])).
% 0.68/0.85 tff(216,plain,
% 0.68/0.85 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))),
% 0.68/0.85 inference(transitivity,[status(thm)],[215, 213])).
% 0.68/0.85 tff(217,plain,
% 0.68/0.85 ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29)))),
% 0.68/0.85 inference(quant_inst,[status(thm)],[])).
% 0.68/0.85 tff(218,plain,
% 0.68/0.85 ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.68/0.85 tff(219,plain,
% 0.68/0.85 ($false),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[218, 108, 212, 125, 131, 170, 160])).
% 0.68/0.85 tff(220,plain,(hskp16 | (~hskp21)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.85 tff(221,plain,
% 0.68/0.85 (hskp16),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[220, 42])).
% 0.68/0.85 tff(222,plain,
% 0.68/0.85 (((~hskp16) | (~c1_1(a30))) <=> ((~hskp16) | (~c1_1(a30)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(223,plain,
% 0.68/0.85 (((~c1_1(a30)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a30)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(224,axiom,((~c1_1(a30)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.68/0.85 tff(225,plain,
% 0.68/0.85 ((~hskp16) | (~c1_1(a30))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.68/0.85 tff(226,plain,
% 0.68/0.85 ((~hskp16) | (~c1_1(a30))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[225, 222])).
% 0.68/0.85 tff(227,plain,
% 0.68/0.85 (~c1_1(a30)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[226, 221])).
% 0.68/0.85 tff(228,plain,
% 0.68/0.85 (((~hskp16) | c2_1(a30)) <=> ((~hskp16) | c2_1(a30))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(229,axiom,((~hskp16) | c2_1(a30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.68/0.85 tff(230,plain,
% 0.68/0.85 ((~hskp16) | c2_1(a30)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.68/0.85 tff(231,plain,
% 0.68/0.85 ((~hskp16) | c2_1(a30)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[230, 228])).
% 0.68/0.85 tff(232,plain,
% 0.68/0.85 ((~hskp16) | c2_1(a30)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[231, 228])).
% 0.68/0.85 tff(233,plain,
% 0.68/0.85 ((~hskp16) | c2_1(a30)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.68/0.85 tff(234,plain,
% 0.68/0.85 ((~hskp16) | c2_1(a30)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[233, 228])).
% 0.68/0.85 tff(235,plain,
% 0.68/0.85 (c2_1(a30)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[234, 221])).
% 0.68/0.85 tff(236,plain,
% 0.68/0.85 (((~hskp16) | c3_1(a30)) <=> ((~hskp16) | c3_1(a30))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(237,axiom,((~hskp16) | c3_1(a30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.68/0.85 tff(238,plain,
% 0.68/0.85 ((~hskp16) | c3_1(a30)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.68/0.85 tff(239,plain,
% 0.68/0.85 ((~hskp16) | c3_1(a30)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[238, 236])).
% 0.68/0.85 tff(240,plain,
% 0.68/0.85 ((~hskp16) | c3_1(a30)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[239, 236])).
% 0.68/0.85 tff(241,plain,
% 0.68/0.85 ((~hskp16) | c3_1(a30)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[240, 236])).
% 0.68/0.85 tff(242,plain,
% 0.68/0.85 ((~hskp16) | c3_1(a30)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[241, 236])).
% 0.68/0.85 tff(243,plain,
% 0.68/0.85 (c3_1(a30)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[242, 221])).
% 0.68/0.85 tff(244,assumption,(~c0_1(a13)), introduced(assumption)).
% 0.68/0.85 tff(245,assumption,(~c0_1(a24)), introduced(assumption)).
% 0.68/0.85 tff(246,plain,
% 0.68/0.85 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(247,plain,
% 0.68/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[246])).
% 0.68/0.85 tff(248,plain,
% 0.68/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(249,plain,
% 0.68/0.85 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(250,plain,
% 0.68/0.85 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[249])).
% 0.68/0.85 tff(251,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.68/0.85 tff(252,plain,
% 0.68/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.68/0.85 tff(253,plain,
% 0.68/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[252, 248])).
% 0.68/0.85 tff(254,plain,(
% 0.68/0.85 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.68/0.85 inference(skolemize,[status(sab)],[253])).
% 0.68/0.85 tff(255,plain,
% 0.68/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[254, 247])).
% 0.68/0.85 tff(256,plain,
% 0.68/0.85 (^[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)) | c0_1(W) | c2_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)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(257,plain,
% 0.68/0.85 (![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)) | c0_1(W) | c2_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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[256])).
% 0.68/0.85 tff(258,plain,
% 0.68/0.85 (![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)) | c0_1(W) | c2_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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(259,plain,
% 0.68/0.85 (^[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))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | 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)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c3_1(W))) | 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) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | 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) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_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) | (~c3_1(W))) | c2_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) | (~c3_1(W))) | c2_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(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_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(W) | (~c3_1(W)))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(260,plain,
% 0.68/0.85 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[259])).
% 0.68/0.85 tff(261,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.68/0.85 tff(262,plain,
% 0.68/0.85 (![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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.68/0.85 tff(263,plain,
% 0.68/0.85 (![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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[262, 258])).
% 0.68/0.85 tff(264,plain,(
% 0.68/0.85 ![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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.68/0.85 inference(skolemize,[status(sab)],[263])).
% 0.68/0.85 tff(265,plain,
% 0.68/0.85 (![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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[264, 257])).
% 0.68/0.85 tff(266,plain,
% 0.68/0.85 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(267,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[266])).
% 0.68/0.85 tff(268,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(269,plain,
% 0.68/0.85 (^[V: $i, U: $i] : 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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~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(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(270,plain,
% 0.68/0.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_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)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[269])).
% 0.68/0.85 tff(271,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.68/0.85 tff(272,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.68/0.85 tff(273,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[272, 268])).
% 0.68/0.85 tff(274,plain,(
% 0.68/0.85 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.85 inference(skolemize,[status(sab)],[273])).
% 0.68/0.85 tff(275,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[274, 267])).
% 0.68/0.85 tff(276,plain,
% 0.68/0.85 (^[V: $i, U: $i] : refl((hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(277,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[276])).
% 0.68/0.85 tff(278,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(279,plain,
% 0.68/0.85 (^[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)) | (~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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp30) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp30))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.68/0.85 inference(bind,[status(th)],[])).
% 0.68/0.85 tff(280,plain,
% 0.68/0.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp30) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.85 inference(quant_intro,[status(thm)],[279])).
% 0.68/0.85 tff(281,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 0.68/0.85 tff(282,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.68/0.85 tff(283,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[282, 278])).
% 0.68/0.85 tff(284,plain,(
% 0.68/0.85 ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.85 inference(skolemize,[status(sab)],[283])).
% 0.68/0.85 tff(285,plain,
% 0.68/0.85 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[284, 277])).
% 0.68/0.85 tff(286,assumption,(~c1_1(a13)), introduced(assumption)).
% 0.68/0.85 tff(287,plain,
% 0.68/0.85 (((~hskp8) | c1_1(a13)) <=> ((~hskp8) | c1_1(a13))),
% 0.68/0.85 inference(rewrite,[status(thm)],[])).
% 0.68/0.85 tff(288,axiom,((~hskp8) | c1_1(a13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.68/0.85 tff(289,plain,
% 0.68/0.85 ((~hskp8) | c1_1(a13)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.68/0.85 tff(290,plain,
% 0.68/0.85 ((~hskp8) | c1_1(a13)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[289, 287])).
% 0.68/0.85 tff(291,plain,
% 0.68/0.85 ((~hskp8) | c1_1(a13)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[290, 287])).
% 0.68/0.85 tff(292,plain,
% 0.68/0.85 ((~hskp8) | c1_1(a13)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[291, 287])).
% 0.68/0.85 tff(293,plain,
% 0.68/0.85 ((~hskp8) | c1_1(a13)),
% 0.68/0.85 inference(modus_ponens,[status(thm)],[292, 287])).
% 0.68/0.85 tff(294,plain,
% 0.68/0.85 (~hskp8),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[293, 286])).
% 0.68/0.85 tff(295,assumption,(~c2_1(a13)), introduced(assumption)).
% 0.68/0.85 tff(296,assumption,(hskp16), introduced(assumption)).
% 0.68/0.85 tff(297,plain,
% 0.68/0.85 (~c1_1(a30)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[226, 296])).
% 0.68/0.85 tff(298,plain,
% 0.68/0.85 (c2_1(a30)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[234, 296])).
% 0.68/0.85 tff(299,plain,
% 0.68/0.85 (c3_1(a30)),
% 0.68/0.85 inference(unit_resolution,[status(thm)],[242, 296])).
% 0.68/0.85 tff(300,assumption,(~c3_1(a13)), introduced(assumption)).
% 0.68/0.85 tff(301,assumption,(~c1_1(a30)), introduced(assumption)).
% 0.68/0.85 tff(302,assumption,(c3_1(a30)), introduced(assumption)).
% 0.68/0.85 tff(303,assumption,(c2_1(a30)), introduced(assumption)).
% 0.68/0.86 tff(304,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a30) | (~ndr1_0) | c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a30) | (~ndr1_0) | c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(305,plain,
% 0.68/0.86 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c1_1(a13) | c2_1(a13)) <=> (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a30) | (~ndr1_0) | c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(306,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a30) | (~ndr1_0) | c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.68/0.86 inference(monotonicity,[status(thm)],[305])).
% 0.68/0.86 tff(307,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a30) | (~ndr1_0) | c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.86 inference(transitivity,[status(thm)],[306, 304])).
% 0.68/0.86 tff(308,plain,
% 0.68/0.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c1_1(a13) | c2_1(a13))),
% 0.68/0.86 inference(quant_inst,[status(thm)],[])).
% 0.68/0.86 tff(309,plain,
% 0.68/0.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a30) | (~ndr1_0) | c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.68/0.86 tff(310,plain,
% 0.68/0.86 ($false),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[309, 108, 294, 303, 302, 286, 295, 301, 31, 300])).
% 0.68/0.86 tff(311,plain,(c3_1(a13) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a13) | c2_1(a13) | c1_1(a30)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.86 tff(312,plain,
% 0.68/0.86 (c3_1(a13)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[311, 299, 298, 286, 295, 297])).
% 0.68/0.86 tff(313,plain,
% 0.68/0.86 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(314,plain,
% 0.68/0.86 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c3_1(a13))) <=> (hskp30 | hskp11 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(315,plain,
% 0.68/0.86 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13))))),
% 0.68/0.86 inference(monotonicity,[status(thm)],[314])).
% 0.68/0.86 tff(316,plain,
% 0.68/0.86 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)))),
% 0.68/0.86 inference(transitivity,[status(thm)],[315, 313])).
% 0.68/0.86 tff(317,plain,
% 0.68/0.86 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c3_1(a13)))),
% 0.68/0.86 inference(quant_inst,[status(thm)],[])).
% 0.68/0.86 tff(318,plain,
% 0.68/0.86 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.68/0.86 tff(319,plain,
% 0.68/0.86 (hskp30 | hskp11 | c2_1(a13) | (~c3_1(a13))),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[318, 108, 244, 41])).
% 0.68/0.86 tff(320,plain,
% 0.68/0.86 (hskp11),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[319, 312, 1, 295])).
% 0.68/0.86 tff(321,plain,
% 0.68/0.86 (((~hskp11) | (~c3_1(a21))) <=> ((~hskp11) | (~c3_1(a21)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(322,plain,
% 0.68/0.86 (((~c3_1(a21)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a21)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(323,axiom,((~c3_1(a21)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.68/0.86 tff(324,plain,
% 0.68/0.86 ((~hskp11) | (~c3_1(a21))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.68/0.86 tff(325,plain,
% 0.68/0.86 ((~hskp11) | (~c3_1(a21))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[324, 321])).
% 0.68/0.86 tff(326,plain,
% 0.68/0.86 (~c3_1(a21)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[325, 320])).
% 0.68/0.86 tff(327,plain,
% 0.68/0.86 (((~hskp11) | (~c2_1(a21))) <=> ((~hskp11) | (~c2_1(a21)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(328,plain,
% 0.68/0.86 (((~c2_1(a21)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a21)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(329,axiom,((~c2_1(a21)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.68/0.86 tff(330,plain,
% 0.68/0.86 ((~hskp11) | (~c2_1(a21))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.68/0.86 tff(331,plain,
% 0.68/0.86 ((~hskp11) | (~c2_1(a21))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[330, 327])).
% 0.68/0.86 tff(332,plain,
% 0.68/0.86 (~c2_1(a21)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[331, 320])).
% 0.68/0.86 tff(333,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(334,plain,
% 0.68/0.86 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a21) | c1_1(a21) | c2_1(a21)) <=> (hskp8 | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(335,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a21) | c1_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.68/0.86 inference(monotonicity,[status(thm)],[334])).
% 0.68/0.86 tff(336,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a21) | c1_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.86 inference(transitivity,[status(thm)],[335, 333])).
% 0.68/0.86 tff(337,plain,
% 0.68/0.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a21) | c1_1(a21) | c2_1(a21))),
% 0.68/0.86 inference(quant_inst,[status(thm)],[])).
% 0.68/0.86 tff(338,plain,
% 0.68/0.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.68/0.86 tff(339,plain,
% 0.68/0.86 (c1_1(a21)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[338, 108, 294, 298, 299, 297, 332, 326, 31])).
% 0.68/0.86 tff(340,plain,
% 0.68/0.86 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(341,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[340])).
% 0.68/0.86 tff(342,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(343,plain,
% 0.68/0.86 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(344,plain,
% 0.68/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[343])).
% 0.68/0.86 tff(345,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 0.68/0.86 tff(346,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.68/0.86 tff(347,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[346, 342])).
% 0.68/0.86 tff(348,plain,(
% 0.68/0.86 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(skolemize,[status(sab)],[347])).
% 0.68/0.86 tff(349,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[348, 341])).
% 0.68/0.86 tff(350,plain,
% 0.68/0.86 (((~hskp11) | c0_1(a21)) <=> ((~hskp11) | c0_1(a21))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(351,axiom,((~hskp11) | c0_1(a21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.68/0.86 tff(352,plain,
% 0.68/0.86 ((~hskp11) | c0_1(a21)),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.68/0.86 tff(353,plain,
% 0.68/0.86 ((~hskp11) | c0_1(a21)),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[352, 350])).
% 0.68/0.86 tff(354,plain,
% 0.68/0.86 ((~hskp11) | c0_1(a21)),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[353, 350])).
% 0.68/0.86 tff(355,plain,
% 0.68/0.86 ((~hskp11) | c0_1(a21)),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[354, 350])).
% 0.68/0.86 tff(356,plain,
% 0.68/0.86 ((~hskp11) | c0_1(a21)),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[355, 350])).
% 0.68/0.86 tff(357,plain,
% 0.68/0.86 (c0_1(a21)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[356, 320])).
% 0.68/0.86 tff(358,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(359,plain,
% 0.68/0.86 ((hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30))) <=> (hskp15 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(360,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.68/0.86 inference(monotonicity,[status(thm)],[359])).
% 0.68/0.86 tff(361,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.86 inference(transitivity,[status(thm)],[360, 358])).
% 0.68/0.86 tff(362,plain,
% 0.68/0.86 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)))),
% 0.68/0.86 inference(quant_inst,[status(thm)],[])).
% 0.68/0.86 tff(363,plain,
% 0.68/0.86 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.68/0.86 tff(364,plain,
% 0.68/0.86 (hskp15 | (~c1_1(a21))),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[363, 108, 298, 299, 357, 297, 332, 349])).
% 0.68/0.86 tff(365,plain,
% 0.68/0.86 (hskp15),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[364, 339])).
% 0.68/0.86 tff(366,plain,
% 0.68/0.86 (c1_1(a29)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[124, 365])).
% 0.68/0.86 tff(367,plain,
% 0.68/0.86 (~c3_1(a29)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[130, 365])).
% 0.68/0.86 tff(368,plain,
% 0.68/0.86 (~c2_1(a29)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[136, 365])).
% 0.68/0.86 tff(369,plain,
% 0.68/0.86 (^[U: $i] : refl((hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(370,plain,
% 0.68/0.86 (![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[369])).
% 0.68/0.86 tff(371,plain,
% 0.68/0.86 (![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(372,plain,
% 0.68/0.86 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp30) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp30))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp30) | hskp8) <=> ((hskp30 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp8))), rewrite(((hskp30 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U))) | hskp8) <=> (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp30) | hskp8) <=> (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(373,plain,
% 0.68/0.86 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp30) | hskp8) <=> ![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[372])).
% 0.68/0.86 tff(374,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp30) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.68/0.86 tff(375,plain,
% 0.68/0.86 (![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.68/0.86 tff(376,plain,
% 0.68/0.86 (![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[375, 371])).
% 0.68/0.86 tff(377,plain,(
% 0.68/0.86 ![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.86 inference(skolemize,[status(sab)],[376])).
% 0.68/0.86 tff(378,plain,
% 0.68/0.86 (![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[377, 370])).
% 0.68/0.86 tff(379,plain,
% 0.68/0.86 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(380,plain,
% 0.68/0.86 ((hskp30 | hskp8 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29))) <=> (hskp30 | hskp8 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(381,plain,
% 0.68/0.86 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29)))),
% 0.68/0.86 inference(monotonicity,[status(thm)],[380])).
% 0.68/0.86 tff(382,plain,
% 0.68/0.86 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29))),
% 0.68/0.86 inference(transitivity,[status(thm)],[381, 379])).
% 0.68/0.86 tff(383,plain,
% 0.68/0.86 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a29) | c3_1(a29) | (~c1_1(a29)))),
% 0.68/0.86 inference(quant_inst,[status(thm)],[])).
% 0.68/0.86 tff(384,plain,
% 0.68/0.86 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29)),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.68/0.86 tff(385,plain,
% 0.68/0.86 (c0_1(a29)),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[384, 108, 1, 294, 366, 367, 378])).
% 0.68/0.86 tff(386,plain,
% 0.68/0.86 (~hskp21),
% 0.68/0.86 inference(unit_resolution,[status(thm)],[159, 385, 368, 367, 366])).
% 0.68/0.86 tff(387,plain,
% 0.68/0.86 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(388,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[387])).
% 0.68/0.86 tff(389,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(390,plain,
% 0.68/0.86 (^[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)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_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)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_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)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_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)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(391,plain,
% 0.68/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[390])).
% 0.68/0.86 tff(392,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.68/0.86 tff(393,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.68/0.86 tff(394,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[393, 389])).
% 0.68/0.86 tff(395,plain,(
% 0.68/0.86 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.86 inference(skolemize,[status(sab)],[394])).
% 0.68/0.86 tff(396,plain,
% 0.68/0.86 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[395, 388])).
% 0.68/0.86 tff(397,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a13) | c2_1(a21) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a13) | c2_1(a21) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(398,plain,
% 0.68/0.86 ((hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | c0_1(a13) | (~c3_1(a13))) <=> (hskp3 | c1_1(a13) | c2_1(a21) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(399,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | c0_1(a13) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a13) | c2_1(a21) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))))),
% 0.68/0.86 inference(monotonicity,[status(thm)],[398])).
% 0.68/0.86 tff(400,plain,
% 0.68/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | c0_1(a13) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a13) | c2_1(a21) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.68/0.86 inference(transitivity,[status(thm)],[399, 397])).
% 0.68/0.86 tff(401,plain,
% 0.68/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | c0_1(a13) | (~c3_1(a13)))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(402,plain,
% 0.68/0.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a13) | c2_1(a21) | c0_1(a13) | (~ndr1_0) | (~c3_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.68/0.87 tff(403,plain,
% 0.68/0.87 (hskp3 | (~c1_1(a21))),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[402, 108, 357, 286, 332, 244, 396, 312])).
% 0.68/0.87 tff(404,plain,
% 0.68/0.87 (hskp3),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[403, 339])).
% 0.68/0.87 tff(405,plain,
% 0.68/0.87 (((~hskp3) | c3_1(a6)) <=> ((~hskp3) | c3_1(a6))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(406,axiom,((~hskp3) | c3_1(a6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.68/0.87 tff(407,plain,
% 0.68/0.87 ((~hskp3) | c3_1(a6)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.68/0.87 tff(408,plain,
% 0.68/0.87 ((~hskp3) | c3_1(a6)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[407, 405])).
% 0.68/0.87 tff(409,plain,
% 0.68/0.87 ((~hskp3) | c3_1(a6)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[408, 405])).
% 0.68/0.87 tff(410,plain,
% 0.68/0.87 ((~hskp3) | c3_1(a6)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[409, 405])).
% 0.68/0.87 tff(411,plain,
% 0.68/0.87 ((~hskp3) | c3_1(a6)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[410, 405])).
% 0.68/0.87 tff(412,plain,
% 0.68/0.87 (c3_1(a6)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[411, 404])).
% 0.68/0.87 tff(413,plain,
% 0.68/0.87 (((~hskp3) | c0_1(a6)) <=> ((~hskp3) | c0_1(a6))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(414,axiom,((~hskp3) | c0_1(a6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.68/0.87 tff(415,plain,
% 0.68/0.87 ((~hskp3) | c0_1(a6)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.68/0.87 tff(416,plain,
% 0.68/0.87 ((~hskp3) | c0_1(a6)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[415, 413])).
% 0.68/0.87 tff(417,plain,
% 0.68/0.87 ((~hskp3) | c0_1(a6)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[416, 413])).
% 0.68/0.87 tff(418,plain,
% 0.68/0.87 ((~hskp3) | c0_1(a6)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[417, 413])).
% 0.68/0.87 tff(419,plain,
% 0.68/0.87 ((~hskp3) | c0_1(a6)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[418, 413])).
% 0.68/0.87 tff(420,plain,
% 0.68/0.87 (c0_1(a6)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[419, 404])).
% 0.68/0.87 tff(421,plain,
% 0.68/0.87 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(422,plain,
% 0.68/0.87 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(423,plain,
% 0.68/0.87 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.68/0.87 tff(424,plain,
% 0.68/0.87 (hskp21 | c1_1(a6)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[423, 108, 294, 420, 412, 21])).
% 0.68/0.87 tff(425,plain,
% 0.68/0.87 (c1_1(a6)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[424, 386])).
% 0.68/0.87 tff(426,plain,
% 0.68/0.87 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a30) | (~ndr1_0) | (~c0_1(a30)) | (~c3_1(a30)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a30) | (~ndr1_0) | (~c0_1(a30)) | (~c3_1(a30)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(427,plain,
% 0.68/0.87 ((hskp21 | hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30))) <=> (hskp21 | hskp8 | c1_1(a30) | (~ndr1_0) | (~c0_1(a30)) | (~c3_1(a30)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(428,plain,
% 0.68/0.87 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a30) | (~ndr1_0) | (~c0_1(a30)) | (~c3_1(a30))))),
% 0.68/0.87 inference(monotonicity,[status(thm)],[427])).
% 0.68/0.87 tff(429,plain,
% 0.68/0.87 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a30) | (~ndr1_0) | (~c0_1(a30)) | (~c3_1(a30)))),
% 0.68/0.87 inference(transitivity,[status(thm)],[428, 426])).
% 0.68/0.87 tff(430,plain,
% 0.68/0.87 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(431,plain,
% 0.68/0.87 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a30) | (~ndr1_0) | (~c0_1(a30)) | (~c3_1(a30))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.68/0.87 tff(432,plain,
% 0.68/0.87 (hskp21 | (~c0_1(a30))),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[431, 108, 294, 299, 297, 21])).
% 0.68/0.87 tff(433,plain,
% 0.68/0.87 (~c0_1(a30)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[432, 386])).
% 0.68/0.87 tff(434,plain,
% 0.68/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(435,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[434])).
% 0.68/0.87 tff(436,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(437,plain,
% 0.68/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(438,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[437])).
% 0.68/0.87 tff(439,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.68/0.87 tff(440,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.68/0.87 tff(441,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[440, 436])).
% 0.68/0.87 tff(442,plain,(
% 0.68/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.68/0.87 inference(skolemize,[status(sab)],[441])).
% 0.68/0.87 tff(443,plain,
% 0.68/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[442, 435])).
% 0.68/0.87 tff(444,plain,
% 0.68/0.87 (((~hskp3) | (~c2_1(a6))) <=> ((~hskp3) | (~c2_1(a6)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(445,plain,
% 0.68/0.87 (((~c2_1(a6)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a6)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(446,axiom,((~c2_1(a6)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.68/0.87 tff(447,plain,
% 0.68/0.87 ((~hskp3) | (~c2_1(a6))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.68/0.87 tff(448,plain,
% 0.68/0.87 ((~hskp3) | (~c2_1(a6))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[447, 444])).
% 0.68/0.87 tff(449,plain,
% 0.68/0.87 (~c2_1(a6)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[448, 404])).
% 0.68/0.87 tff(450,plain,
% 0.68/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a13) | c2_1(a13) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(451,plain,
% 0.68/0.87 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a13) | c0_1(a13) | c2_1(a13)) <=> (c1_1(a13) | c2_1(a13) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(452,plain,
% 0.68/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a13) | c0_1(a13) | c2_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a13) | c2_1(a13) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.68/0.87 inference(monotonicity,[status(thm)],[451])).
% 0.68/0.87 tff(453,plain,
% 0.68/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a13) | c0_1(a13) | c2_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.87 inference(transitivity,[status(thm)],[452, 450])).
% 0.68/0.87 tff(454,plain,
% 0.68/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a13) | c0_1(a13) | c2_1(a13))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(455,plain,
% 0.68/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.68/0.87 tff(456,plain,
% 0.68/0.87 ($false),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[455, 108, 298, 299, 286, 295, 412, 244, 449, 443, 433, 425])).
% 0.68/0.87 tff(457,plain,((~hskp16) | c1_1(a13) | c2_1(a13) | c0_1(a13) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.68/0.87 tff(458,plain,
% 0.68/0.87 (~hskp16),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[457, 295, 286, 244, 1])).
% 0.68/0.87 tff(459,assumption,(hskp9), introduced(assumption)).
% 0.68/0.87 tff(460,plain,
% 0.68/0.87 (((~hskp9) | (~c1_1(a15))) <=> ((~hskp9) | (~c1_1(a15)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(461,plain,
% 0.68/0.87 (((~c1_1(a15)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a15)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(462,axiom,((~c1_1(a15)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.68/0.87 tff(463,plain,
% 0.68/0.87 ((~hskp9) | (~c1_1(a15))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.68/0.87 tff(464,plain,
% 0.68/0.87 ((~hskp9) | (~c1_1(a15))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[463, 460])).
% 0.68/0.87 tff(465,plain,
% 0.68/0.87 (~c1_1(a15)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[464, 459])).
% 0.68/0.87 tff(466,plain,
% 0.68/0.87 (((~hskp9) | (~c2_1(a15))) <=> ((~hskp9) | (~c2_1(a15)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(467,plain,
% 0.68/0.87 (((~c2_1(a15)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a15)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(468,axiom,((~c2_1(a15)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 0.68/0.87 tff(469,plain,
% 0.68/0.87 ((~hskp9) | (~c2_1(a15))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.68/0.87 tff(470,plain,
% 0.68/0.87 ((~hskp9) | (~c2_1(a15))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[469, 466])).
% 0.68/0.87 tff(471,plain,
% 0.68/0.87 (~c2_1(a15)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[470, 459])).
% 0.68/0.87 tff(472,assumption,(~c1_1(a15)), introduced(assumption)).
% 0.68/0.87 tff(473,assumption,(~c2_1(a15)), introduced(assumption)).
% 0.68/0.87 tff(474,plain,
% 0.68/0.87 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(475,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[474])).
% 0.68/0.87 tff(476,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(477,plain,
% 0.68/0.87 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_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) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.68/0.87 inference(bind,[status(th)],[])).
% 0.68/0.87 tff(478,plain,
% 0.68/0.87 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(quant_intro,[status(thm)],[477])).
% 0.68/0.87 tff(479,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.68/0.87 tff(480,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.68/0.87 tff(481,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[480, 476])).
% 0.68/0.87 tff(482,plain,(
% 0.68/0.87 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(skolemize,[status(sab)],[481])).
% 0.68/0.87 tff(483,plain,
% 0.68/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[482, 475])).
% 0.68/0.87 tff(484,assumption,(~c0_1(a5)), introduced(assumption)).
% 0.68/0.87 tff(485,assumption,(~c1_1(a5)), introduced(assumption)).
% 0.68/0.87 tff(486,assumption,(~hskp3), introduced(assumption)).
% 0.68/0.87 tff(487,assumption,(~hskp8), introduced(assumption)).
% 0.68/0.87 tff(488,assumption,(~c3_1(a15)), introduced(assumption)).
% 0.68/0.87 tff(489,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(490,plain,
% 0.68/0.87 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a15) | c1_1(a15) | c2_1(a15)) <=> (hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(491,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.68/0.87 inference(monotonicity,[status(thm)],[490])).
% 0.68/0.87 tff(492,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.87 inference(transitivity,[status(thm)],[491, 489])).
% 0.68/0.87 tff(493,plain,
% 0.68/0.87 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a15) | c1_1(a15) | c2_1(a15))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(494,plain,
% 0.68/0.87 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[493, 492])).
% 0.68/0.87 tff(495,plain,
% 0.68/0.87 ((~c2_1(a30)) | (~c3_1(a30))),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[494, 108, 487, 301, 472, 473, 488, 31])).
% 0.68/0.87 tff(496,plain,
% 0.68/0.87 ($false),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[495, 299, 298])).
% 0.68/0.87 tff(497,plain,((~hskp16) | hskp8 | c1_1(a30) | c1_1(a15) | c2_1(a15) | c3_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.87 tff(498,plain,
% 0.68/0.87 (~hskp16),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[497, 301, 487, 472, 473, 488])).
% 0.68/0.87 tff(499,assumption,(hskp10), introduced(assumption)).
% 0.68/0.87 tff(500,plain,
% 0.68/0.87 (((~hskp10) | (~c2_1(a17))) <=> ((~hskp10) | (~c2_1(a17)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(501,plain,
% 0.68/0.87 (((~c2_1(a17)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a17)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(502,axiom,((~c2_1(a17)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.68/0.87 tff(503,plain,
% 0.68/0.87 ((~hskp10) | (~c2_1(a17))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.68/0.87 tff(504,plain,
% 0.68/0.87 ((~hskp10) | (~c2_1(a17))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[503, 500])).
% 0.68/0.87 tff(505,plain,
% 0.68/0.87 (~c2_1(a17)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[504, 499])).
% 0.68/0.87 tff(506,plain,
% 0.68/0.87 (((~hskp10) | c1_1(a17)) <=> ((~hskp10) | c1_1(a17))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(507,axiom,((~hskp10) | c1_1(a17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.68/0.87 tff(508,plain,
% 0.68/0.87 ((~hskp10) | c1_1(a17)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[507, 506])).
% 0.68/0.87 tff(509,plain,
% 0.68/0.87 ((~hskp10) | c1_1(a17)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[508, 506])).
% 0.68/0.87 tff(510,plain,
% 0.68/0.87 ((~hskp10) | c1_1(a17)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[509, 506])).
% 0.68/0.87 tff(511,plain,
% 0.68/0.87 ((~hskp10) | c1_1(a17)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[510, 506])).
% 0.68/0.87 tff(512,plain,
% 0.68/0.87 ((~hskp10) | c1_1(a17)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[511, 506])).
% 0.68/0.87 tff(513,plain,
% 0.68/0.87 (c1_1(a17)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[512, 499])).
% 0.68/0.87 tff(514,plain,
% 0.68/0.87 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a17) | (~ndr1_0) | (~c1_1(a17)) | (~c3_1(a17)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a17) | (~ndr1_0) | (~c1_1(a17)) | (~c3_1(a17)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(515,plain,
% 0.68/0.87 ((hskp16 | (~ndr1_0) | c2_1(a17) | (~c1_1(a17)) | (~c3_1(a17))) <=> (hskp16 | c2_1(a17) | (~ndr1_0) | (~c1_1(a17)) | (~c3_1(a17)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(516,plain,
% 0.68/0.87 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a17) | (~c1_1(a17)) | (~c3_1(a17)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a17) | (~ndr1_0) | (~c1_1(a17)) | (~c3_1(a17))))),
% 0.68/0.87 inference(monotonicity,[status(thm)],[515])).
% 0.68/0.87 tff(517,plain,
% 0.68/0.87 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a17) | (~c1_1(a17)) | (~c3_1(a17)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a17) | (~ndr1_0) | (~c1_1(a17)) | (~c3_1(a17)))),
% 0.68/0.87 inference(transitivity,[status(thm)],[516, 514])).
% 0.68/0.87 tff(518,plain,
% 0.68/0.87 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a17) | (~c1_1(a17)) | (~c3_1(a17)))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(519,plain,
% 0.68/0.87 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a17) | (~ndr1_0) | (~c1_1(a17)) | (~c3_1(a17))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.68/0.87 tff(520,plain,
% 0.68/0.87 (~c3_1(a17)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[519, 108, 43, 513, 505, 180])).
% 0.68/0.87 tff(521,plain,
% 0.68/0.87 (((~hskp10) | (~c0_1(a17))) <=> ((~hskp10) | (~c0_1(a17)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(522,plain,
% 0.68/0.87 (((~c0_1(a17)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a17)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(523,axiom,((~c0_1(a17)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.68/0.87 tff(524,plain,
% 0.68/0.87 ((~hskp10) | (~c0_1(a17))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.68/0.87 tff(525,plain,
% 0.68/0.87 ((~hskp10) | (~c0_1(a17))),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[524, 521])).
% 0.68/0.87 tff(526,plain,
% 0.68/0.87 (~c0_1(a17)),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[525, 499])).
% 0.68/0.87 tff(527,plain,
% 0.68/0.87 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a17) | (~ndr1_0) | (~c1_1(a17)) | c3_1(a17))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a17) | (~ndr1_0) | (~c1_1(a17)) | c3_1(a17))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(528,plain,
% 0.68/0.87 ((hskp30 | hskp8 | (~ndr1_0) | c0_1(a17) | c3_1(a17) | (~c1_1(a17))) <=> (hskp30 | hskp8 | c0_1(a17) | (~ndr1_0) | (~c1_1(a17)) | c3_1(a17))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(529,plain,
% 0.68/0.87 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a17) | c3_1(a17) | (~c1_1(a17)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a17) | (~ndr1_0) | (~c1_1(a17)) | c3_1(a17)))),
% 0.68/0.87 inference(monotonicity,[status(thm)],[528])).
% 0.68/0.87 tff(530,plain,
% 0.68/0.87 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a17) | c3_1(a17) | (~c1_1(a17)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a17) | (~ndr1_0) | (~c1_1(a17)) | c3_1(a17))),
% 0.68/0.87 inference(transitivity,[status(thm)],[529, 527])).
% 0.68/0.87 tff(531,plain,
% 0.68/0.87 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a17) | c3_1(a17) | (~c1_1(a17)))),
% 0.68/0.87 inference(quant_inst,[status(thm)],[])).
% 0.68/0.87 tff(532,plain,
% 0.68/0.87 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a17) | (~ndr1_0) | (~c1_1(a17)) | c3_1(a17)),
% 0.68/0.87 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.68/0.87 tff(533,plain,
% 0.68/0.87 ($false),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[532, 108, 1, 487, 513, 526, 378, 520])).
% 0.68/0.87 tff(534,plain,((~hskp10) | hskp30 | hskp8 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.68/0.87 tff(535,plain,
% 0.68/0.87 (~hskp10),
% 0.68/0.87 inference(unit_resolution,[status(thm)],[534, 498, 487, 1])).
% 0.68/0.87 tff(536,assumption,(c2_1(a5)), introduced(assumption)).
% 0.68/0.87 tff(537,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(538,plain,
% 0.68/0.87 ((hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a15) | c1_1(a15) | c2_1(a15)) <=> (hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.68/0.87 inference(rewrite,[status(thm)],[])).
% 0.68/0.87 tff(539,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))))),
% 0.68/0.87 inference(monotonicity,[status(thm)],[538])).
% 0.68/0.87 tff(540,plain,
% 0.68/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[539, 537])).
% 0.68/0.88 tff(541,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a15) | c1_1(a15) | c2_1(a15))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(542,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.68/0.88 tff(543,plain,
% 0.68/0.88 ((~c2_1(a5)) | (~c3_1(a5))),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[542, 108, 487, 472, 473, 488, 485, 31])).
% 0.68/0.88 tff(544,plain,
% 0.68/0.88 (~c3_1(a5)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[543, 536])).
% 0.68/0.88 tff(545,plain,
% 0.68/0.88 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(546,plain,
% 0.68/0.88 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c2_1(a5))) <=> (hskp16 | hskp15 | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(547,plain,
% 0.68/0.88 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c2_1(a5)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5)))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[546])).
% 0.68/0.88 tff(548,plain,
% 0.68/0.88 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c2_1(a5)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5))),
% 0.68/0.88 inference(transitivity,[status(thm)],[547, 545])).
% 0.68/0.88 tff(549,plain,
% 0.68/0.88 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c2_1(a5)))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(550,plain,
% 0.68/0.88 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[549, 548])).
% 0.68/0.88 tff(551,plain,
% 0.68/0.88 (hskp16 | hskp15 | (~c2_1(a5)) | c3_1(a5)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[550, 108, 484, 53])).
% 0.68/0.88 tff(552,plain,
% 0.68/0.88 (hskp15),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[551, 536, 498, 544])).
% 0.68/0.88 tff(553,plain,
% 0.68/0.88 (~c2_1(a29)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[136, 552])).
% 0.68/0.88 tff(554,plain,
% 0.68/0.88 (~c3_1(a29)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[130, 552])).
% 0.68/0.88 tff(555,assumption,(ndr1_0), introduced(assumption)).
% 0.68/0.88 tff(556,plain,
% 0.68/0.88 (hskp8 | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[542, 488, 485, 31])).
% 0.68/0.88 tff(557,plain,
% 0.68/0.88 (~c3_1(a5)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[556, 487, 555, 472, 473, 536])).
% 0.68/0.88 tff(558,assumption,(~c0_1(a29)), introduced(assumption)).
% 0.68/0.88 tff(559,plain,
% 0.68/0.88 (hskp8 | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[384, 1, 149, 378])).
% 0.68/0.88 tff(560,plain,
% 0.68/0.88 (~c1_1(a29)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[559, 487, 555, 558])).
% 0.68/0.88 tff(561,plain,
% 0.68/0.88 (~hskp15),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[124, 560])).
% 0.68/0.88 tff(562,plain,
% 0.68/0.88 (hskp16 | hskp15 | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[550, 484, 53])).
% 0.68/0.88 tff(563,plain,
% 0.68/0.88 (hskp16),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[562, 561, 555, 536, 557])).
% 0.68/0.88 tff(564,plain,
% 0.68/0.88 (c2_1(a30)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[234, 563])).
% 0.68/0.88 tff(565,plain,
% 0.68/0.88 (c3_1(a30)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[242, 563])).
% 0.68/0.88 tff(566,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a29) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(567,plain,
% 0.68/0.88 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a29) | c1_1(a29) | c2_1(a29)) <=> (hskp8 | c1_1(a29) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(568,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a29) | c1_1(a29) | c2_1(a29))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a29) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[567])).
% 0.68/0.88 tff(569,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a29) | c1_1(a29) | c2_1(a29))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[568, 566])).
% 0.68/0.88 tff(570,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a29) | c1_1(a29) | c2_1(a29))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(571,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.68/0.88 tff(572,plain,
% 0.68/0.88 (hskp8 | c1_1(a29) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[571, 301, 150, 149, 31])).
% 0.68/0.88 tff(573,plain,
% 0.68/0.88 ($false),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[572, 565, 564, 555, 487, 560])).
% 0.68/0.88 tff(574,plain,(hskp8 | (~ndr1_0) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~c2_1(a5)) | c0_1(a5) | c0_1(a29) | hskp30 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.88 tff(575,plain,
% 0.68/0.88 (c0_1(a29)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[574, 487, 301, 150, 149, 536, 484, 555, 1, 472, 473, 488, 485])).
% 0.68/0.88 tff(576,plain,
% 0.68/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(577,plain,
% 0.68/0.88 (((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a5) | (~c2_1(a5)) | c3_1(a5)) <=> (c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(578,plain,
% 0.68/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a5) | (~c2_1(a5)) | c3_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[577])).
% 0.68/0.88 tff(579,plain,
% 0.68/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a5) | (~c2_1(a5)) | c3_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[578, 576])).
% 0.68/0.88 tff(580,plain,
% 0.68/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a29) | c2_1(a29) | (~c0_1(a29)) | c0_1(a5) | (~c2_1(a5)) | c3_1(a5))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(581,plain,
% 0.68/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.68/0.88 tff(582,plain,
% 0.68/0.88 (c2_1(a29) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[581, 149, 484, 148])).
% 0.68/0.88 tff(583,plain,
% 0.68/0.88 (~c1_1(a29)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[582, 575, 555, 150, 536, 557])).
% 0.68/0.88 tff(584,plain,
% 0.68/0.88 (~hskp15),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[124, 583])).
% 0.68/0.88 tff(585,plain,
% 0.68/0.88 (hskp16),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[562, 584, 555, 536, 557])).
% 0.68/0.88 tff(586,plain,
% 0.68/0.88 (c2_1(a30)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[234, 585])).
% 0.68/0.88 tff(587,plain,
% 0.68/0.88 (c3_1(a30)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[242, 585])).
% 0.68/0.88 tff(588,plain,
% 0.68/0.88 ($false),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[572, 587, 586, 555, 487, 583])).
% 0.68/0.88 tff(589,plain,(hskp8 | (~ndr1_0) | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~c2_1(a5)) | c0_1(a5) | hskp30 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.88 tff(590,plain,
% 0.68/0.88 (hskp8 | c1_1(a30) | c2_1(a29) | c3_1(a29) | (~c2_1(a5)) | c0_1(a5) | hskp30 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[589, 108])).
% 0.68/0.88 tff(591,plain,
% 0.68/0.88 ($false),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[590, 554, 553, 487, 301, 536, 484, 1, 472, 473, 488, 485])).
% 0.68/0.88 tff(592,plain,((~c2_1(a5)) | hskp8 | c1_1(a30) | c0_1(a5) | hskp30 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.88 tff(593,plain,
% 0.68/0.88 (~c2_1(a5)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[592, 301, 487, 484, 1, 472, 473, 488, 485])).
% 0.68/0.88 tff(594,plain,
% 0.68/0.88 (((~hskp2) | c2_1(a5)) <=> ((~hskp2) | c2_1(a5))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(595,axiom,((~hskp2) | c2_1(a5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.68/0.88 tff(596,plain,
% 0.68/0.88 ((~hskp2) | c2_1(a5)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.68/0.88 tff(597,plain,
% 0.68/0.88 ((~hskp2) | c2_1(a5)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[596, 594])).
% 0.68/0.88 tff(598,plain,
% 0.68/0.88 ((~hskp2) | c2_1(a5)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[597, 594])).
% 0.68/0.88 tff(599,plain,
% 0.68/0.88 ((~hskp2) | c2_1(a5)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[598, 594])).
% 0.68/0.88 tff(600,plain,
% 0.68/0.88 ((~hskp2) | c2_1(a5)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[599, 594])).
% 0.68/0.88 tff(601,plain,
% 0.68/0.88 (~hskp2),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[600, 593])).
% 0.68/0.88 tff(602,assumption,(~hskp2), introduced(assumption)).
% 0.68/0.88 tff(603,assumption,(~hskp10), introduced(assumption)).
% 0.68/0.88 tff(604,assumption,(hskp13), introduced(assumption)).
% 0.68/0.88 tff(605,plain,
% 0.68/0.88 (((~hskp13) | (~c1_1(a26))) <=> ((~hskp13) | (~c1_1(a26)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(606,plain,
% 0.68/0.88 (((~c1_1(a26)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a26)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(607,axiom,((~c1_1(a26)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.68/0.88 tff(608,plain,
% 0.68/0.88 ((~hskp13) | (~c1_1(a26))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.68/0.88 tff(609,plain,
% 0.68/0.88 ((~hskp13) | (~c1_1(a26))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[608, 605])).
% 0.68/0.88 tff(610,plain,
% 0.68/0.88 (~c1_1(a26)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[609, 604])).
% 0.68/0.88 tff(611,plain,
% 0.68/0.88 (((~hskp13) | c3_1(a26)) <=> ((~hskp13) | c3_1(a26))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(612,axiom,((~hskp13) | c3_1(a26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.68/0.88 tff(613,plain,
% 0.68/0.88 ((~hskp13) | c3_1(a26)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.68/0.88 tff(614,plain,
% 0.68/0.88 ((~hskp13) | c3_1(a26)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[613, 611])).
% 0.68/0.88 tff(615,plain,
% 0.68/0.88 ((~hskp13) | c3_1(a26)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[614, 611])).
% 0.68/0.88 tff(616,plain,
% 0.68/0.88 ((~hskp13) | c3_1(a26)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[615, 611])).
% 0.68/0.88 tff(617,plain,
% 0.68/0.88 ((~hskp13) | c3_1(a26)),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[616, 611])).
% 0.68/0.88 tff(618,plain,
% 0.68/0.88 (c3_1(a26)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[617, 604])).
% 0.68/0.88 tff(619,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a26) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a26) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(620,plain,
% 0.68/0.88 ((hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a15) | c1_1(a15) | c2_1(a15)) <=> (hskp8 | c1_1(a26) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(621,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a26) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[620])).
% 0.68/0.88 tff(622,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a26) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[621, 619])).
% 0.68/0.88 tff(623,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a15) | c1_1(a15) | c2_1(a15))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(624,plain,
% 0.68/0.88 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a26) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[623, 622])).
% 0.68/0.88 tff(625,plain,
% 0.68/0.88 (~c2_1(a26)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[624, 108, 487, 618, 610, 472, 473, 488, 31])).
% 0.68/0.88 tff(626,plain,
% 0.68/0.88 (((~hskp13) | (~c0_1(a26))) <=> ((~hskp13) | (~c0_1(a26)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(627,plain,
% 0.68/0.88 (((~c0_1(a26)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a26)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(628,axiom,((~c0_1(a26)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.68/0.88 tff(629,plain,
% 0.68/0.88 ((~hskp13) | (~c0_1(a26))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[628, 627])).
% 0.68/0.88 tff(630,plain,
% 0.68/0.88 ((~hskp13) | (~c0_1(a26))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[629, 626])).
% 0.68/0.88 tff(631,plain,
% 0.68/0.88 (~c0_1(a26)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[630, 604])).
% 0.68/0.88 tff(632,plain,
% 0.68/0.88 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a26) | (~ndr1_0) | c2_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a26) | (~ndr1_0) | c2_1(a26) | (~c3_1(a26)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(633,plain,
% 0.68/0.88 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a26) | c0_1(a26) | (~c3_1(a26))) <=> (hskp30 | hskp11 | c0_1(a26) | (~ndr1_0) | c2_1(a26) | (~c3_1(a26)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(634,plain,
% 0.68/0.88 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a26) | (~ndr1_0) | c2_1(a26) | (~c3_1(a26))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[633])).
% 0.68/0.88 tff(635,plain,
% 0.68/0.88 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a26) | (~ndr1_0) | c2_1(a26) | (~c3_1(a26)))),
% 0.68/0.88 inference(transitivity,[status(thm)],[634, 632])).
% 0.68/0.88 tff(636,plain,
% 0.68/0.88 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a26) | c0_1(a26) | (~c3_1(a26)))),
% 0.68/0.88 inference(quant_inst,[status(thm)],[])).
% 0.68/0.88 tff(637,plain,
% 0.68/0.88 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a26) | (~ndr1_0) | c2_1(a26) | (~c3_1(a26))),
% 0.68/0.88 inference(modus_ponens,[status(thm)],[636, 635])).
% 0.68/0.88 tff(638,plain,
% 0.68/0.88 (hskp11 | c2_1(a26)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[637, 108, 1, 618, 631, 41])).
% 0.68/0.88 tff(639,plain,
% 0.68/0.88 (hskp11),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[638, 625])).
% 0.68/0.88 tff(640,plain,
% 0.68/0.88 (~c2_1(a21)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[331, 639])).
% 0.68/0.88 tff(641,plain,
% 0.68/0.88 (c0_1(a21)),
% 0.68/0.88 inference(unit_resolution,[status(thm)],[356, 639])).
% 0.68/0.88 tff(642,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a26) | c1_1(a26) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a26) | c1_1(a26) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c3_1(a26)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(643,plain,
% 0.68/0.88 ((hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26))) <=> (hskp3 | c0_1(a26) | c1_1(a26) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c3_1(a26)))),
% 0.68/0.88 inference(rewrite,[status(thm)],[])).
% 0.68/0.88 tff(644,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a26) | c1_1(a26) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c3_1(a26))))),
% 0.68/0.88 inference(monotonicity,[status(thm)],[643])).
% 0.68/0.88 tff(645,plain,
% 0.68/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a26) | c1_1(a26) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c3_1(a26)))),
% 0.72/0.88 inference(transitivity,[status(thm)],[644, 642])).
% 0.72/0.88 tff(646,plain,
% 0.72/0.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(647,plain,
% 0.72/0.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a26) | c1_1(a26) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c3_1(a26))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.72/0.88 tff(648,plain,
% 0.72/0.88 (~c1_1(a21)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[647, 108, 486, 618, 641, 631, 610, 640, 396])).
% 0.72/0.88 tff(649,plain,
% 0.72/0.88 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(650,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[649])).
% 0.72/0.88 tff(651,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(652,plain,
% 0.72/0.88 (^[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)) | (~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)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(653,plain,
% 0.72/0.88 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[652])).
% 0.72/0.88 tff(654,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 0.72/0.88 tff(655,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.72/0.88 tff(656,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[655, 651])).
% 0.72/0.88 tff(657,plain,(
% 0.72/0.88 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.88 inference(skolemize,[status(sab)],[656])).
% 0.72/0.88 tff(658,plain,
% 0.72/0.88 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[657, 650])).
% 0.72/0.88 tff(659,plain,
% 0.72/0.88 (~c3_1(a21)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[325, 639])).
% 0.72/0.88 tff(660,plain,
% 0.72/0.88 (^[U: $i] : refl((hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(661,plain,
% 0.72/0.88 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[660])).
% 0.72/0.88 tff(662,plain,
% 0.72/0.88 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(663,plain,
% 0.72/0.88 (^[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)) | 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)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | 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) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp24) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp24))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp24) <=> (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(664,plain,
% 0.72/0.89 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp24) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[663])).
% 0.72/0.89 tff(665,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp3) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.72/0.89 tff(666,plain,
% 0.72/0.89 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.72/0.89 tff(667,plain,
% 0.72/0.89 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[666, 662])).
% 0.72/0.89 tff(668,plain,(
% 0.72/0.89 ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[667])).
% 0.72/0.89 tff(669,plain,
% 0.72/0.89 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[668, 661])).
% 0.72/0.89 tff(670,plain,
% 0.72/0.89 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp24 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(671,plain,
% 0.72/0.89 ((hskp24 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c0_1(a21))) <=> (hskp24 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(672,plain,
% 0.72/0.89 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c0_1(a21)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[671])).
% 0.72/0.89 tff(673,plain,
% 0.72/0.89 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c0_1(a21)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp24 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[672, 670])).
% 0.72/0.89 tff(674,plain,
% 0.72/0.89 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c0_1(a21)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(675,plain,
% 0.72/0.89 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp24 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.72/0.89 tff(676,plain,
% 0.72/0.89 (hskp24),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[675, 108, 486, 641, 640, 659, 669])).
% 0.72/0.89 tff(677,plain,
% 0.72/0.89 (((~hskp24) | (~c2_1(a52))) <=> ((~hskp24) | (~c2_1(a52)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(678,plain,
% 0.72/0.89 (((~c2_1(a52)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a52)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(679,axiom,((~c2_1(a52)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.72/0.89 tff(680,plain,
% 0.72/0.89 ((~hskp24) | (~c2_1(a52))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[679, 678])).
% 0.72/0.89 tff(681,plain,
% 0.72/0.89 ((~hskp24) | (~c2_1(a52))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[680, 677])).
% 0.72/0.89 tff(682,plain,
% 0.72/0.89 (~c2_1(a52)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[681, 676])).
% 0.72/0.89 tff(683,plain,
% 0.72/0.89 (((~hskp24) | (~c0_1(a52))) <=> ((~hskp24) | (~c0_1(a52)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(684,plain,
% 0.72/0.89 (((~c0_1(a52)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a52)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(685,axiom,((~c0_1(a52)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.72/0.89 tff(686,plain,
% 0.72/0.89 ((~hskp24) | (~c0_1(a52))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[685, 684])).
% 0.72/0.89 tff(687,plain,
% 0.72/0.89 ((~hskp24) | (~c0_1(a52))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[686, 683])).
% 0.72/0.89 tff(688,plain,
% 0.72/0.89 (~c0_1(a52)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[687, 676])).
% 0.72/0.89 tff(689,plain,
% 0.72/0.89 (((~hskp24) | c3_1(a52)) <=> ((~hskp24) | c3_1(a52))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(690,axiom,((~hskp24) | c3_1(a52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.72/0.89 tff(691,plain,
% 0.72/0.89 ((~hskp24) | c3_1(a52)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.72/0.89 tff(692,plain,
% 0.72/0.89 ((~hskp24) | c3_1(a52)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[691, 689])).
% 0.72/0.89 tff(693,plain,
% 0.72/0.89 ((~hskp24) | c3_1(a52)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[692, 689])).
% 0.72/0.89 tff(694,plain,
% 0.72/0.89 ((~hskp24) | c3_1(a52)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[693, 689])).
% 0.72/0.89 tff(695,plain,
% 0.72/0.89 ((~hskp24) | c3_1(a52)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[694, 689])).
% 0.72/0.89 tff(696,plain,
% 0.72/0.89 (c3_1(a52)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[695, 676])).
% 0.72/0.89 tff(697,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a52) | c2_1(a52) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c3_1(a52)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a52) | c2_1(a52) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c3_1(a52)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(698,plain,
% 0.72/0.89 ((hskp10 | (~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a52) | c2_1(a52) | (~c3_1(a52))) <=> (hskp10 | c0_1(a52) | c2_1(a52) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c3_1(a52)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(699,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a52) | c2_1(a52) | (~c3_1(a52)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a52) | c2_1(a52) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c3_1(a52))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[698])).
% 0.72/0.89 tff(700,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a52) | c2_1(a52) | (~c3_1(a52)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a52) | c2_1(a52) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c3_1(a52)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[699, 697])).
% 0.72/0.89 tff(701,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a52) | c2_1(a52) | (~c3_1(a52)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(702,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a52) | c2_1(a52) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c3_1(a52))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[701, 700])).
% 0.72/0.89 tff(703,plain,
% 0.72/0.89 ($false),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[702, 108, 603, 696, 641, 688, 682, 659, 658, 648])).
% 0.72/0.89 tff(704,plain,((~hskp13) | hskp10 | hskp3 | hskp30 | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.89 tff(705,plain,
% 0.72/0.89 (~hskp13),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[704, 486, 603, 1, 487, 472, 473, 488])).
% 0.72/0.89 tff(706,plain,
% 0.72/0.89 ((hskp13 | hskp3 | hskp2) <=> (hskp13 | hskp3 | hskp2)),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(707,plain,
% 0.72/0.89 (((hskp3 | hskp2) | hskp13) <=> (hskp13 | hskp3 | hskp2)),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(708,plain,
% 0.72/0.89 ((hskp3 | hskp2) <=> (hskp3 | hskp2)),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(709,plain,
% 0.72/0.89 (((hskp3 | hskp2) | hskp13) <=> ((hskp3 | hskp2) | hskp13)),
% 0.72/0.89 inference(monotonicity,[status(thm)],[708])).
% 0.72/0.89 tff(710,plain,
% 0.72/0.89 (((hskp3 | hskp2) | hskp13) <=> (hskp13 | hskp3 | hskp2)),
% 0.72/0.89 inference(transitivity,[status(thm)],[709, 707])).
% 0.72/0.89 tff(711,axiom,((hskp3 | hskp2) | hskp13), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 0.72/0.89 tff(712,plain,
% 0.72/0.89 (hskp13 | hskp3 | hskp2),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[711, 710])).
% 0.72/0.89 tff(713,plain,
% 0.72/0.89 (hskp13 | hskp3 | hskp2),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[712, 706])).
% 0.72/0.89 tff(714,plain,
% 0.72/0.89 (hskp13 | hskp3 | hskp2),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[713, 706])).
% 0.72/0.89 tff(715,plain,
% 0.72/0.89 (hskp13 | hskp3 | hskp2),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[714, 706])).
% 0.72/0.89 tff(716,plain,
% 0.72/0.89 (hskp13 | hskp3 | hskp2),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[715, 706])).
% 0.72/0.89 tff(717,plain,
% 0.72/0.89 ($false),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[716, 705, 486, 602])).
% 0.72/0.89 tff(718,plain,(hskp3 | hskp2 | hskp10 | hskp30 | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.89 tff(719,plain,
% 0.72/0.89 (hskp3),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[718, 601, 535, 1, 487, 472, 473, 488])).
% 0.72/0.89 tff(720,plain,
% 0.72/0.89 (~c2_1(a6)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[448, 719])).
% 0.72/0.89 tff(721,plain,
% 0.72/0.89 (c3_1(a6)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[411, 719])).
% 0.72/0.89 tff(722,plain,
% 0.72/0.89 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(723,plain,
% 0.72/0.89 ((hskp16 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6))) <=> (hskp16 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(724,plain,
% 0.72/0.89 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[723])).
% 0.72/0.89 tff(725,plain,
% 0.72/0.89 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[724, 722])).
% 0.72/0.89 tff(726,plain,
% 0.72/0.89 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(727,plain,
% 0.72/0.89 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.72/0.89 tff(728,plain,
% 0.72/0.89 (~c1_1(a6)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[727, 108, 498, 721, 720, 180])).
% 0.72/0.89 tff(729,plain,
% 0.72/0.89 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(730,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[729])).
% 0.72/0.89 tff(731,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(732,plain,
% 0.72/0.89 (^[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(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_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(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_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(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(733,plain,
% 0.72/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[732])).
% 0.72/0.89 tff(734,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.72/0.89 tff(735,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[734, 733])).
% 0.72/0.89 tff(736,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[735, 731])).
% 0.72/0.89 tff(737,plain,(
% 0.72/0.89 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[736])).
% 0.72/0.89 tff(738,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[737, 730])).
% 0.72/0.89 tff(739,plain,
% 0.72/0.89 (^[U: $i] : refl((hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(740,plain,
% 0.72/0.89 (![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[739])).
% 0.72/0.89 tff(741,plain,
% 0.72/0.89 (![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(742,plain,
% 0.72/0.89 (^[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)) | hskp30) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp23) <=> ((hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp23))), rewrite(((hskp30 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp23) <=> (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp23) <=> (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(743,plain,
% 0.72/0.89 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp23) <=> ![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[742])).
% 0.72/0.89 tff(744,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 0.72/0.89 tff(745,plain,
% 0.72/0.89 (![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.72/0.89 tff(746,plain,
% 0.72/0.89 (![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[745, 741])).
% 0.72/0.89 tff(747,plain,(
% 0.72/0.89 ![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[746])).
% 0.72/0.89 tff(748,plain,
% 0.72/0.89 (![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[747, 740])).
% 0.72/0.89 tff(749,plain,
% 0.72/0.89 (c0_1(a6)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[419, 719])).
% 0.72/0.89 tff(750,plain,
% 0.72/0.89 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | c2_1(a6) | (~ndr1_0) | c1_1(a6) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c2_1(a6) | (~ndr1_0) | c1_1(a6) | (~c0_1(a6)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(751,plain,
% 0.72/0.89 ((hskp30 | hskp23 | (~ndr1_0) | c2_1(a6) | c1_1(a6) | (~c0_1(a6))) <=> (hskp30 | hskp23 | c2_1(a6) | (~ndr1_0) | c1_1(a6) | (~c0_1(a6)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(752,plain,
% 0.72/0.89 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a6) | c1_1(a6) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | c2_1(a6) | (~ndr1_0) | c1_1(a6) | (~c0_1(a6))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[751])).
% 0.72/0.89 tff(753,plain,
% 0.72/0.89 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a6) | c1_1(a6) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c2_1(a6) | (~ndr1_0) | c1_1(a6) | (~c0_1(a6)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[752, 750])).
% 0.72/0.89 tff(754,plain,
% 0.72/0.89 ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a6) | c1_1(a6) | (~c0_1(a6)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(755,plain,
% 0.72/0.89 ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c2_1(a6) | (~ndr1_0) | c1_1(a6) | (~c0_1(a6))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[754, 753])).
% 0.72/0.89 tff(756,plain,
% 0.72/0.89 (hskp23 | c1_1(a6)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[755, 108, 1, 749, 720, 748])).
% 0.72/0.89 tff(757,plain,
% 0.72/0.89 (hskp23),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[756, 728])).
% 0.72/0.89 tff(758,plain,
% 0.72/0.89 (((~hskp23) | (~c3_1(a42))) <=> ((~hskp23) | (~c3_1(a42)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(759,plain,
% 0.72/0.89 (((~c3_1(a42)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a42)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(760,axiom,((~c3_1(a42)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.72/0.89 tff(761,plain,
% 0.72/0.89 ((~hskp23) | (~c3_1(a42))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.72/0.89 tff(762,plain,
% 0.72/0.89 ((~hskp23) | (~c3_1(a42))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[761, 758])).
% 0.72/0.89 tff(763,plain,
% 0.72/0.89 (~c3_1(a42)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[762, 757])).
% 0.72/0.89 tff(764,plain,
% 0.72/0.89 (((~hskp23) | (~c1_1(a42))) <=> ((~hskp23) | (~c1_1(a42)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(765,plain,
% 0.72/0.89 (((~c1_1(a42)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a42)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(766,axiom,((~c1_1(a42)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.72/0.89 tff(767,plain,
% 0.72/0.89 ((~hskp23) | (~c1_1(a42))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[766, 765])).
% 0.72/0.89 tff(768,plain,
% 0.72/0.89 ((~hskp23) | (~c1_1(a42))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[767, 764])).
% 0.72/0.89 tff(769,plain,
% 0.72/0.89 (~c1_1(a42)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[768, 757])).
% 0.72/0.89 tff(770,plain,
% 0.72/0.89 (((~hskp23) | c0_1(a42)) <=> ((~hskp23) | c0_1(a42))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(771,axiom,((~hskp23) | c0_1(a42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.72/0.89 tff(772,plain,
% 0.72/0.89 ((~hskp23) | c0_1(a42)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[771, 770])).
% 0.72/0.89 tff(773,plain,
% 0.72/0.89 ((~hskp23) | c0_1(a42)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[772, 770])).
% 0.72/0.89 tff(774,plain,
% 0.72/0.89 ((~hskp23) | c0_1(a42)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[773, 770])).
% 0.72/0.89 tff(775,plain,
% 0.72/0.89 ((~hskp23) | c0_1(a42)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[774, 770])).
% 0.72/0.89 tff(776,plain,
% 0.72/0.89 ((~hskp23) | c0_1(a42)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[775, 770])).
% 0.72/0.89 tff(777,plain,
% 0.72/0.89 (c0_1(a42)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[776, 757])).
% 0.72/0.89 tff(778,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a42) | c3_1(a42) | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a42) | c3_1(a42) | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | (~c0_1(a42)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(779,plain,
% 0.72/0.89 ((hskp2 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42))) <=> (hskp2 | c1_1(a42) | c3_1(a42) | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | (~c0_1(a42)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(780,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a42) | c3_1(a42) | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | (~c0_1(a42))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[779])).
% 0.72/0.89 tff(781,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a42) | c3_1(a42) | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | (~c0_1(a42)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[780, 778])).
% 0.72/0.89 tff(782,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(783,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a42) | c3_1(a42) | (~ndr1_0) | c1_1(a6) | (~c3_1(a6)) | (~c0_1(a6)) | (~c0_1(a42))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[782, 781])).
% 0.72/0.89 tff(784,plain,
% 0.72/0.89 ($false),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[783, 108, 601, 777, 749, 721, 769, 763, 738, 728])).
% 0.72/0.89 tff(785,plain,(c1_1(a30) | hskp30 | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a5) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.89 tff(786,plain,
% 0.72/0.89 (c1_1(a30)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[785, 488, 487, 472, 473, 1, 484, 485])).
% 0.72/0.89 tff(787,plain,
% 0.72/0.89 (~hskp16),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[226, 786])).
% 0.72/0.89 tff(788,plain,
% 0.72/0.89 (~hskp10),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[534, 787, 487, 1])).
% 0.72/0.89 tff(789,plain,
% 0.72/0.89 (hskp2),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[718, 486, 788, 1, 487, 472, 473, 488])).
% 0.72/0.89 tff(790,plain,
% 0.72/0.89 (c2_1(a5)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[600, 789])).
% 0.72/0.89 tff(791,plain,
% 0.72/0.89 (~c3_1(a5)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[543, 790])).
% 0.72/0.89 tff(792,plain,
% 0.72/0.89 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(793,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[792])).
% 0.72/0.89 tff(794,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(795,plain,
% 0.72/0.89 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_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) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_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) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_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) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(796,plain,
% 0.72/0.90 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[795])).
% 0.72/0.90 tff(797,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.72/0.90 tff(798,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[797, 796])).
% 0.72/0.90 tff(799,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[798, 794])).
% 0.72/0.90 tff(800,plain,(
% 0.72/0.90 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.72/0.90 inference(skolemize,[status(sab)],[799])).
% 0.72/0.90 tff(801,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[800, 793])).
% 0.72/0.90 tff(802,plain,
% 0.72/0.90 (hskp15),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[551, 790, 787, 791])).
% 0.72/0.90 tff(803,plain,
% 0.72/0.90 (~c3_1(a29)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[130, 802])).
% 0.72/0.90 tff(804,plain,
% 0.72/0.90 (~c2_1(a29)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[136, 802])).
% 0.72/0.90 tff(805,plain,
% 0.72/0.90 (c1_1(a29)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[124, 802])).
% 0.72/0.90 tff(806,plain,
% 0.72/0.90 (~hskp13),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[704, 486, 788, 1, 487, 472, 473, 488])).
% 0.72/0.90 tff(807,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp13 | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(808,plain,
% 0.72/0.90 ((hskp13 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a5) | c0_1(a5) | (~c2_1(a5))) <=> (hskp13 | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(809,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[808])).
% 0.72/0.90 tff(810,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a5) | c0_1(a5) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp13 | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[809, 807])).
% 0.72/0.90 tff(811,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a5) | c0_1(a5) | (~c2_1(a5)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(812,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp13 | c2_1(a29) | c3_1(a29) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | c3_1(a5) | (~c1_1(a29))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[811, 810])).
% 0.72/0.90 tff(813,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[812, 108, 806, 805, 790, 804, 803, 484, 801, 791])).
% 0.72/0.90 tff(814,plain,(hskp3 | c0_1(a5) | hskp8 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a5) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(815,plain,
% 0.72/0.90 (hskp3),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[814, 488, 487, 472, 473, 484, 485, 1])).
% 0.72/0.90 tff(816,plain,
% 0.72/0.90 (~c2_1(a6)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[448, 815])).
% 0.72/0.90 tff(817,plain,
% 0.72/0.90 (c3_1(a6)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[411, 815])).
% 0.72/0.90 tff(818,plain,
% 0.72/0.90 (~c1_1(a6)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[727, 108, 787, 817, 816, 180])).
% 0.72/0.90 tff(819,plain,
% 0.72/0.90 (c0_1(a6)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[419, 815])).
% 0.72/0.90 tff(820,plain,
% 0.72/0.90 (hskp21 | c1_1(a6)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[423, 108, 487, 819, 817, 21])).
% 0.72/0.90 tff(821,plain,
% 0.72/0.90 (hskp21),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[820, 818])).
% 0.72/0.90 tff(822,plain,
% 0.72/0.90 (~c3_1(a39)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[58, 821])).
% 0.72/0.90 tff(823,plain,
% 0.72/0.90 (~c0_1(a39)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[64, 821])).
% 0.72/0.90 tff(824,plain,
% 0.72/0.90 (c2_1(a39)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[72, 821])).
% 0.72/0.90 tff(825,plain,
% 0.72/0.90 (hskp15),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[114, 108, 787, 824, 823, 822, 53])).
% 0.72/0.90 tff(826,plain,
% 0.72/0.90 (~c3_1(a29)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[130, 825])).
% 0.72/0.90 tff(827,plain,
% 0.72/0.90 (~c2_1(a29)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[136, 825])).
% 0.72/0.90 tff(828,plain,
% 0.72/0.90 (c1_1(a29)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[124, 825])).
% 0.72/0.90 tff(829,plain,
% 0.72/0.90 (~c0_1(a29)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[157, 108, 824, 828, 823, 822, 827, 826, 148])).
% 0.72/0.90 tff(830,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[384, 108, 1, 487, 828, 826, 378, 829])).
% 0.72/0.90 tff(831,plain,(c3_1(a15) | hskp30 | hskp8 | c1_1(a15) | c2_1(a15) | c0_1(a5) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(832,plain,
% 0.72/0.90 (c3_1(a15)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[831, 485, 294, 472, 473, 484, 1])).
% 0.72/0.90 tff(833,plain,
% 0.72/0.90 (~hskp10),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[534, 43, 294, 1])).
% 0.72/0.90 tff(834,plain,
% 0.72/0.90 (hskp13),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[716, 602, 486])).
% 0.72/0.90 tff(835,plain,
% 0.72/0.90 (~c0_1(a26)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[630, 834])).
% 0.72/0.90 tff(836,plain,
% 0.72/0.90 (c3_1(a26)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[617, 834])).
% 0.72/0.90 tff(837,assumption,(c3_1(a15)), introduced(assumption)).
% 0.72/0.90 tff(838,assumption,(hskp11), introduced(assumption)).
% 0.72/0.90 tff(839,plain,
% 0.72/0.90 (~c2_1(a21)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[331, 838])).
% 0.72/0.90 tff(840,plain,
% 0.72/0.90 (~c1_1(a26)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[609, 834])).
% 0.72/0.90 tff(841,plain,
% 0.72/0.90 (c0_1(a21)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[356, 838])).
% 0.72/0.90 tff(842,plain,
% 0.72/0.90 (~c1_1(a21)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[647, 108, 486, 836, 841, 835, 840, 839, 396])).
% 0.72/0.90 tff(843,plain,
% 0.72/0.90 (~c3_1(a21)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[325, 838])).
% 0.72/0.90 tff(844,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c3_1(a21) | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a21) | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)) | c1_1(a21) | (~c0_1(a21)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(845,plain,
% 0.72/0.90 ((hskp2 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21))) <=> (hskp2 | c3_1(a21) | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)) | c1_1(a21) | (~c0_1(a21)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(846,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | c3_1(a21) | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)) | c1_1(a21) | (~c0_1(a21))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[845])).
% 0.72/0.90 tff(847,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a21) | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)) | c1_1(a21) | (~c0_1(a21)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[846, 844])).
% 0.72/0.90 tff(848,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(849,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp2 | c3_1(a21) | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)) | c1_1(a21) | (~c0_1(a21))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[848, 847])).
% 0.72/0.90 tff(850,plain,
% 0.72/0.90 (~c0_1(a15)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[849, 108, 602, 841, 843, 472, 837, 738, 842])).
% 0.72/0.90 tff(851,plain,
% 0.72/0.90 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(852,plain,
% 0.72/0.90 ((hskp30 | hskp23 | (~ndr1_0) | c2_1(a21) | c1_1(a21) | (~c0_1(a21))) <=> (hskp30 | hskp23 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(853,plain,
% 0.72/0.90 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[852])).
% 0.72/0.90 tff(854,plain,
% 0.72/0.90 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[853, 851])).
% 0.72/0.90 tff(855,plain,
% 0.72/0.90 ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a21) | c1_1(a21) | (~c0_1(a21)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(856,plain,
% 0.72/0.90 ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[855, 854])).
% 0.72/0.90 tff(857,plain,
% 0.72/0.90 (hskp23 | c1_1(a21)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[856, 108, 1, 841, 839, 748])).
% 0.72/0.90 tff(858,plain,
% 0.72/0.90 (hskp23),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[857, 842])).
% 0.72/0.90 tff(859,plain,
% 0.72/0.90 (~c3_1(a42)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[762, 858])).
% 0.72/0.90 tff(860,plain,
% 0.72/0.90 (~c1_1(a42)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[768, 858])).
% 0.72/0.90 tff(861,plain,
% 0.72/0.90 (c0_1(a42)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[776, 858])).
% 0.72/0.90 tff(862,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c1_1(a42) | c3_1(a42) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a42) | c3_1(a42) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c0_1(a42)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(863,plain,
% 0.72/0.90 ((hskp10 | (~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a15) | c2_1(a15) | (~c3_1(a15))) <=> (hskp10 | c1_1(a42) | c3_1(a42) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c0_1(a42)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(864,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a15) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c1_1(a42) | c3_1(a42) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c0_1(a42))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[863])).
% 0.72/0.90 tff(865,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a15) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a42) | c3_1(a42) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c0_1(a42)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[864, 862])).
% 0.72/0.90 tff(866,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a15) | c2_1(a15) | (~c3_1(a15)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(867,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a42) | c3_1(a42) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c0_1(a42))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[866, 865])).
% 0.72/0.90 tff(868,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[867, 108, 603, 861, 860, 859, 473, 837, 658, 850])).
% 0.72/0.90 tff(869,plain,((~hskp11) | hskp10 | c2_1(a15) | (~c3_1(a15)) | hskp30 | hskp2 | c1_1(a15) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(870,plain,
% 0.72/0.90 (~hskp11),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[869, 602, 473, 837, 1, 603, 472, 486])).
% 0.72/0.90 tff(871,plain,
% 0.72/0.90 (c2_1(a26)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[637, 108, 1, 870, 836, 835, 41])).
% 0.72/0.90 tff(872,plain,
% 0.72/0.90 (~c3_1(a13)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[319, 870, 1, 295])).
% 0.72/0.90 tff(873,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a26) | (~ndr1_0) | c3_1(a13) | (~c2_1(a26)) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a26) | (~ndr1_0) | c3_1(a13) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(874,plain,
% 0.72/0.90 ((hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a13) | c1_1(a13) | c2_1(a13)) <=> (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a26) | (~ndr1_0) | c3_1(a13) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(875,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a26) | (~ndr1_0) | c3_1(a13) | (~c2_1(a26)) | (~c3_1(a26))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[874])).
% 0.72/0.90 tff(876,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a26) | (~ndr1_0) | c3_1(a13) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[875, 873])).
% 0.72/0.90 tff(877,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a13) | c1_1(a13) | c2_1(a13))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(878,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a26) | (~ndr1_0) | c3_1(a13) | (~c2_1(a26)) | (~c3_1(a26))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[877, 876])).
% 0.72/0.90 tff(879,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[878, 108, 294, 836, 286, 295, 840, 31, 872, 871])).
% 0.72/0.90 tff(880,plain,(hskp2 | c1_1(a13) | c2_1(a13) | hskp30 | c0_1(a13) | c2_1(a15) | (~c3_1(a15)) | hskp10 | c1_1(a15) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(881,plain,
% 0.72/0.90 (hskp2),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[880, 833, 295, 1, 244, 473, 832, 286, 472, 486])).
% 0.72/0.90 tff(882,plain,
% 0.72/0.90 (c2_1(a5)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[600, 881])).
% 0.72/0.90 tff(883,plain,
% 0.72/0.90 (c3_1(a5)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[551, 74, 43, 536])).
% 0.72/0.90 tff(884,plain,
% 0.72/0.90 (c3_1(a15)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[831, 485, 487, 472, 473, 484, 1])).
% 0.72/0.90 tff(885,plain,
% 0.72/0.90 (~hskp21),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[116, 74, 43])).
% 0.72/0.90 tff(886,plain,
% 0.72/0.90 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(887,plain,
% 0.72/0.90 ((hskp21 | hskp8 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15))) <=> (hskp21 | hskp8 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(888,plain,
% 0.72/0.90 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[887])).
% 0.72/0.90 tff(889,plain,
% 0.72/0.90 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[888, 886])).
% 0.72/0.90 tff(890,plain,
% 0.72/0.90 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(891,plain,
% 0.72/0.90 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[890, 889])).
% 0.72/0.90 tff(892,plain,
% 0.72/0.90 (hskp21 | (~c3_1(a15)) | (~c0_1(a15))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[891, 108, 487, 472, 21])).
% 0.72/0.90 tff(893,plain,
% 0.72/0.90 (~c0_1(a15)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[892, 885, 884])).
% 0.72/0.90 tff(894,plain,
% 0.72/0.90 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(895,plain,
% 0.72/0.90 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (hskp30 | hskp11 | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(896,plain,
% 0.72/0.90 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15)))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[895])).
% 0.72/0.90 tff(897,plain,
% 0.72/0.90 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15))),
% 0.72/0.90 inference(transitivity,[status(thm)],[896, 894])).
% 0.72/0.90 tff(898,plain,
% 0.72/0.90 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(899,plain,
% 0.72/0.90 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[898, 897])).
% 0.72/0.90 tff(900,plain,
% 0.72/0.90 (hskp11 | (~c3_1(a15)) | c0_1(a15)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[899, 108, 1, 473, 41])).
% 0.72/0.90 tff(901,plain,
% 0.72/0.90 (hskp11),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[900, 893, 884])).
% 0.72/0.90 tff(902,plain,
% 0.72/0.90 (~c2_1(a21)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[331, 901])).
% 0.72/0.90 tff(903,plain,
% 0.72/0.90 (c0_1(a21)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[356, 901])).
% 0.72/0.90 tff(904,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(905,plain,
% 0.72/0.90 ((hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5))) <=> (hskp15 | c2_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(906,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c2_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a21)) | (~c0_1(a21))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[905])).
% 0.72/0.90 tff(907,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[906, 904])).
% 0.72/0.90 tff(908,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(909,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c2_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a21)) | (~c0_1(a21))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[908, 907])).
% 0.72/0.90 tff(910,plain,
% 0.72/0.90 (~c1_1(a21)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[909, 108, 74, 903, 536, 902, 485, 349, 883])).
% 0.72/0.90 tff(911,plain,
% 0.72/0.90 (~c3_1(a21)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[325, 901])).
% 0.72/0.90 tff(912,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c2_1(a21) | c3_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c2_1(a21) | c3_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a21))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(913,plain,
% 0.72/0.90 ((hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a21) | c1_1(a21) | c2_1(a21)) <=> (hskp8 | c2_1(a21) | c3_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a21))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(914,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a21) | c1_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c2_1(a21) | c3_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a21)))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[913])).
% 0.72/0.90 tff(915,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a21) | c1_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c2_1(a21) | c3_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a21))),
% 0.72/0.90 inference(transitivity,[status(thm)],[914, 912])).
% 0.72/0.90 tff(916,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a21) | c1_1(a21) | c2_1(a21))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(917,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c2_1(a21) | c3_1(a21) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a21)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[916, 915])).
% 0.72/0.90 tff(918,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[917, 108, 487, 536, 902, 911, 485, 31, 883, 910])).
% 0.72/0.90 tff(919,plain,(hskp15 | hskp8 | (~c2_1(a5)) | c1_1(a5) | hskp30 | c2_1(a15) | c1_1(a15) | hskp16 | c0_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(920,plain,
% 0.72/0.90 (hskp15),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[919, 882, 294, 485, 1, 473, 472, 43, 484])).
% 0.72/0.90 tff(921,plain,
% 0.72/0.90 (~c2_1(a29)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[136, 920])).
% 0.72/0.91 tff(922,plain,
% 0.72/0.91 (~c3_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[130, 920])).
% 0.72/0.91 tff(923,plain,
% 0.72/0.91 (~hskp10),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[534, 43, 487, 1])).
% 0.72/0.91 tff(924,plain,
% 0.72/0.91 (hskp11 | c2_1(a26)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[637, 108, 1, 836, 835, 41])).
% 0.72/0.91 tff(925,plain,
% 0.72/0.91 (c2_1(a26)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[924, 870])).
% 0.72/0.91 tff(926,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a26) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a26) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(927,plain,
% 0.72/0.91 ((hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a29) | c1_1(a29) | c2_1(a29)) <=> (hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a26) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(928,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a29) | c1_1(a29) | c2_1(a29))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a26) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[927])).
% 0.72/0.91 tff(929,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a29) | c1_1(a29) | c2_1(a29))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a26) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[928, 926])).
% 0.72/0.91 tff(930,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a26) | (~c3_1(a26)) | (~c2_1(a26)) | c3_1(a29) | c1_1(a29) | c2_1(a29))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(931,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a26) | (~ndr1_0) | (~c2_1(a26)) | (~c3_1(a26))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[930, 929])).
% 0.72/0.91 tff(932,plain,
% 0.72/0.91 (c1_1(a29) | (~c2_1(a26))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[931, 108, 487, 836, 150, 149, 840, 31])).
% 0.72/0.91 tff(933,plain,
% 0.72/0.91 (c1_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[932, 925])).
% 0.72/0.91 tff(934,plain,
% 0.72/0.91 ((~c1_1(a29)) | c0_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[384, 108, 1, 487, 149, 378])).
% 0.72/0.91 tff(935,plain,
% 0.72/0.91 (c0_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[934, 933])).
% 0.72/0.91 tff(936,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a29) | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)) | (~c1_1(a29)) | (~c0_1(a29)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a29) | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(937,plain,
% 0.72/0.91 ((hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26))) <=> (hskp3 | c2_1(a29) | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(938,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a29) | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)) | (~c1_1(a29)) | (~c0_1(a29))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[937])).
% 0.72/0.91 tff(939,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a29) | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[938, 936])).
% 0.72/0.91 tff(940,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(941,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a29) | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.72/0.91 tff(942,plain,
% 0.72/0.91 ((~c1_1(a29)) | (~c0_1(a29))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[941, 108, 486, 836, 150, 835, 840, 396])).
% 0.72/0.91 tff(943,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[942, 935, 933])).
% 0.72/0.91 tff(944,plain,(hskp2 | hskp3 | c2_1(a29) | hskp30 | hskp8 | c3_1(a29) | c2_1(a15) | (~c3_1(a15)) | hskp10 | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(945,plain,
% 0.72/0.91 (hskp2),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[944, 149, 150, 1, 487, 486, 473, 884, 923, 472])).
% 0.72/0.91 tff(946,plain,
% 0.72/0.91 (c2_1(a5)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[600, 945])).
% 0.72/0.91 tff(947,assumption,(~c1_1(a29)), introduced(assumption)).
% 0.72/0.91 tff(948,plain,
% 0.72/0.91 (~hskp15),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[124, 947])).
% 0.72/0.91 tff(949,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(950,plain,
% 0.72/0.91 ((hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a29) | c1_1(a29) | c2_1(a29)) <=> (hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(951,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a29) | c1_1(a29) | c2_1(a29))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[950])).
% 0.72/0.91 tff(952,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a29) | c1_1(a29) | c2_1(a29))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[951, 949])).
% 0.72/0.91 tff(953,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a29) | c1_1(a29) | c2_1(a29))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(954,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.72/0.91 tff(955,plain,
% 0.72/0.91 (c1_1(a29) | (~c2_1(a5)) | (~c3_1(a5))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[954, 108, 487, 150, 149, 485, 31])).
% 0.72/0.91 tff(956,plain,
% 0.72/0.91 (~c3_1(a5)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[955, 947, 536])).
% 0.72/0.91 tff(957,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[551, 956, 948, 43, 536])).
% 0.72/0.91 tff(958,plain,(c1_1(a29) | hskp16 | (~c2_1(a5)) | c0_1(a5) | hskp8 | c2_1(a29) | c3_1(a29) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(959,plain,
% 0.72/0.91 (c1_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[958, 946, 43, 484, 487, 150, 149, 485])).
% 0.72/0.91 tff(960,plain,
% 0.72/0.91 (c0_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[934, 959])).
% 0.72/0.91 tff(961,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a29) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a29) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(962,plain,
% 0.72/0.91 ((hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5))) <=> (hskp3 | c2_1(a29) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(963,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a29) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[962])).
% 0.72/0.91 tff(964,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a29) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[963, 961])).
% 0.72/0.91 tff(965,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c1_1(a5) | c0_1(a5) | (~c3_1(a5)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(966,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a29) | c0_1(a5) | c1_1(a5) | (~ndr1_0) | (~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[965, 964])).
% 0.72/0.91 tff(967,plain,
% 0.72/0.91 ((~c3_1(a5)) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[966, 108, 486, 150, 484, 485, 396])).
% 0.72/0.91 tff(968,plain,
% 0.72/0.91 (~c3_1(a5)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[967, 960, 959])).
% 0.72/0.91 tff(969,plain,
% 0.72/0.91 ((~c2_1(a5)) | c3_1(a5) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[581, 108, 150, 149, 484, 148])).
% 0.72/0.91 tff(970,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[969, 968, 960, 946, 959])).
% 0.72/0.91 tff(971,plain,(c3_1(a29) | c2_1(a29) | c0_1(a5) | hskp3 | c1_1(a5) | hskp30 | hskp8 | hskp16 | c2_1(a15) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(972,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[971, 922, 921, 484, 486, 485, 1, 294, 43, 473, 472])).
% 0.72/0.91 tff(973,plain,(hskp16 | c0_1(a5) | hskp3 | c1_1(a5) | hskp30 | c2_1(a15) | c1_1(a15) | c2_1(a13) | c0_1(a13) | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(974,plain,
% 0.72/0.91 (hskp16),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[973, 486, 484, 485, 1, 473, 472, 295, 244, 286])).
% 0.72/0.91 tff(975,plain,
% 0.72/0.91 (~c1_1(a30)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[226, 974])).
% 0.72/0.91 tff(976,plain,
% 0.72/0.91 (c3_1(a30)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[242, 974])).
% 0.72/0.91 tff(977,plain,
% 0.72/0.91 (c2_1(a30)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[234, 974])).
% 0.72/0.91 tff(978,plain,
% 0.72/0.91 (c3_1(a13)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[311, 977, 976, 286, 295, 975])).
% 0.72/0.91 tff(979,plain,
% 0.72/0.91 (hskp11),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[319, 978, 1, 295])).
% 0.72/0.91 tff(980,plain,
% 0.72/0.91 (~c3_1(a21)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[325, 979])).
% 0.72/0.91 tff(981,plain,
% 0.72/0.91 (~c2_1(a21)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[331, 979])).
% 0.72/0.91 tff(982,plain,
% 0.72/0.91 (c1_1(a21)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[338, 108, 294, 977, 976, 975, 981, 980, 31])).
% 0.72/0.91 tff(983,plain,
% 0.72/0.91 (c0_1(a21)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[356, 979])).
% 0.72/0.91 tff(984,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[402, 108, 486, 983, 286, 981, 244, 396, 978, 982])).
% 0.72/0.91 tff(985,plain,(hskp3 | c1_1(a13) | c0_1(a13) | hskp30 | c2_1(a13) | c0_1(a5) | c1_1(a5) | c2_1(a15) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(986,plain,
% 0.72/0.91 (hskp3),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[985, 485, 244, 1, 295, 484, 286, 473, 472])).
% 0.72/0.91 tff(987,plain,
% 0.72/0.91 (~c2_1(a6)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[448, 986])).
% 0.72/0.91 tff(988,plain,
% 0.72/0.91 (c3_1(a6)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[411, 986])).
% 0.72/0.91 tff(989,plain,
% 0.72/0.91 (c0_1(a6)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[419, 986])).
% 0.72/0.91 tff(990,plain,
% 0.72/0.91 (((~hskp9) | (~c3_1(a15))) <=> ((~hskp9) | (~c3_1(a15)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(991,plain,
% 0.72/0.91 (((~c3_1(a15)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a15)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(992,axiom,((~c3_1(a15)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 0.72/0.91 tff(993,plain,
% 0.72/0.91 ((~hskp9) | (~c3_1(a15))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[992, 991])).
% 0.72/0.91 tff(994,plain,
% 0.72/0.91 ((~hskp9) | (~c3_1(a15))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[993, 990])).
% 0.72/0.91 tff(995,plain,
% 0.72/0.91 (~hskp9),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[994, 832])).
% 0.72/0.91 tff(996,assumption,(~c2_1(a6)), introduced(assumption)).
% 0.72/0.91 tff(997,assumption,(c3_1(a6)), introduced(assumption)).
% 0.72/0.91 tff(998,plain,
% 0.72/0.91 (hskp16 | (~c1_1(a6))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[727, 108, 997, 996, 180])).
% 0.72/0.91 tff(999,plain,
% 0.72/0.91 (~c1_1(a6)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[998, 43])).
% 0.72/0.91 tff(1000,assumption,(c0_1(a6)), introduced(assumption)).
% 0.72/0.91 tff(1001,plain,
% 0.72/0.91 (hskp21 | c1_1(a6)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[423, 108, 487, 1000, 997, 21])).
% 0.72/0.91 tff(1002,plain,
% 0.72/0.91 (hskp21),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1001, 999])).
% 0.72/0.91 tff(1003,plain,
% 0.72/0.91 (hskp15),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[116, 1002, 43])).
% 0.72/0.91 tff(1004,plain,
% 0.72/0.91 (~c3_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[130, 1003])).
% 0.72/0.91 tff(1005,plain,
% 0.72/0.91 (~c2_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[136, 1003])).
% 0.72/0.91 tff(1006,plain,
% 0.72/0.91 (~c3_1(a39)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[58, 1002])).
% 0.72/0.91 tff(1007,plain,
% 0.72/0.91 (c1_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[124, 1003])).
% 0.72/0.91 tff(1008,plain,
% 0.72/0.91 (c2_1(a39)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[72, 1002])).
% 0.72/0.91 tff(1009,assumption,(~hskp9), introduced(assumption)).
% 0.72/0.91 tff(1010,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39) | (~c2_1(a39)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39) | (~c2_1(a39)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1011,plain,
% 0.72/0.91 ((hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | (~c2_1(a39))) <=> (hskp9 | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39) | (~c2_1(a39)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1012,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | (~c2_1(a39)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39) | (~c2_1(a39))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1011])).
% 0.72/0.91 tff(1013,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | (~c2_1(a39)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39) | (~c2_1(a39)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1012, 1010])).
% 0.72/0.91 tff(1014,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | (~c2_1(a39)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1015,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39) | (~c2_1(a39))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 0.72/0.91 tff(1016,plain,
% 0.72/0.91 (c1_1(a39)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1015, 108, 1009, 1008, 1007, 1006, 1005, 1004, 483])).
% 0.72/0.91 tff(1017,plain,
% 0.72/0.91 (~c0_1(a39)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[64, 1002])).
% 0.72/0.91 tff(1018,plain,
% 0.72/0.91 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c1_1(a39)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c1_1(a39)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1019,plain,
% 0.72/0.91 ((hskp30 | hskp8 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c1_1(a39))) <=> (hskp30 | hskp8 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c1_1(a39)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1020,plain,
% 0.72/0.91 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c1_1(a39)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c1_1(a39))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1019])).
% 0.72/0.91 tff(1021,plain,
% 0.72/0.91 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c1_1(a39)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c1_1(a39)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1020, 1018])).
% 0.72/0.91 tff(1022,plain,
% 0.72/0.91 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c1_1(a39)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1023,plain,
% 0.72/0.91 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a39) | c3_1(a39) | (~ndr1_0) | (~c1_1(a39))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 0.72/0.91 tff(1024,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1023, 108, 1, 487, 1017, 1006, 378, 1016])).
% 0.72/0.91 tff(1025,plain,(hskp16 | hskp30 | hskp8 | hskp9 | (~c0_1(a6)) | (~c3_1(a6)) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(1026,plain,
% 0.72/0.91 (hskp16),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1025, 995, 294, 1, 989, 988, 987])).
% 0.72/0.91 tff(1027,plain,
% 0.72/0.91 (~c1_1(a30)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[226, 1026])).
% 0.72/0.91 tff(1028,plain,
% 0.72/0.91 (c3_1(a30)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[242, 1026])).
% 0.72/0.91 tff(1029,plain,
% 0.72/0.91 (c2_1(a30)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[234, 1026])).
% 0.72/0.91 tff(1030,plain,
% 0.72/0.91 (c3_1(a13)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[311, 1029, 1028, 286, 295, 1027])).
% 0.72/0.91 tff(1031,plain,
% 0.72/0.91 (hskp11),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[319, 1030, 1, 295])).
% 0.72/0.91 tff(1032,plain,
% 0.72/0.91 (~c3_1(a21)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[325, 1031])).
% 0.72/0.91 tff(1033,plain,
% 0.72/0.91 (~c2_1(a21)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[331, 1031])).
% 0.72/0.91 tff(1034,plain,
% 0.72/0.91 (c1_1(a21)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[338, 108, 294, 1029, 1028, 1027, 1033, 1032, 31])).
% 0.72/0.91 tff(1035,plain,
% 0.72/0.91 (c0_1(a21)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[356, 1031])).
% 0.72/0.91 tff(1036,plain,
% 0.72/0.91 (hskp15 | (~c1_1(a21))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[363, 108, 1029, 1028, 1035, 1027, 1033, 349])).
% 0.72/0.91 tff(1037,plain,
% 0.72/0.91 (hskp15),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1036, 1034])).
% 0.72/0.91 tff(1038,plain,
% 0.72/0.91 (~c3_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[130, 1037])).
% 0.72/0.91 tff(1039,plain,
% 0.72/0.91 (c1_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[124, 1037])).
% 0.72/0.91 tff(1040,plain,
% 0.72/0.91 (c0_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[384, 108, 1, 294, 1039, 1038, 378])).
% 0.72/0.91 tff(1041,plain,
% 0.72/0.91 (~c2_1(a29)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[136, 1037])).
% 0.72/0.91 tff(1042,plain,
% 0.72/0.91 (~hskp21),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[159, 1039, 1041, 1038, 1040])).
% 0.72/0.91 tff(1043,plain,
% 0.72/0.91 (hskp21 | (~c0_1(a30))),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[431, 108, 294, 1028, 1027, 21])).
% 0.72/0.91 tff(1044,plain,
% 0.72/0.91 (~c0_1(a30)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1043, 1042])).
% 0.72/0.91 tff(1045,plain,
% 0.72/0.91 (hskp21 | c1_1(a6)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[423, 108, 294, 989, 988, 21])).
% 0.72/0.91 tff(1046,plain,
% 0.72/0.91 (c1_1(a6)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1045, 1042])).
% 0.72/0.91 tff(1047,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[455, 108, 1029, 1028, 286, 295, 988, 244, 987, 443, 1046, 1044])).
% 0.72/0.91 tff(1048,plain,(c1_1(a5) | c1_1(a13) | c2_1(a13) | c0_1(a13) | hskp30 | c0_1(a5) | c2_1(a15) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(1049,plain,
% 0.72/0.91 (c1_1(a5)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1048, 484, 295, 244, 1, 286, 473, 472])).
% 0.72/0.91 tff(1050,plain,
% 0.72/0.91 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0) | c3_1(a5))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0) | c3_1(a5))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1051,plain,
% 0.72/0.91 ((hskp30 | hskp8 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c1_1(a5))) <=> (hskp30 | hskp8 | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0) | c3_1(a5))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1052,plain,
% 0.72/0.91 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c1_1(a5)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0) | c3_1(a5)))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1051])).
% 0.72/0.91 tff(1053,plain,
% 0.72/0.91 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c1_1(a5)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0) | c3_1(a5))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1052, 1050])).
% 0.72/0.91 tff(1054,plain,
% 0.72/0.91 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a5) | c3_1(a5) | (~c1_1(a5)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1055,plain,
% 0.72/0.91 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0) | c3_1(a5)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 0.72/0.91 tff(1056,plain,
% 0.72/0.91 ((~c1_1(a5)) | c3_1(a5)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1055, 108, 1, 294, 484, 378])).
% 0.72/0.91 tff(1057,plain,
% 0.72/0.91 (c3_1(a5)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1056, 1049])).
% 0.72/0.91 tff(1058,assumption,(c3_1(a5)), introduced(assumption)).
% 0.72/0.91 tff(1059,plain,
% 0.72/0.91 (^[U: $i] : refl((hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(1060,plain,
% 0.72/0.91 (![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[1059])).
% 0.72/0.91 tff(1061,plain,
% 0.72/0.91 (![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1062,plain,
% 0.72/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp12))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp2) <=> ((hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp2))), rewrite(((hskp12 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | hskp2) <=> (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp2) <=> (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(1063,plain,
% 0.72/0.91 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp2) <=> ![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[1062])).
% 0.72/0.91 tff(1064,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 0.72/0.91 tff(1065,plain,
% 0.72/0.91 (![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 0.72/0.91 tff(1066,plain,
% 0.72/0.91 (![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1065, 1061])).
% 0.72/0.91 tff(1067,plain,(
% 0.72/0.91 ![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.72/0.91 inference(skolemize,[status(sab)],[1066])).
% 0.72/0.91 tff(1068,plain,
% 0.72/0.91 (![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1067, 1060])).
% 0.72/0.91 tff(1069,assumption,(c1_1(a5)), introduced(assumption)).
% 0.72/0.91 tff(1070,plain,
% 0.72/0.91 (((~hskp2) | (~c1_1(a5))) <=> ((~hskp2) | (~c1_1(a5)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1071,plain,
% 0.72/0.91 (((~c1_1(a5)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a5)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1072,axiom,((~c1_1(a5)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 0.72/0.91 tff(1073,plain,
% 0.72/0.91 ((~hskp2) | (~c1_1(a5))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 0.72/0.92 tff(1074,plain,
% 0.72/0.92 ((~hskp2) | (~c1_1(a5))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1073, 1070])).
% 0.72/0.92 tff(1075,plain,
% 0.72/0.92 (~hskp2),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1074, 1069])).
% 0.72/0.92 tff(1076,plain,
% 0.72/0.92 (((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp12 | hskp2 | (~c1_1(a5)) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp12 | hskp2 | (~c1_1(a5)) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1077,plain,
% 0.72/0.92 ((hskp12 | hskp2 | (~ndr1_0) | (~c1_1(a5)) | (~c3_1(a5)) | (~c2_1(a5))) <=> (hskp12 | hskp2 | (~c1_1(a5)) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1078,plain,
% 0.72/0.92 (((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(a5)) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp12 | hskp2 | (~c1_1(a5)) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1077])).
% 0.72/0.92 tff(1079,plain,
% 0.72/0.92 (((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(a5)) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp12 | hskp2 | (~c1_1(a5)) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1078, 1076])).
% 0.72/0.92 tff(1080,plain,
% 0.72/0.92 ((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(a5)) | (~c3_1(a5)) | (~c2_1(a5)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1081,plain,
% 0.72/0.92 ((~![U: $i] : (hskp12 | hskp2 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp12 | hskp2 | (~c1_1(a5)) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 0.72/0.92 tff(1082,plain,
% 0.72/0.92 (hskp12 | (~c2_1(a5))),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1081, 108, 1075, 1069, 1068, 1058])).
% 0.72/0.92 tff(1083,plain,
% 0.72/0.92 (hskp12),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1082, 536])).
% 0.72/0.92 tff(1084,plain,
% 0.72/0.92 (~c2_1(a24)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[186, 1083])).
% 0.72/0.92 tff(1085,plain,
% 0.72/0.92 (c3_1(a24)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[194, 1083])).
% 0.72/0.92 tff(1086,plain,
% 0.72/0.92 (c1_1(a24)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[202, 1083])).
% 0.72/0.92 tff(1087,plain,
% 0.72/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a13) | c2_1(a13) | c2_1(a24) | c0_1(a13) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a24)) | (~c3_1(a24)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a13) | c2_1(a13) | c2_1(a24) | c0_1(a13) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a24)) | (~c3_1(a24)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1088,plain,
% 0.72/0.92 (((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c1_1(a13) | c0_1(a13) | c2_1(a13)) <=> (c1_1(a13) | c2_1(a13) | c2_1(a24) | c0_1(a13) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a24)) | (~c3_1(a24)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1089,plain,
% 0.72/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c1_1(a13) | c0_1(a13) | c2_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a13) | c2_1(a13) | c2_1(a24) | c0_1(a13) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a24)) | (~c3_1(a24))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1088])).
% 0.72/0.92 tff(1090,plain,
% 0.72/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c1_1(a13) | c0_1(a13) | c2_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a13) | c2_1(a13) | c2_1(a24) | c0_1(a13) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a24)) | (~c3_1(a24)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1089, 1087])).
% 0.72/0.92 tff(1091,plain,
% 0.72/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c1_1(a13) | c0_1(a13) | c2_1(a13))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1092,plain,
% 0.72/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c1_1(a13) | c2_1(a13) | c2_1(a24) | c0_1(a13) | c0_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a24)) | (~c3_1(a24))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 0.72/0.92 tff(1093,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1092, 108, 1086, 1085, 286, 295, 536, 1084, 244, 484, 443, 1058])).
% 0.72/0.92 tff(1094,plain,((~c2_1(a5)) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a5))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(1095,plain,
% 0.72/0.92 (~c2_1(a5)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1094, 484, 295, 244, 286, 1057, 1049])).
% 0.72/0.92 tff(1096,plain,
% 0.72/0.92 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a5) | c0_1(a5) | (~ndr1_0) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a5) | c0_1(a5) | (~ndr1_0) | (~c3_1(a5)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1097,plain,
% 0.72/0.92 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c3_1(a5))) <=> (hskp30 | hskp11 | c2_1(a5) | c0_1(a5) | (~ndr1_0) | (~c3_1(a5)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1098,plain,
% 0.72/0.92 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a5) | c0_1(a5) | (~ndr1_0) | (~c3_1(a5))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1097])).
% 0.72/0.92 tff(1099,plain,
% 0.72/0.92 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a5) | c0_1(a5) | (~ndr1_0) | (~c3_1(a5)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1098, 1096])).
% 0.72/0.92 tff(1100,plain,
% 0.72/0.92 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c3_1(a5)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1101,plain,
% 0.72/0.92 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a5) | c0_1(a5) | (~ndr1_0) | (~c3_1(a5))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1100, 1099])).
% 0.72/0.92 tff(1102,plain,
% 0.72/0.92 (hskp11 | c2_1(a5) | (~c3_1(a5))),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1101, 108, 1, 484, 41])).
% 0.72/0.92 tff(1103,plain,
% 0.72/0.92 (hskp11),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1102, 1095, 1057])).
% 0.72/0.92 tff(1104,plain,
% 0.72/0.92 (~c3_1(a21)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[325, 1103])).
% 0.72/0.92 tff(1105,plain,
% 0.72/0.92 (~c2_1(a21)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[331, 1103])).
% 0.72/0.92 tff(1106,plain,
% 0.72/0.92 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a5) | (~c1_1(a5)) | (~ndr1_0) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a5) | (~c1_1(a5)) | (~ndr1_0) | (~c3_1(a5)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1107,plain,
% 0.72/0.92 ((hskp16 | (~ndr1_0) | c2_1(a5) | (~c1_1(a5)) | (~c3_1(a5))) <=> (hskp16 | c2_1(a5) | (~c1_1(a5)) | (~ndr1_0) | (~c3_1(a5)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1108,plain,
% 0.72/0.92 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a5) | (~c1_1(a5)) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a5) | (~c1_1(a5)) | (~ndr1_0) | (~c3_1(a5))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1107])).
% 0.72/0.92 tff(1109,plain,
% 0.72/0.92 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a5) | (~c1_1(a5)) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a5) | (~c1_1(a5)) | (~ndr1_0) | (~c3_1(a5)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1108, 1106])).
% 0.72/0.92 tff(1110,plain,
% 0.72/0.92 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a5) | (~c1_1(a5)) | (~c3_1(a5)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1111,plain,
% 0.72/0.92 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a5) | (~c1_1(a5)) | (~ndr1_0) | (~c3_1(a5))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 0.72/0.92 tff(1112,plain,
% 0.72/0.92 (hskp16 | c2_1(a5)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1111, 108, 1049, 180, 1057])).
% 0.72/0.92 tff(1113,plain,
% 0.72/0.92 (hskp16),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1112, 1095])).
% 0.72/0.92 tff(1114,plain,
% 0.72/0.92 (~c1_1(a30)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[226, 1113])).
% 0.72/0.92 tff(1115,plain,
% 0.72/0.92 (c3_1(a30)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[242, 1113])).
% 0.72/0.92 tff(1116,plain,
% 0.72/0.92 (c2_1(a30)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[234, 1113])).
% 0.72/0.92 tff(1117,plain,
% 0.72/0.92 (c1_1(a21)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[338, 108, 294, 1116, 1115, 1114, 1105, 1104, 31])).
% 0.72/0.92 tff(1118,plain,
% 0.72/0.92 (c0_1(a21)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[356, 1103])).
% 0.72/0.92 tff(1119,plain,
% 0.72/0.92 (hskp15 | (~c1_1(a21))),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[363, 108, 1116, 1115, 1118, 1114, 1105, 349])).
% 0.72/0.92 tff(1120,plain,
% 0.72/0.92 (hskp15),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1119, 1117])).
% 0.72/0.92 tff(1121,plain,
% 0.72/0.92 (~c3_1(a29)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[130, 1120])).
% 0.72/0.92 tff(1122,plain,
% 0.72/0.92 (~c2_1(a29)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[136, 1120])).
% 0.72/0.92 tff(1123,plain,
% 0.72/0.92 (c3_1(a15)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[497, 1114, 294, 472, 473, 1113])).
% 0.72/0.92 tff(1124,plain,
% 0.72/0.92 (~hskp9),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[994, 1123])).
% 0.72/0.92 tff(1125,plain,
% 0.72/0.92 (^[U: $i] : refl((hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(1126,plain,
% 0.72/0.92 (![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[1125])).
% 0.72/0.92 tff(1127,plain,
% 0.72/0.92 (![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1128,plain,
% 0.72/0.92 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp9) <=> ((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9) <=> (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp9) <=> (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.72/0.92 inference(bind,[status(th)],[])).
% 0.72/0.92 tff(1129,plain,
% 0.72/0.92 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp9) <=> ![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.72/0.92 inference(quant_intro,[status(thm)],[1128])).
% 0.72/0.92 tff(1130,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp0) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 0.72/0.92 tff(1131,plain,
% 0.72/0.92 (![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 0.72/0.92 tff(1132,plain,
% 0.72/0.92 (![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1131, 1127])).
% 0.72/0.92 tff(1133,plain,(
% 0.72/0.92 ![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.72/0.92 inference(skolemize,[status(sab)],[1132])).
% 0.72/0.92 tff(1134,plain,
% 0.72/0.92 (![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1133, 1126])).
% 0.72/0.92 tff(1135,plain,
% 0.72/0.92 (((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp0 | c2_1(a5) | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp0 | c2_1(a5) | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1136,plain,
% 0.72/0.92 ((hskp9 | hskp0 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c1_1(a5))) <=> (hskp9 | hskp0 | c2_1(a5) | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1137,plain,
% 0.72/0.92 (((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp0 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c1_1(a5)))) <=> ((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp0 | c2_1(a5) | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0)))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1136])).
% 0.72/0.92 tff(1138,plain,
% 0.72/0.92 (((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp0 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c1_1(a5)))) <=> ((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp0 | c2_1(a5) | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1137, 1135])).
% 0.72/0.92 tff(1139,plain,
% 0.72/0.92 ((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp0 | (~ndr1_0) | c2_1(a5) | c0_1(a5) | (~c1_1(a5)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1140,plain,
% 0.72/0.92 ((~![U: $i] : (hskp9 | hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp0 | c2_1(a5) | c0_1(a5) | (~c1_1(a5)) | (~ndr1_0)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 0.72/0.92 tff(1141,plain,
% 0.72/0.92 (hskp9 | hskp0 | c2_1(a5) | (~c1_1(a5))),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1140, 108, 484, 1134])).
% 0.72/0.92 tff(1142,plain,
% 0.72/0.92 (hskp0),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1141, 1124, 1049, 1095])).
% 0.72/0.92 tff(1143,plain,
% 0.72/0.92 (((~hskp0) | (~c2_1(a1))) <=> ((~hskp0) | (~c2_1(a1)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1144,plain,
% 0.72/0.92 (((~c2_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1145,axiom,((~c2_1(a1)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 0.72/0.92 tff(1146,plain,
% 0.72/0.92 ((~hskp0) | (~c2_1(a1))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 0.72/0.92 tff(1147,plain,
% 0.72/0.92 ((~hskp0) | (~c2_1(a1))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1146, 1143])).
% 0.72/0.92 tff(1148,plain,
% 0.72/0.92 (~c2_1(a1)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1147, 1142])).
% 0.72/0.92 tff(1149,plain,
% 0.72/0.92 (((~hskp0) | (~c1_1(a1))) <=> ((~hskp0) | (~c1_1(a1)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1150,plain,
% 0.72/0.92 (((~c1_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a1)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1151,axiom,((~c1_1(a1)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.72/0.92 tff(1152,plain,
% 0.72/0.92 ((~hskp0) | (~c1_1(a1))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 0.72/0.92 tff(1153,plain,
% 0.72/0.92 ((~hskp0) | (~c1_1(a1))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1152, 1149])).
% 0.72/0.92 tff(1154,plain,
% 0.72/0.92 (~c1_1(a1)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1153, 1142])).
% 0.72/0.92 tff(1155,plain,
% 0.72/0.92 (((~hskp0) | c0_1(a1)) <=> ((~hskp0) | c0_1(a1))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1156,axiom,((~hskp0) | c0_1(a1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.72/0.92 tff(1157,plain,
% 0.72/0.92 ((~hskp0) | c0_1(a1)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1156, 1155])).
% 0.72/0.92 tff(1158,plain,
% 0.72/0.92 ((~hskp0) | c0_1(a1)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1157, 1155])).
% 0.72/0.92 tff(1159,plain,
% 0.72/0.92 ((~hskp0) | c0_1(a1)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1158, 1155])).
% 0.72/0.92 tff(1160,plain,
% 0.72/0.92 ((~hskp0) | c0_1(a1)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1159, 1155])).
% 0.72/0.92 tff(1161,plain,
% 0.72/0.92 ((~hskp0) | c0_1(a1)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1160, 1155])).
% 0.72/0.92 tff(1162,plain,
% 0.72/0.92 (c0_1(a1)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1161, 1142])).
% 0.72/0.92 tff(1163,plain,
% 0.72/0.92 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | c1_1(a1) | c2_1(a1) | (~ndr1_0) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c1_1(a1) | c2_1(a1) | (~ndr1_0) | (~c0_1(a1)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1164,plain,
% 0.72/0.92 ((hskp30 | hskp23 | (~ndr1_0) | c2_1(a1) | c1_1(a1) | (~c0_1(a1))) <=> (hskp30 | hskp23 | c1_1(a1) | c2_1(a1) | (~ndr1_0) | (~c0_1(a1)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1165,plain,
% 0.72/0.92 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a1) | c1_1(a1) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | c1_1(a1) | c2_1(a1) | (~ndr1_0) | (~c0_1(a1))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1164])).
% 0.72/0.92 tff(1166,plain,
% 0.72/0.92 (((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a1) | c1_1(a1) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c1_1(a1) | c2_1(a1) | (~ndr1_0) | (~c0_1(a1)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1165, 1163])).
% 0.72/0.92 tff(1167,plain,
% 0.72/0.92 ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp30 | hskp23 | (~ndr1_0) | c2_1(a1) | c1_1(a1) | (~c0_1(a1)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1168,plain,
% 0.72/0.92 ((~![U: $i] : (hskp30 | hskp23 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp30 | hskp23 | c1_1(a1) | c2_1(a1) | (~ndr1_0) | (~c0_1(a1))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 0.72/0.92 tff(1169,plain,
% 0.72/0.92 (hskp23),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1168, 108, 1, 1162, 1154, 1148, 748])).
% 0.72/0.92 tff(1170,plain,
% 0.72/0.92 (~c3_1(a42)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[762, 1169])).
% 0.72/0.92 tff(1171,plain,
% 0.72/0.92 (~c1_1(a42)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[768, 1169])).
% 0.72/0.92 tff(1172,plain,
% 0.72/0.92 (c1_1(a29)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[124, 1120])).
% 0.72/0.92 tff(1173,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c1_1(a42) | c3_1(a42) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c2_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a42) | c3_1(a42) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c2_1(a42)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1174,plain,
% 0.72/0.92 ((hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42))) <=> (hskp9 | c1_1(a42) | c3_1(a42) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c2_1(a42)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1175,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | c1_1(a42) | c3_1(a42) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c2_1(a42))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1174])).
% 0.72/0.92 tff(1176,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a42) | c3_1(a42) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c2_1(a42)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1175, 1173])).
% 0.72/0.92 tff(1177,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1178,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp9 | c1_1(a42) | c3_1(a42) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | (~c2_1(a42))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 0.72/0.92 tff(1179,plain,
% 0.72/0.92 (~c2_1(a42)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1178, 108, 1124, 1172, 1171, 1170, 1122, 1121, 483])).
% 0.72/0.92 tff(1180,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a42) | c3_1(a42) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | c2_1(a42))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a42) | c3_1(a42) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | c2_1(a42))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1181,plain,
% 0.72/0.92 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a42) | c1_1(a42) | c2_1(a42)) <=> (hskp8 | c1_1(a42) | c3_1(a42) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | c2_1(a42))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1182,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a42) | c1_1(a42) | c2_1(a42))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a42) | c3_1(a42) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | c2_1(a42)))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1181])).
% 0.72/0.92 tff(1183,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a42) | c1_1(a42) | c2_1(a42))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a42) | c3_1(a42) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | c2_1(a42))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1182, 1180])).
% 0.72/0.92 tff(1184,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a42) | c1_1(a42) | c2_1(a42))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1185,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a42) | c3_1(a42) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | c2_1(a42)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 0.72/0.92 tff(1186,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1185, 108, 294, 1116, 1115, 1171, 1170, 1114, 31, 1179])).
% 0.72/0.92 tff(1187,plain,(c0_1(a5) | hskp30 | c1_1(a15) | c2_1(a15) | c2_1(a13) | c0_1(a13) | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(1188,plain,
% 0.72/0.92 (c0_1(a5)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1187, 472, 1, 473, 295, 244, 286])).
% 0.72/0.92 tff(1189,plain,
% 0.72/0.92 (((~hskp2) | (~c0_1(a5))) <=> ((~hskp2) | (~c0_1(a5)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1190,plain,
% 0.72/0.92 (((~c0_1(a5)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a5)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1191,axiom,((~c0_1(a5)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.72/0.92 tff(1192,plain,
% 0.72/0.92 ((~hskp2) | (~c0_1(a5))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 0.72/0.92 tff(1193,plain,
% 0.72/0.92 ((~hskp2) | (~c0_1(a5))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1192, 1189])).
% 0.72/0.92 tff(1194,plain,
% 0.72/0.92 (~hskp2),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1193, 1188])).
% 0.72/0.92 tff(1195,plain,
% 0.72/0.92 (hskp13),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[716, 486, 602])).
% 0.72/0.92 tff(1196,plain,
% 0.72/0.92 (hskp10),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[704, 488, 486, 1, 487, 472, 473, 604])).
% 0.72/0.92 tff(1197,plain,
% 0.72/0.92 (hskp16),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[534, 1196, 487, 1])).
% 0.72/0.92 tff(1198,plain,
% 0.72/0.92 (~c1_1(a30)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[226, 1197])).
% 0.72/0.92 tff(1199,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[497, 1198, 1197, 487, 472, 473, 488])).
% 0.72/0.92 tff(1200,plain,(c3_1(a15) | hskp8 | c1_1(a15) | c2_1(a15) | hskp30 | hskp3 | (~hskp13)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(1201,plain,
% 0.72/0.92 (c3_1(a15)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1200, 486, 472, 473, 1, 294, 1195])).
% 0.72/0.92 tff(1202,plain,
% 0.72/0.92 (hskp10),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[880, 1201, 295, 1, 244, 473, 602, 286, 472, 486])).
% 0.72/0.92 tff(1203,plain,
% 0.72/0.92 (hskp16),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[534, 1202, 294, 1])).
% 0.72/0.92 tff(1204,plain,
% 0.72/0.92 (~c1_1(a30)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[226, 1203])).
% 0.72/0.92 tff(1205,plain,
% 0.72/0.92 (c2_1(a30)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[234, 1203])).
% 0.72/0.92 tff(1206,plain,
% 0.72/0.92 (c3_1(a30)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[242, 1203])).
% 0.72/0.92 tff(1207,plain,
% 0.72/0.92 (hskp10),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[880, 602, 295, 1, 244, 473, 837, 286, 472, 486])).
% 0.72/0.92 tff(1208,plain,
% 0.72/0.92 (~c0_1(a17)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[525, 1207])).
% 0.72/0.92 tff(1209,plain,
% 0.72/0.92 (c1_1(a17)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[512, 1207])).
% 0.72/0.92 tff(1210,plain,
% 0.72/0.92 (c3_1(a17)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[532, 108, 1, 294, 1209, 1208, 378])).
% 0.72/0.92 tff(1211,plain,
% 0.72/0.92 (~c2_1(a17)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[504, 1207])).
% 0.72/0.92 tff(1212,plain,
% 0.72/0.92 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a17) | c2_1(a17) | (~ndr1_0) | (~c3_1(a17)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a17) | c2_1(a17) | (~ndr1_0) | (~c3_1(a17)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1213,plain,
% 0.72/0.92 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a17) | c0_1(a17) | (~c3_1(a17))) <=> (hskp30 | hskp11 | c0_1(a17) | c2_1(a17) | (~ndr1_0) | (~c3_1(a17)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1214,plain,
% 0.72/0.92 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a17) | c0_1(a17) | (~c3_1(a17)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a17) | c2_1(a17) | (~ndr1_0) | (~c3_1(a17))))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[1213])).
% 0.72/0.93 tff(1215,plain,
% 0.72/0.93 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a17) | c0_1(a17) | (~c3_1(a17)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a17) | c2_1(a17) | (~ndr1_0) | (~c3_1(a17)))),
% 0.72/0.93 inference(transitivity,[status(thm)],[1214, 1212])).
% 0.72/0.93 tff(1216,plain,
% 0.72/0.93 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a17) | c0_1(a17) | (~c3_1(a17)))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(1217,plain,
% 0.72/0.93 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a17) | c2_1(a17) | (~ndr1_0) | (~c3_1(a17))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 0.72/0.93 tff(1218,plain,
% 0.72/0.93 (hskp11),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1217, 108, 1, 1208, 1211, 41, 1210])).
% 0.72/0.93 tff(1219,plain,
% 0.72/0.93 (~c3_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[325, 1218])).
% 0.72/0.93 tff(1220,plain,
% 0.72/0.93 (~c2_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[331, 1218])).
% 0.72/0.93 tff(1221,plain,
% 0.72/0.93 (c1_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[338, 108, 294, 303, 302, 301, 1220, 1219, 31])).
% 0.72/0.93 tff(1222,plain,
% 0.72/0.93 (c0_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[356, 1218])).
% 0.72/0.93 tff(1223,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[647, 108, 486, 836, 1222, 835, 840, 1220, 396, 1221])).
% 0.72/0.93 tff(1224,plain,(hskp2 | hskp3 | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a30) | hskp30 | c2_1(a13) | c0_1(a13) | c2_1(a15) | (~c3_1(a15)) | c1_1(a13) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1225,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1224, 1206, 1205, 602, 486, 1204, 1, 295, 244, 473, 1201, 286, 472])).
% 0.72/0.93 tff(1226,plain,(hskp3 | hskp2 | hskp30 | c2_1(a13) | c0_1(a13) | c2_1(a15) | c1_1(a13) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1227,plain,
% 0.72/0.93 (hskp3),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1226, 1194, 1, 295, 244, 473, 286, 472])).
% 0.72/0.93 tff(1228,plain,
% 0.72/0.93 (~c2_1(a6)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[448, 1227])).
% 0.72/0.93 tff(1229,plain,
% 0.72/0.93 (c3_1(a6)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[411, 1227])).
% 0.72/0.93 tff(1230,plain,
% 0.72/0.93 (c0_1(a6)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[419, 1227])).
% 0.72/0.93 tff(1231,plain,
% 0.72/0.93 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(1232,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[1231])).
% 0.72/0.93 tff(1233,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1234,plain,
% 0.72/0.93 (^[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)) | 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)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | 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(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_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))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_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)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_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) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(1235,plain,
% 0.72/0.93 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[1234])).
% 0.72/0.93 tff(1236,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 0.72/0.93 tff(1237,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 0.72/0.93 tff(1238,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1237, 1233])).
% 0.72/0.93 tff(1239,plain,(
% 0.72/0.93 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.93 inference(skolemize,[status(sab)],[1238])).
% 0.72/0.93 tff(1240,plain,
% 0.72/0.93 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1239, 1232])).
% 0.72/0.93 tff(1241,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1242,plain,
% 0.72/0.93 ((hskp2 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | c0_1(a39)) <=> (hskp2 | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1243,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | c0_1(a39))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39)))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[1242])).
% 0.72/0.93 tff(1244,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | c0_1(a39))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39))),
% 0.72/0.93 inference(transitivity,[status(thm)],[1243, 1241])).
% 0.72/0.93 tff(1245,plain,
% 0.72/0.93 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)) | c3_1(a39) | c1_1(a39) | c0_1(a39))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(1246,plain,
% 0.72/0.93 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a39) | c3_1(a39) | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c1_1(a39)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 0.72/0.93 tff(1247,plain,
% 0.72/0.93 (c1_1(a39)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1246, 108, 602, 1007, 1017, 1006, 1005, 1004, 1240])).
% 0.72/0.93 tff(1248,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1023, 108, 1, 487, 1017, 1006, 378, 1247])).
% 0.72/0.93 tff(1249,plain,(hskp16 | hskp30 | hskp8 | hskp2 | (~c0_1(a6)) | (~c3_1(a6)) | c2_1(a6)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1250,plain,
% 0.72/0.93 (hskp16),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1249, 1194, 294, 1, 1230, 1229, 1228])).
% 0.72/0.93 tff(1251,plain,
% 0.72/0.93 (~c1_1(a30)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[226, 1250])).
% 0.72/0.93 tff(1252,plain,
% 0.72/0.93 (c2_1(a30)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[234, 1250])).
% 0.72/0.93 tff(1253,plain,
% 0.72/0.93 (c3_1(a30)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[242, 1250])).
% 0.72/0.93 tff(1254,plain,
% 0.72/0.93 (c3_1(a13)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[311, 1253, 1252, 286, 295, 1251])).
% 0.72/0.93 tff(1255,plain,
% 0.72/0.93 (hskp11),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[319, 1254, 1, 295])).
% 0.72/0.93 tff(1256,plain,
% 0.72/0.93 (~c3_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[325, 1255])).
% 0.72/0.93 tff(1257,plain,
% 0.72/0.93 (~c2_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[331, 1255])).
% 0.72/0.93 tff(1258,plain,
% 0.72/0.93 (c1_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[338, 108, 294, 1252, 1253, 1251, 1257, 1256, 31])).
% 0.72/0.93 tff(1259,plain,
% 0.72/0.93 (c0_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[356, 1255])).
% 0.72/0.93 tff(1260,plain,
% 0.72/0.93 (hskp15 | (~c1_1(a21))),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[363, 108, 1252, 1253, 1259, 1251, 1257, 349])).
% 0.72/0.93 tff(1261,plain,
% 0.72/0.93 (hskp15),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1260, 1258])).
% 0.72/0.93 tff(1262,plain,
% 0.72/0.93 (c1_1(a29)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[124, 1261])).
% 0.72/0.93 tff(1263,plain,
% 0.72/0.93 (~c3_1(a29)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[130, 1261])).
% 0.72/0.93 tff(1264,plain,
% 0.72/0.93 (~c2_1(a29)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[136, 1261])).
% 0.72/0.93 tff(1265,plain,
% 0.72/0.93 (c0_1(a29)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[384, 108, 1, 294, 1262, 1263, 378])).
% 0.72/0.93 tff(1266,plain,
% 0.72/0.93 (~hskp21),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[159, 1265, 1264, 1263, 1262])).
% 0.72/0.93 tff(1267,plain,
% 0.72/0.93 (hskp21 | (~c0_1(a30))),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[431, 108, 294, 1253, 1251, 21])).
% 0.72/0.93 tff(1268,plain,
% 0.72/0.93 (~c0_1(a30)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1267, 1266])).
% 0.72/0.93 tff(1269,plain,
% 0.72/0.93 (hskp21 | c1_1(a6)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[423, 108, 294, 1230, 1229, 21])).
% 0.72/0.93 tff(1270,plain,
% 0.72/0.93 (c1_1(a6)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1269, 1266])).
% 0.72/0.93 tff(1271,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[455, 108, 1252, 1253, 286, 295, 1229, 244, 1228, 443, 1270, 1268])).
% 0.72/0.93 tff(1272,plain,(c1_1(a15) | c1_1(a13) | c2_1(a13) | c0_1(a13) | hskp30 | c2_1(a15)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1273,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1272, 471, 465, 295, 244, 1, 286])).
% 0.72/0.93 tff(1274,plain,((~hskp9) | c2_1(a13) | c0_1(a13) | hskp30 | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1275,plain,
% 0.72/0.93 (~hskp9),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1274, 295, 244, 1, 286])).
% 0.72/0.93 tff(1276,assumption,(hskp3), introduced(assumption)).
% 0.72/0.93 tff(1277,plain,
% 0.72/0.93 (~c2_1(a6)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[448, 1276])).
% 0.72/0.93 tff(1278,plain,
% 0.72/0.93 (c0_1(a6)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[419, 1276])).
% 0.72/0.93 tff(1279,plain,
% 0.72/0.93 (c3_1(a6)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[411, 1276])).
% 0.72/0.93 tff(1280,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1025, 1279, 1278, 487, 1, 1009, 43, 1277])).
% 0.72/0.93 tff(1281,plain,((~hskp3) | hskp8 | hskp30 | hskp9 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1282,plain,
% 0.72/0.93 (~hskp3),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1281, 1275, 1, 458, 294])).
% 0.72/0.93 tff(1283,assumption,(~hskp11), introduced(assumption)).
% 0.72/0.93 tff(1284,assumption,(~c0_1(a26)), introduced(assumption)).
% 0.72/0.93 tff(1285,assumption,(c3_1(a26)), introduced(assumption)).
% 0.72/0.93 tff(1286,plain,
% 0.72/0.93 (hskp11 | c2_1(a26)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[637, 108, 1, 1285, 1284, 41])).
% 0.72/0.93 tff(1287,plain,
% 0.72/0.93 (c2_1(a26)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1286, 1283])).
% 0.72/0.93 tff(1288,plain,
% 0.72/0.93 (~c3_1(a13)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[319, 1283, 1, 295])).
% 0.72/0.93 tff(1289,assumption,(~c1_1(a26)), introduced(assumption)).
% 0.72/0.93 tff(1290,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[878, 108, 294, 1285, 286, 295, 1289, 31, 1288, 1287])).
% 0.72/0.93 tff(1291,plain,(hskp11 | (~c3_1(a26)) | c1_1(a13) | c2_1(a13) | c1_1(a26) | hskp30 | c0_1(a26) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1292,plain,
% 0.72/0.93 (hskp11),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1291, 618, 286, 295, 610, 1, 631, 244])).
% 0.72/0.93 tff(1293,plain,
% 0.72/0.93 (~c2_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[331, 1292])).
% 0.72/0.93 tff(1294,plain,
% 0.72/0.93 (c0_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[356, 1292])).
% 0.72/0.93 tff(1295,plain,
% 0.72/0.93 (~c1_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[647, 108, 1282, 618, 1294, 631, 610, 1293, 396])).
% 0.72/0.93 tff(1296,plain,
% 0.72/0.93 (~c3_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[325, 1292])).
% 0.72/0.93 tff(1297,plain,
% 0.72/0.93 (hskp24),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[675, 108, 1282, 1294, 1293, 1296, 669])).
% 0.72/0.93 tff(1298,plain,
% 0.72/0.93 (~c2_1(a52)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[681, 1297])).
% 0.72/0.93 tff(1299,plain,
% 0.72/0.93 (~c0_1(a52)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[687, 1297])).
% 0.72/0.93 tff(1300,plain,
% 0.72/0.93 (c3_1(a52)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[695, 1297])).
% 0.72/0.93 tff(1301,plain,
% 0.72/0.93 (~hskp10),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[534, 458, 294, 1])).
% 0.72/0.93 tff(1302,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[702, 108, 1301, 1300, 1294, 1299, 1298, 1296, 658, 1295])).
% 0.72/0.93 tff(1303,plain,((~hskp13) | c1_1(a13) | c2_1(a13) | hskp30 | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1304,plain,
% 0.72/0.93 (~hskp13),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1303, 295, 286, 1, 244])).
% 0.72/0.93 tff(1305,plain,
% 0.72/0.93 (hskp2),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[716, 1304, 1282])).
% 0.72/0.93 tff(1306,plain,
% 0.72/0.93 (~c0_1(a5)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1193, 1305])).
% 0.72/0.93 tff(1307,plain,
% 0.72/0.93 (c2_1(a5)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[600, 1305])).
% 0.72/0.93 tff(1308,plain,
% 0.72/0.93 (hskp15 | c3_1(a5)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[550, 108, 458, 1307, 1306, 53])).
% 0.72/0.93 tff(1309,plain,
% 0.72/0.93 (c3_1(a5)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1308, 74])).
% 0.72/0.93 tff(1310,plain,
% 0.72/0.93 (~c1_1(a5)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1074, 1305])).
% 0.72/0.93 tff(1311,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c3_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c3_1(a13))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1312,plain,
% 0.72/0.93 ((hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a13) | c1_1(a13) | c2_1(a13)) <=> (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c3_1(a13))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1313,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c3_1(a13)))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[1312])).
% 0.72/0.93 tff(1314,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c3_1(a13))),
% 0.72/0.93 inference(transitivity,[status(thm)],[1313, 1311])).
% 0.72/0.93 tff(1315,plain,
% 0.72/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)) | c3_1(a13) | c1_1(a13) | c2_1(a13))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(1316,plain,
% 0.72/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a13) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | c3_1(a13)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 0.72/0.93 tff(1317,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1316, 108, 294, 286, 295, 536, 485, 31, 300, 1058])).
% 0.72/0.93 tff(1318,plain,(c3_1(a13) | c1_1(a13) | c2_1(a13) | (~c2_1(a5)) | c1_1(a5) | (~c3_1(a5))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1319,plain,
% 0.72/0.93 (c3_1(a13)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1318, 1309, 295, 1307, 1310, 286])).
% 0.72/0.93 tff(1320,plain,
% 0.72/0.93 (hskp11),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[319, 1319, 1, 295])).
% 0.72/0.93 tff(1321,plain,
% 0.72/0.93 (~c3_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[325, 1320])).
% 0.72/0.93 tff(1322,plain,
% 0.72/0.93 (~c2_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[331, 1320])).
% 0.72/0.93 tff(1323,plain,
% 0.72/0.93 (c1_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[917, 108, 294, 1307, 1322, 1321, 1310, 31, 1309])).
% 0.72/0.93 tff(1324,plain,
% 0.72/0.93 (^[U: $i] : refl((hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(1325,plain,
% 0.72/0.93 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[1324])).
% 0.72/0.93 tff(1326,plain,
% 0.72/0.93 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1327,plain,
% 0.72/0.93 (^[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)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp3) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp3))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) | hskp3) <=> (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp3) <=> (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 0.72/0.93 inference(bind,[status(th)],[])).
% 0.72/0.93 tff(1328,plain,
% 0.72/0.93 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp3) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.72/0.93 inference(quant_intro,[status(thm)],[1327])).
% 0.72/0.93 tff(1329,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp25) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.72/0.93 tff(1330,plain,
% 0.72/0.93 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 0.72/0.93 tff(1331,plain,
% 0.72/0.93 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1330, 1326])).
% 0.72/0.93 tff(1332,plain,(
% 0.72/0.93 ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.72/0.93 inference(skolemize,[status(sab)],[1331])).
% 0.72/0.93 tff(1333,plain,
% 0.72/0.93 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1332, 1325])).
% 0.72/0.93 tff(1334,plain,
% 0.72/0.93 (~hskp21),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[116, 74, 458])).
% 0.72/0.93 tff(1335,assumption,(hskp25), introduced(assumption)).
% 0.72/0.93 tff(1336,plain,
% 0.72/0.93 (((~hskp25) | (~c1_1(a54))) <=> ((~hskp25) | (~c1_1(a54)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1337,plain,
% 0.72/0.93 (((~c1_1(a54)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a54)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1338,axiom,((~c1_1(a54)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.72/0.93 tff(1339,plain,
% 0.72/0.93 ((~hskp25) | (~c1_1(a54))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 0.72/0.93 tff(1340,plain,
% 0.72/0.93 ((~hskp25) | (~c1_1(a54))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1339, 1336])).
% 0.72/0.93 tff(1341,plain,
% 0.72/0.93 (~c1_1(a54)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1340, 1335])).
% 0.72/0.93 tff(1342,plain,
% 0.72/0.93 (((~hskp25) | c3_1(a54)) <=> ((~hskp25) | c3_1(a54))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1343,axiom,((~hskp25) | c3_1(a54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.72/0.93 tff(1344,plain,
% 0.72/0.93 ((~hskp25) | c3_1(a54)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 0.72/0.93 tff(1345,plain,
% 0.72/0.93 ((~hskp25) | c3_1(a54)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1344, 1342])).
% 0.72/0.93 tff(1346,plain,
% 0.72/0.93 ((~hskp25) | c3_1(a54)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1345, 1342])).
% 0.72/0.93 tff(1347,plain,
% 0.72/0.93 ((~hskp25) | c3_1(a54)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1346, 1342])).
% 0.72/0.93 tff(1348,plain,
% 0.72/0.93 ((~hskp25) | c3_1(a54)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1347, 1342])).
% 0.72/0.93 tff(1349,plain,
% 0.72/0.93 (c3_1(a54)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1348, 1335])).
% 0.72/0.93 tff(1350,plain,
% 0.72/0.93 (((~hskp25) | c0_1(a54)) <=> ((~hskp25) | c0_1(a54))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1351,axiom,((~hskp25) | c0_1(a54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.72/0.93 tff(1352,plain,
% 0.72/0.93 ((~hskp25) | c0_1(a54)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 0.72/0.93 tff(1353,plain,
% 0.72/0.93 ((~hskp25) | c0_1(a54)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1352, 1350])).
% 0.72/0.93 tff(1354,plain,
% 0.72/0.93 ((~hskp25) | c0_1(a54)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1353, 1350])).
% 0.72/0.93 tff(1355,plain,
% 0.72/0.93 ((~hskp25) | c0_1(a54)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1354, 1350])).
% 0.72/0.93 tff(1356,plain,
% 0.72/0.93 ((~hskp25) | c0_1(a54)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1355, 1350])).
% 0.72/0.93 tff(1357,plain,
% 0.72/0.93 (c0_1(a54)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1356, 1335])).
% 0.72/0.93 tff(1358,assumption,(~hskp21), introduced(assumption)).
% 0.72/0.93 tff(1359,plain,
% 0.72/0.93 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a54) | (~ndr1_0) | (~c0_1(a54)) | (~c3_1(a54)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a54) | (~ndr1_0) | (~c0_1(a54)) | (~c3_1(a54)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1360,plain,
% 0.72/0.93 ((hskp21 | hskp8 | (~ndr1_0) | c1_1(a54) | (~c3_1(a54)) | (~c0_1(a54))) <=> (hskp21 | hskp8 | c1_1(a54) | (~ndr1_0) | (~c0_1(a54)) | (~c3_1(a54)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1361,plain,
% 0.72/0.93 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a54) | (~c3_1(a54)) | (~c0_1(a54)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a54) | (~ndr1_0) | (~c0_1(a54)) | (~c3_1(a54))))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[1360])).
% 0.72/0.93 tff(1362,plain,
% 0.72/0.93 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a54) | (~c3_1(a54)) | (~c0_1(a54)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a54) | (~ndr1_0) | (~c0_1(a54)) | (~c3_1(a54)))),
% 0.72/0.93 inference(transitivity,[status(thm)],[1361, 1359])).
% 0.72/0.93 tff(1363,plain,
% 0.72/0.93 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a54) | (~c3_1(a54)) | (~c0_1(a54)))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(1364,plain,
% 0.72/0.93 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a54) | (~ndr1_0) | (~c0_1(a54)) | (~c3_1(a54))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1363, 1362])).
% 0.72/0.93 tff(1365,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1364, 108, 1358, 487, 1357, 1349, 1341, 21])).
% 0.72/0.93 tff(1366,plain,((~hskp25) | hskp21 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1367,plain,
% 0.72/0.93 (~hskp25),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1366, 1334, 294])).
% 0.72/0.93 tff(1368,plain,
% 0.72/0.93 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1369,plain,
% 0.72/0.93 ((hskp25 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c1_1(a21))) <=> (hskp25 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1370,plain,
% 0.72/0.93 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c1_1(a21)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c1_1(a21))))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[1369])).
% 0.72/0.93 tff(1371,plain,
% 0.72/0.93 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c1_1(a21)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)))),
% 0.72/0.93 inference(transitivity,[status(thm)],[1370, 1368])).
% 0.72/0.93 tff(1372,plain,
% 0.72/0.93 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a21) | c3_1(a21) | (~c1_1(a21)))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(1373,plain,
% 0.72/0.93 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp3 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c1_1(a21))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1372, 1371])).
% 0.72/0.93 tff(1374,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1373, 108, 1367, 1282, 1322, 1321, 1333, 1323])).
% 0.72/0.93 tff(1375,plain,(hskp15 | hskp30 | c2_1(a13) | c0_1(a13) | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1376,plain,
% 0.72/0.93 (hskp15),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1375, 295, 1, 244, 286])).
% 0.72/0.93 tff(1377,plain,
% 0.72/0.93 (~c2_1(a29)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[136, 1376])).
% 0.72/0.93 tff(1378,plain,
% 0.72/0.93 (~c3_1(a29)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[130, 1376])).
% 0.72/0.93 tff(1379,plain,
% 0.72/0.93 (hskp15),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[116, 42, 43])).
% 0.72/0.93 tff(1380,plain,
% 0.72/0.93 (c1_1(a29)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[124, 1379])).
% 0.72/0.93 tff(1381,plain,
% 0.72/0.93 (c0_1(a29)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[934, 1380])).
% 0.72/0.93 tff(1382,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[159, 1381, 1380, 150, 149, 42])).
% 0.72/0.93 tff(1383,plain,((~hskp21) | c2_1(a29) | c3_1(a29) | hskp30 | hskp8 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1384,plain,
% 0.72/0.93 (~hskp21),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1383, 149, 43, 1, 487, 150])).
% 0.72/0.93 tff(1385,plain,
% 0.72/0.93 (~hskp25),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1366, 1384, 487])).
% 0.72/0.93 tff(1386,plain,
% 0.72/0.93 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp3 | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1387,plain,
% 0.72/0.93 ((hskp25 | hskp3 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29))) <=> (hskp25 | hskp3 | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1388,plain,
% 0.72/0.93 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29))))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[1387])).
% 0.72/0.93 tff(1389,plain,
% 0.72/0.93 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp3 | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29)))),
% 0.72/0.93 inference(transitivity,[status(thm)],[1388, 1386])).
% 0.72/0.93 tff(1390,plain,
% 0.72/0.93 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c2_1(a29) | c3_1(a29) | (~c1_1(a29)))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(1391,plain,
% 0.72/0.93 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp25 | hskp3 | c2_1(a29) | c3_1(a29) | (~ndr1_0) | (~c1_1(a29))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1390, 1389])).
% 0.72/0.93 tff(1392,plain,
% 0.72/0.93 (hskp25 | hskp3 | c3_1(a29) | (~c1_1(a29))),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1391, 108, 150, 1333])).
% 0.72/0.93 tff(1393,plain,
% 0.72/0.93 (~c1_1(a29)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1392, 486, 1385, 149])).
% 0.72/0.93 tff(1394,plain,
% 0.72/0.93 (~c2_1(a26)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[931, 108, 487, 947, 618, 150, 149, 610, 31])).
% 0.72/0.93 tff(1395,plain,
% 0.72/0.93 (hskp11),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[638, 1394])).
% 0.72/0.93 tff(1396,plain,
% 0.72/0.93 (~c2_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[331, 1395])).
% 0.72/0.93 tff(1397,plain,
% 0.72/0.93 (c0_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[356, 1395])).
% 0.72/0.93 tff(1398,plain,
% 0.72/0.93 (~c1_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[647, 108, 486, 618, 1397, 631, 610, 1396, 396])).
% 0.72/0.93 tff(1399,plain,
% 0.72/0.93 (~c3_1(a21)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[325, 1395])).
% 0.72/0.93 tff(1400,plain,
% 0.72/0.93 (hskp24),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[675, 108, 486, 1397, 1396, 1399, 669])).
% 0.72/0.93 tff(1401,plain,
% 0.72/0.93 (~c2_1(a52)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[681, 1400])).
% 0.72/0.93 tff(1402,plain,
% 0.72/0.93 (~c0_1(a52)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[687, 1400])).
% 0.72/0.93 tff(1403,plain,
% 0.72/0.93 (c3_1(a52)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[695, 1400])).
% 0.72/0.93 tff(1404,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[702, 108, 603, 1403, 1397, 1402, 1401, 1399, 658, 1398])).
% 0.72/0.93 tff(1405,plain,((~hskp13) | hskp10 | hskp3 | hskp30 | hskp8 | c1_1(a29) | c2_1(a29) | c3_1(a29)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1406,plain,
% 0.72/0.93 (~hskp13),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1405, 486, 923, 1, 487, 1393, 150, 149])).
% 0.72/0.93 tff(1407,plain,
% 0.72/0.93 (hskp2),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[716, 1406, 486])).
% 0.72/0.93 tff(1408,plain,
% 0.72/0.93 (~c0_1(a5)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1193, 1407])).
% 0.72/0.93 tff(1409,plain,
% 0.72/0.93 (c2_1(a5)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[600, 1407])).
% 0.72/0.93 tff(1410,plain,
% 0.72/0.93 (~c1_1(a5)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1074, 1407])).
% 0.72/0.93 tff(1411,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[958, 1410, 1409, 43, 150, 487, 1393, 149, 1408])).
% 0.72/0.93 tff(1412,plain,(hskp3 | hskp16 | c2_1(a29) | hskp8 | c3_1(a29) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1413,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1412, 1378, 1377, 1282, 294, 458, 1])).
% 0.72/0.93 tff(1414,plain,(c2_1(a13) | hskp30 | c0_1(a13) | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1415,plain,
% 0.72/0.93 (c2_1(a13)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1414, 286, 244, 1])).
% 0.72/0.93 tff(1416,plain,
% 0.72/0.93 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1417,plain,
% 0.72/0.93 ((hskp16 | hskp15 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13))) <=> (hskp16 | hskp15 | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1418,plain,
% 0.72/0.93 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13))))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[1417])).
% 0.72/0.93 tff(1419,plain,
% 0.72/0.93 (((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)))) <=> ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)))),
% 0.72/0.93 inference(transitivity,[status(thm)],[1418, 1416])).
% 0.72/0.93 tff(1420,plain,
% 0.72/0.93 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp16 | hskp15 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(1421,plain,
% 0.72/0.93 ((~![U: $i] : (hskp16 | hskp15 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp16 | hskp15 | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 0.72/0.93 tff(1422,plain,
% 0.72/0.93 (hskp16 | hskp15 | c3_1(a13) | (~c2_1(a13))),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1421, 108, 244, 53])).
% 0.72/0.93 tff(1423,plain,
% 0.72/0.93 (c3_1(a13)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1422, 74, 1415, 43])).
% 0.72/0.93 tff(1424,assumption,(hskp24), introduced(assumption)).
% 0.72/0.93 tff(1425,plain,
% 0.72/0.93 (~c2_1(a52)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[681, 1424])).
% 0.72/0.93 tff(1426,plain,
% 0.72/0.93 (~c0_1(a52)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[687, 1424])).
% 0.72/0.93 tff(1427,plain,
% 0.72/0.93 (c3_1(a52)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[695, 1424])).
% 0.72/0.93 tff(1428,plain,
% 0.72/0.93 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a52) | c2_1(a52) | (~ndr1_0) | (~c3_1(a52)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a52) | c2_1(a52) | (~ndr1_0) | (~c3_1(a52)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1429,plain,
% 0.78/0.94 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a52) | c0_1(a52) | (~c3_1(a52))) <=> (hskp30 | hskp11 | c0_1(a52) | c2_1(a52) | (~ndr1_0) | (~c3_1(a52)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1430,plain,
% 0.78/0.94 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a52) | c0_1(a52) | (~c3_1(a52)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a52) | c2_1(a52) | (~ndr1_0) | (~c3_1(a52))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1429])).
% 0.78/0.94 tff(1431,plain,
% 0.78/0.94 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a52) | c0_1(a52) | (~c3_1(a52)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a52) | c2_1(a52) | (~ndr1_0) | (~c3_1(a52)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1430, 1428])).
% 0.78/0.94 tff(1432,plain,
% 0.78/0.94 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a52) | c0_1(a52) | (~c3_1(a52)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1433,plain,
% 0.78/0.94 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a52) | c2_1(a52) | (~ndr1_0) | (~c3_1(a52))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 0.78/0.94 tff(1434,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1433, 108, 1, 1283, 1427, 1426, 1425, 41])).
% 0.78/0.94 tff(1435,plain,((~hskp24) | hskp30 | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1436,plain,
% 0.78/0.94 (~hskp24),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1435, 1283, 1])).
% 0.78/0.94 tff(1437,plain,
% 0.78/0.94 ((hskp24 | hskp21 | hskp5) <=> (hskp24 | hskp21 | hskp5)),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1438,plain,
% 0.78/0.94 (((hskp21 | hskp24) | hskp5) <=> (hskp24 | hskp21 | hskp5)),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1439,axiom,((hskp21 | hskp24) | hskp5), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.78/0.94 tff(1440,plain,
% 0.78/0.94 (hskp24 | hskp21 | hskp5),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 0.78/0.94 tff(1441,plain,
% 0.78/0.94 (hskp24 | hskp21 | hskp5),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1440, 1437])).
% 0.78/0.94 tff(1442,plain,
% 0.78/0.94 (hskp24 | hskp21 | hskp5),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1441, 1437])).
% 0.78/0.94 tff(1443,plain,
% 0.78/0.94 (hskp24 | hskp21 | hskp5),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1442, 1437])).
% 0.78/0.94 tff(1444,plain,
% 0.78/0.94 (hskp24 | hskp21 | hskp5),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1443, 1437])).
% 0.78/0.94 tff(1445,plain,
% 0.78/0.94 (hskp5),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1444, 1436, 1358])).
% 0.78/0.94 tff(1446,plain,
% 0.78/0.94 (((~hskp5) | (~c2_1(a9))) <=> ((~hskp5) | (~c2_1(a9)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1447,plain,
% 0.78/0.94 (((~c2_1(a9)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a9)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1448,axiom,((~c2_1(a9)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.78/0.94 tff(1449,plain,
% 0.78/0.94 ((~hskp5) | (~c2_1(a9))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 0.78/0.94 tff(1450,plain,
% 0.78/0.94 ((~hskp5) | (~c2_1(a9))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1449, 1446])).
% 0.78/0.94 tff(1451,plain,
% 0.78/0.94 (~c2_1(a9)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1450, 1445])).
% 0.78/0.94 tff(1452,plain,
% 0.78/0.94 (((~hskp5) | (~c0_1(a9))) <=> ((~hskp5) | (~c0_1(a9)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1453,plain,
% 0.78/0.94 (((~c0_1(a9)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a9)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1454,axiom,((~c0_1(a9)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.78/0.94 tff(1455,plain,
% 0.78/0.94 ((~hskp5) | (~c0_1(a9))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 0.78/0.94 tff(1456,plain,
% 0.78/0.94 ((~hskp5) | (~c0_1(a9))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1455, 1452])).
% 0.78/0.94 tff(1457,plain,
% 0.78/0.94 (~c0_1(a9)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1456, 1445])).
% 0.78/0.94 tff(1458,plain,
% 0.78/0.94 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c3_1(a9)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c3_1(a9)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1459,plain,
% 0.78/0.94 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a9) | c0_1(a9) | (~c3_1(a9))) <=> (hskp30 | hskp11 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c3_1(a9)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1460,plain,
% 0.78/0.94 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a9) | c0_1(a9) | (~c3_1(a9)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c3_1(a9))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1459])).
% 0.78/0.94 tff(1461,plain,
% 0.78/0.94 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a9) | c0_1(a9) | (~c3_1(a9)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c3_1(a9)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1460, 1458])).
% 0.78/0.94 tff(1462,plain,
% 0.78/0.94 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a9) | c0_1(a9) | (~c3_1(a9)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1463,plain,
% 0.78/0.94 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c3_1(a9))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 0.78/0.94 tff(1464,plain,
% 0.78/0.94 (~c3_1(a9)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1463, 108, 1, 1283, 1457, 1451, 41])).
% 0.78/0.94 tff(1465,assumption,(c3_1(a13)), introduced(assumption)).
% 0.78/0.94 tff(1466,plain,
% 0.78/0.94 (((~hskp5) | (~c1_1(a9))) <=> ((~hskp5) | (~c1_1(a9)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1467,plain,
% 0.78/0.94 (((~c1_1(a9)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a9)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1468,axiom,((~c1_1(a9)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.78/0.94 tff(1469,plain,
% 0.78/0.94 ((~hskp5) | (~c1_1(a9))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 0.78/0.94 tff(1470,plain,
% 0.78/0.94 ((~hskp5) | (~c1_1(a9))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1469, 1466])).
% 0.78/0.94 tff(1471,plain,
% 0.78/0.94 (~c1_1(a9)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1470, 1445])).
% 0.78/0.94 tff(1472,assumption,(c2_1(a13)), introduced(assumption)).
% 0.78/0.94 tff(1473,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c3_1(a13)) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c3_1(a13)) | (~c2_1(a13)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1474,plain,
% 0.78/0.94 ((hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a9) | c1_1(a9) | c2_1(a9)) <=> (hskp8 | c1_1(a13) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c3_1(a13)) | (~c2_1(a13)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1475,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a9) | c1_1(a9) | c2_1(a9))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c3_1(a13)) | (~c2_1(a13))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1474])).
% 0.78/0.94 tff(1476,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a9) | c1_1(a9) | c2_1(a9))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c3_1(a13)) | (~c2_1(a13)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1475, 1473])).
% 0.78/0.94 tff(1477,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a9) | c1_1(a9) | c2_1(a9))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1478,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c3_1(a13)) | (~c2_1(a13))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1477, 1476])).
% 0.78/0.94 tff(1479,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1478, 108, 294, 286, 1472, 1471, 1451, 31, 1465, 1464])).
% 0.78/0.94 tff(1480,plain,(hskp11 | c1_1(a13) | (~c2_1(a13)) | (~c3_1(a13)) | hskp30 | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1481,plain,
% 0.78/0.94 (hskp11),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1480, 1423, 1415, 286, 1, 885])).
% 0.78/0.94 tff(1482,plain,
% 0.78/0.94 (~c2_1(a21)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[331, 1481])).
% 0.78/0.94 tff(1483,plain,
% 0.78/0.94 (c0_1(a21)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[356, 1481])).
% 0.78/0.94 tff(1484,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a13) | c2_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a13) | c2_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1485,plain,
% 0.78/0.94 ((hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13))) <=> (hskp15 | c1_1(a13) | c2_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1486,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a13) | c2_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1485])).
% 0.78/0.94 tff(1487,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a13) | c2_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1486, 1484])).
% 0.78/0.94 tff(1488,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1489,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a13) | c2_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 0.78/0.94 tff(1490,plain,
% 0.78/0.94 (~c1_1(a21)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1489, 108, 74, 1483, 286, 1415, 1482, 349, 1423])).
% 0.78/0.94 tff(1491,plain,
% 0.78/0.94 (~c3_1(a21)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[325, 1481])).
% 0.78/0.94 tff(1492,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1493,plain,
% 0.78/0.94 ((hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a21) | c1_1(a21) | c2_1(a21)) <=> (hskp8 | c1_1(a13) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1494,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a21) | c1_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a13) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21)))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1493])).
% 0.78/0.94 tff(1495,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a21) | c1_1(a21) | c2_1(a21))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1494, 1492])).
% 0.78/0.94 tff(1496,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c3_1(a21) | c1_1(a21) | c2_1(a21))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1497,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a13) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21)),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 0.78/0.94 tff(1498,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1497, 108, 294, 286, 1415, 1482, 1491, 31, 1423, 1490])).
% 0.78/0.94 tff(1499,plain,(hskp15 | c1_1(a13) | hskp30 | hskp16 | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1500,plain,
% 0.78/0.94 (hskp15),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1499, 43, 1, 286, 244])).
% 0.78/0.94 tff(1501,plain,
% 0.78/0.94 (~c2_1(a29)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[136, 1500])).
% 0.78/0.94 tff(1502,plain,
% 0.78/0.94 (~c3_1(a29)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[130, 1500])).
% 0.78/0.94 tff(1503,plain,
% 0.78/0.94 (hskp3),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1412, 1502, 1501, 294, 43, 1])).
% 0.78/0.94 tff(1504,plain,
% 0.78/0.94 (hskp9),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1281, 1503, 1, 43, 294])).
% 0.78/0.94 tff(1505,plain,
% 0.78/0.94 (~c3_1(a15)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[994, 1504])).
% 0.78/0.94 tff(1506,plain,
% 0.78/0.94 (~c2_1(a6)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[448, 1503])).
% 0.78/0.94 tff(1507,plain,
% 0.78/0.94 (c0_1(a6)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[419, 1503])).
% 0.78/0.94 tff(1508,plain,
% 0.78/0.94 (c3_1(a6)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[411, 1503])).
% 0.78/0.94 tff(1509,plain,
% 0.78/0.94 (hskp2),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1249, 1508, 294, 1, 43, 1507, 1506])).
% 0.78/0.94 tff(1510,plain,
% 0.78/0.94 (~c1_1(a5)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1074, 1509])).
% 0.78/0.94 tff(1511,plain,
% 0.78/0.94 (~c1_1(a15)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[464, 1504])).
% 0.78/0.94 tff(1512,plain,
% 0.78/0.94 (~c2_1(a15)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[470, 1504])).
% 0.78/0.94 tff(1513,plain,
% 0.78/0.94 (~c0_1(a5)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1193, 1509])).
% 0.78/0.94 tff(1514,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[831, 1513, 1512, 294, 1511, 1510, 1505, 1])).
% 0.78/0.94 tff(1515,plain,(hskp16 | hskp30 | c1_1(a13) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1516,plain,
% 0.78/0.94 (hskp16),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1515, 286, 1, 244])).
% 0.78/0.94 tff(1517,plain,
% 0.78/0.94 (~c1_1(a30)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[226, 1516])).
% 0.78/0.94 tff(1518,plain,
% 0.78/0.94 (c3_1(a30)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[242, 1516])).
% 0.78/0.94 tff(1519,plain,
% 0.78/0.94 (c2_1(a30)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[234, 1516])).
% 0.78/0.94 tff(1520,plain,
% 0.78/0.94 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(1521,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[1520])).
% 0.78/0.94 tff(1522,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1523,plain,
% 0.78/0.94 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.78/0.94 inference(bind,[status(th)],[])).
% 0.78/0.94 tff(1524,plain,
% 0.78/0.94 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.78/0.94 inference(quant_intro,[status(thm)],[1523])).
% 0.78/0.94 tff(1525,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.78/0.94 tff(1526,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1525, 1524])).
% 0.78/0.94 tff(1527,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1526, 1522])).
% 0.78/0.94 tff(1528,plain,(
% 0.78/0.94 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.78/0.94 inference(skolemize,[status(sab)],[1527])).
% 0.78/0.94 tff(1529,plain,
% 0.78/0.94 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1528, 1521])).
% 0.78/0.94 tff(1530,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1531,plain,
% 0.78/0.94 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13))) <=> (hskp8 | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1532,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1531])).
% 0.78/0.94 tff(1533,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1532, 1530])).
% 0.78/0.94 tff(1534,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1535,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 0.78/0.94 tff(1536,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1535, 108, 487, 303, 302, 1472, 301, 244, 1529, 300])).
% 0.78/0.94 tff(1537,plain,(c3_1(a13) | hskp8 | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a13)) | c1_1(a30) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1538,plain,
% 0.78/0.94 (c3_1(a13)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1537, 294, 1519, 1518, 1415, 1517, 244])).
% 0.78/0.94 tff(1539,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a39) | c3_1(a39) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a39)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a39) | c3_1(a39) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a39)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1540,plain,
% 0.78/0.94 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a39) | c0_1(a39) | (~c2_1(a39))) <=> (hskp8 | c0_1(a39) | c3_1(a39) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a39)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1541,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a39) | c0_1(a39) | (~c2_1(a39)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | c0_1(a39) | c3_1(a39) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a39))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1540])).
% 0.78/0.94 tff(1542,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a39) | c0_1(a39) | (~c2_1(a39)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a39) | c3_1(a39) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a39)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1541, 1539])).
% 0.78/0.94 tff(1543,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a39) | c0_1(a39) | (~c2_1(a39)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1544,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp8 | c0_1(a39) | c3_1(a39) | c1_1(a30) | (~ndr1_0) | (~c2_1(a30)) | (~c3_1(a30)) | (~c2_1(a39))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 0.78/0.94 tff(1545,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1544, 108, 487, 73, 303, 302, 65, 59, 301, 1529])).
% 0.78/0.94 tff(1546,plain,((~hskp21) | hskp8 | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a30)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1547,plain,
% 0.78/0.94 (~hskp21),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1546, 294, 1519, 1518, 1517])).
% 0.78/0.94 tff(1548,plain,
% 0.78/0.94 (hskp11),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1480, 1538, 1415, 286, 1, 1547])).
% 0.78/0.94 tff(1549,plain,
% 0.78/0.94 (~c3_1(a21)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[325, 1548])).
% 0.78/0.94 tff(1550,plain,
% 0.78/0.94 (~c2_1(a21)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[331, 1548])).
% 0.78/0.94 tff(1551,plain,
% 0.78/0.94 (c1_1(a21)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1497, 108, 294, 286, 1415, 1550, 1549, 31, 1538])).
% 0.78/0.94 tff(1552,plain,
% 0.78/0.94 (~hskp25),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1366, 1547, 294])).
% 0.78/0.94 tff(1553,plain,
% 0.78/0.94 (hskp3),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1373, 108, 1552, 1550, 1549, 1333, 1551])).
% 0.78/0.94 tff(1554,plain,
% 0.78/0.94 (c3_1(a6)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[411, 1553])).
% 0.78/0.94 tff(1555,plain,
% 0.78/0.94 (c0_1(a6)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[419, 1553])).
% 0.78/0.94 tff(1556,plain,
% 0.78/0.94 (c1_1(a6)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[423, 108, 1547, 294, 1555, 1554, 21])).
% 0.78/0.94 tff(1557,plain,
% 0.78/0.94 (c0_1(a21)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[356, 1548])).
% 0.78/0.94 tff(1558,plain,
% 0.78/0.94 (hskp15),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1489, 108, 1557, 286, 1415, 1550, 349, 1538, 1551])).
% 0.78/0.94 tff(1559,plain,
% 0.78/0.94 (~c3_1(a29)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[130, 1558])).
% 0.78/0.94 tff(1560,plain,
% 0.78/0.94 (c1_1(a29)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[124, 1558])).
% 0.78/0.94 tff(1561,plain,
% 0.78/0.94 (c0_1(a29)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[384, 108, 1, 294, 1560, 1559, 378])).
% 0.78/0.94 tff(1562,plain,
% 0.78/0.94 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(1563,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1562])).
% 0.78/0.95 tff(1564,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1565,plain,
% 0.78/0.95 (^[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))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_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))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(1566,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1565])).
% 0.78/0.95 tff(1567,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.78/0.95 tff(1568,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1567, 1566])).
% 0.78/0.95 tff(1569,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1568, 1564])).
% 0.78/0.95 tff(1570,plain,(
% 0.78/0.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(skolemize,[status(sab)],[1569])).
% 0.78/0.95 tff(1571,plain,
% 0.78/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1570, 1563])).
% 0.78/0.95 tff(1572,plain,
% 0.78/0.95 (~c2_1(a6)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[448, 1553])).
% 0.78/0.95 tff(1573,assumption,(c1_1(a6)), introduced(assumption)).
% 0.78/0.95 tff(1574,assumption,(~hskp24), introduced(assumption)).
% 0.78/0.95 tff(1575,plain,
% 0.78/0.95 (hskp5),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1444, 1574, 1358])).
% 0.78/0.95 tff(1576,plain,
% 0.78/0.95 (~c2_1(a9)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1450, 1575])).
% 0.78/0.95 tff(1577,plain,
% 0.78/0.95 (~c1_1(a9)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1470, 1575])).
% 0.78/0.95 tff(1578,plain,
% 0.78/0.95 (~c0_1(a9)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1456, 1575])).
% 0.78/0.95 tff(1579,plain,
% 0.78/0.95 (^[U: $i] : refl((hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(1580,plain,
% 0.78/0.95 (![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1579])).
% 0.78/0.95 tff(1581,plain,
% 0.78/0.95 (![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1582,plain,
% 0.78/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp24) <=> ((hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp24) <=> (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.78/0.95 inference(bind,[status(th)],[])).
% 0.78/0.95 tff(1583,plain,
% 0.78/0.95 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp24) <=> ![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.95 inference(quant_intro,[status(thm)],[1582])).
% 0.78/0.95 tff(1584,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.78/0.95 tff(1585,plain,
% 0.78/0.95 (![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 0.78/0.95 tff(1586,plain,
% 0.78/0.95 (![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1585, 1581])).
% 0.78/0.95 tff(1587,plain,(
% 0.78/0.95 ![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.95 inference(skolemize,[status(sab)],[1586])).
% 0.78/0.95 tff(1588,plain,
% 0.78/0.95 (![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1587, 1580])).
% 0.78/0.95 tff(1589,plain,
% 0.78/0.95 (((~![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp14 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1590,plain,
% 0.78/0.95 ((~![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1591,plain,
% 0.78/0.95 ((~![U: $i] : (hskp24 | hskp14 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp14 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 0.78/0.95 tff(1592,plain,
% 0.78/0.95 (hskp24 | hskp14 | (~c1_1(a6))),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1591, 108, 1000, 997, 1588])).
% 0.78/0.95 tff(1593,plain,
% 0.78/0.95 (hskp14),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1592, 1574, 1573])).
% 0.78/0.95 tff(1594,plain,
% 0.78/0.95 (((~hskp14) | (~c0_1(a28))) <=> ((~hskp14) | (~c0_1(a28)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1595,plain,
% 0.78/0.95 (((~c0_1(a28)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a28)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1596,axiom,((~c0_1(a28)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.78/0.95 tff(1597,plain,
% 0.78/0.95 ((~hskp14) | (~c0_1(a28))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1596, 1595])).
% 0.78/0.95 tff(1598,plain,
% 0.78/0.95 ((~hskp14) | (~c0_1(a28))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1597, 1594])).
% 0.78/0.95 tff(1599,plain,
% 0.78/0.95 (~c0_1(a28)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1598, 1593])).
% 0.78/0.95 tff(1600,plain,
% 0.78/0.95 (((~hskp14) | c3_1(a28)) <=> ((~hskp14) | c3_1(a28))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1601,axiom,((~hskp14) | c3_1(a28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.79/0.95 tff(1602,plain,
% 0.79/0.95 ((~hskp14) | c3_1(a28)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1601, 1600])).
% 0.79/0.95 tff(1603,plain,
% 0.79/0.95 ((~hskp14) | c3_1(a28)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1602, 1600])).
% 0.79/0.95 tff(1604,plain,
% 0.79/0.95 ((~hskp14) | c3_1(a28)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1603, 1600])).
% 0.79/0.95 tff(1605,plain,
% 0.79/0.95 ((~hskp14) | c3_1(a28)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1604, 1600])).
% 0.79/0.95 tff(1606,plain,
% 0.79/0.95 ((~hskp14) | c3_1(a28)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1605, 1600])).
% 0.79/0.95 tff(1607,plain,
% 0.79/0.95 (c3_1(a28)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1606, 1593])).
% 0.79/0.95 tff(1608,plain,
% 0.79/0.95 (((~hskp14) | c2_1(a28)) <=> ((~hskp14) | c2_1(a28))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1609,axiom,((~hskp14) | c2_1(a28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 0.79/0.95 tff(1610,plain,
% 0.79/0.95 ((~hskp14) | c2_1(a28)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 0.79/0.95 tff(1611,plain,
% 0.79/0.95 ((~hskp14) | c2_1(a28)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1610, 1608])).
% 0.79/0.95 tff(1612,plain,
% 0.79/0.95 ((~hskp14) | c2_1(a28)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1611, 1608])).
% 0.79/0.95 tff(1613,plain,
% 0.79/0.95 ((~hskp14) | c2_1(a28)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1612, 1608])).
% 0.79/0.95 tff(1614,plain,
% 0.79/0.95 ((~hskp14) | c2_1(a28)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1613, 1608])).
% 0.79/0.95 tff(1615,plain,
% 0.79/0.95 (c2_1(a28)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1614, 1593])).
% 0.79/0.95 tff(1616,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a28) | c0_1(a9) | c1_1(a9) | c2_1(a9) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a28)) | (~c2_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a28) | c0_1(a9) | c1_1(a9) | c2_1(a9) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a28)) | (~c2_1(a28)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1617,plain,
% 0.79/0.95 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a28) | (~c3_1(a28)) | (~c2_1(a28)) | c1_1(a9) | c0_1(a9) | c2_1(a9)) <=> (c0_1(a28) | c0_1(a9) | c1_1(a9) | c2_1(a9) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a28)) | (~c2_1(a28)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1618,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a28) | (~c3_1(a28)) | (~c2_1(a28)) | c1_1(a9) | c0_1(a9) | c2_1(a9))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a28) | c0_1(a9) | c1_1(a9) | c2_1(a9) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a28)) | (~c2_1(a28))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[1617])).
% 0.79/0.95 tff(1619,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a28) | (~c3_1(a28)) | (~c2_1(a28)) | c1_1(a9) | c0_1(a9) | c2_1(a9))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a28) | c0_1(a9) | c1_1(a9) | c2_1(a9) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a28)) | (~c2_1(a28)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[1618, 1616])).
% 0.79/0.95 tff(1620,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a28) | (~c3_1(a28)) | (~c2_1(a28)) | c1_1(a9) | c0_1(a9) | c2_1(a9))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(1621,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a28) | c0_1(a9) | c1_1(a9) | c2_1(a9) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a28)) | (~c2_1(a28))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 0.79/0.95 tff(1622,plain,
% 0.79/0.95 ($false),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1621, 108, 1615, 1607, 997, 1599, 1578, 1577, 1576, 996, 443, 1573])).
% 0.79/0.95 tff(1623,plain,(hskp24 | (~c3_1(a6)) | c2_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.79/0.95 tff(1624,plain,
% 0.79/0.95 (hskp24),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1623, 1554, 1572, 1556, 1555, 1547])).
% 0.79/0.95 tff(1625,plain,
% 0.79/0.95 (~c2_1(a52)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[681, 1624])).
% 0.79/0.95 tff(1626,plain,
% 0.79/0.95 (~c0_1(a52)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[687, 1624])).
% 0.79/0.95 tff(1627,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a52) | c2_1(a52) | c3_1(a29) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | (~c1_1(a29)) | (~c0_1(a29)) | (~c1_1(a52)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a52) | c2_1(a52) | c3_1(a29) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | (~c1_1(a29)) | (~c0_1(a29)) | (~c1_1(a52)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1628,plain,
% 0.79/0.95 (((~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c0_1(a52) | c2_1(a52) | (~c1_1(a52))) <=> (c0_1(a52) | c2_1(a52) | c3_1(a29) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | (~c1_1(a29)) | (~c0_1(a29)) | (~c1_1(a52)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1629,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c0_1(a52) | c2_1(a52) | (~c1_1(a52)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a52) | c2_1(a52) | c3_1(a29) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | (~c1_1(a29)) | (~c0_1(a29)) | (~c1_1(a52))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[1628])).
% 0.79/0.95 tff(1630,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c0_1(a52) | c2_1(a52) | (~c1_1(a52)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a52) | c2_1(a52) | c3_1(a29) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | (~c1_1(a29)) | (~c0_1(a29)) | (~c1_1(a52)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[1629, 1627])).
% 0.79/0.95 tff(1631,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c0_1(a52) | c2_1(a52) | (~c1_1(a52)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(1632,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a52) | c2_1(a52) | c3_1(a29) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)) | (~c1_1(a29)) | (~c0_1(a29)) | (~c1_1(a52))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 0.79/0.95 tff(1633,plain,
% 0.79/0.95 (~c1_1(a52)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1632, 108, 1560, 1555, 1554, 1626, 1625, 1559, 1571, 1561, 1556])).
% 0.79/0.95 tff(1634,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a52) | c2_1(a52) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a52) | c2_1(a52) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1635,plain,
% 0.79/0.95 (((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52) | c0_1(a52) | c2_1(a52)) <=> (c0_1(a52) | c2_1(a52) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1636,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52) | c0_1(a52) | c2_1(a52))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a52) | c2_1(a52) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52)))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[1635])).
% 0.79/0.95 tff(1637,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52) | c0_1(a52) | c2_1(a52))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a52) | c2_1(a52) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52))),
% 0.79/0.95 inference(transitivity,[status(thm)],[1636, 1634])).
% 0.79/0.95 tff(1638,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a6) | (~c1_1(a6)) | (~c3_1(a6)) | c0_1(a13) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52) | c0_1(a52) | c2_1(a52))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(1639,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a52) | c2_1(a52) | c0_1(a13) | c2_1(a6) | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a52)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 0.79/0.95 tff(1640,plain,
% 0.79/0.95 ($false),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1639, 108, 1415, 1554, 1626, 1625, 244, 1572, 443, 1538, 1556, 1633])).
% 0.79/0.95 tff(1641,plain,(c1_1(a13) | c0_1(a13) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.79/0.95 tff(1642,plain,
% 0.79/0.95 (c1_1(a13)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1641, 1, 244])).
% 0.79/0.95 tff(1643,assumption,(~hskp12), introduced(assumption)).
% 0.79/0.95 tff(1644,plain,
% 0.79/0.95 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1645,plain,
% 0.79/0.95 ((hskp12 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13))) <=> (hskp12 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1646,plain,
% 0.79/0.95 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13)))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[1645])).
% 0.79/0.95 tff(1647,plain,
% 0.79/0.95 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))),
% 0.79/0.95 inference(transitivity,[status(thm)],[1646, 1644])).
% 0.79/0.95 tff(1648,plain,
% 0.79/0.95 ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(1649,plain,
% 0.79/0.95 ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1648, 1647])).
% 0.79/0.95 tff(1650,plain,
% 0.79/0.95 (hskp12 | (~c1_1(a13)) | c3_1(a13)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1649, 108, 244, 170])).
% 0.79/0.95 tff(1651,plain,
% 0.79/0.95 (c3_1(a13)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1650, 1643, 1642])).
% 0.79/0.95 tff(1652,assumption,(hskp19), introduced(assumption)).
% 0.79/0.95 tff(1653,plain,
% 0.79/0.95 (((~hskp19) | (~c3_1(a35))) <=> ((~hskp19) | (~c3_1(a35)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1654,plain,
% 0.79/0.95 (((~c3_1(a35)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a35)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1655,axiom,((~c3_1(a35)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.79/0.95 tff(1656,plain,
% 0.79/0.95 ((~hskp19) | (~c3_1(a35))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 0.79/0.95 tff(1657,plain,
% 0.79/0.95 ((~hskp19) | (~c3_1(a35))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1656, 1653])).
% 0.79/0.95 tff(1658,plain,
% 0.79/0.95 (~c3_1(a35)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1657, 1652])).
% 0.79/0.95 tff(1659,plain,
% 0.79/0.95 (((~hskp19) | (~c0_1(a35))) <=> ((~hskp19) | (~c0_1(a35)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1660,plain,
% 0.79/0.95 (((~c0_1(a35)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a35)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1661,axiom,((~c0_1(a35)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.79/0.95 tff(1662,plain,
% 0.79/0.95 ((~hskp19) | (~c0_1(a35))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 0.79/0.95 tff(1663,plain,
% 0.79/0.95 ((~hskp19) | (~c0_1(a35))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1662, 1659])).
% 0.79/0.95 tff(1664,plain,
% 0.79/0.95 (~c0_1(a35)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1663, 1652])).
% 0.79/0.95 tff(1665,plain,
% 0.79/0.95 (((~hskp19) | c1_1(a35)) <=> ((~hskp19) | c1_1(a35))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1666,axiom,((~hskp19) | c1_1(a35)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.79/0.95 tff(1667,plain,
% 0.79/0.95 ((~hskp19) | c1_1(a35)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 0.79/0.95 tff(1668,plain,
% 0.79/0.95 ((~hskp19) | c1_1(a35)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1667, 1665])).
% 0.79/0.95 tff(1669,plain,
% 0.79/0.95 ((~hskp19) | c1_1(a35)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1668, 1665])).
% 0.79/0.95 tff(1670,plain,
% 0.79/0.95 ((~hskp19) | c1_1(a35)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1669, 1665])).
% 0.79/0.95 tff(1671,plain,
% 0.79/0.95 ((~hskp19) | c1_1(a35)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1670, 1665])).
% 0.79/0.95 tff(1672,plain,
% 0.79/0.95 (c1_1(a35)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1671, 1652])).
% 0.79/0.95 tff(1673,plain,
% 0.79/0.95 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1674,plain,
% 0.79/0.95 ((hskp12 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35))) <=> (hskp12 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(1675,plain,
% 0.79/0.95 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[1674])).
% 0.79/0.95 tff(1676,plain,
% 0.79/0.95 (((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[1675, 1673])).
% 0.79/0.95 tff(1677,plain,
% 0.79/0.95 ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp12 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(1678,plain,
% 0.79/0.95 ((~![U: $i] : (hskp12 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp12 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[1677, 1676])).
% 0.79/0.95 tff(1679,plain,
% 0.79/0.95 ($false),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1678, 108, 1643, 1672, 1664, 1658, 170])).
% 0.79/0.95 tff(1680,plain,((~hskp19) | hskp12), inference(lemma,lemma(discharge,[]))).
% 0.79/0.95 tff(1681,plain,
% 0.79/0.95 (~hskp19),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1680, 1643])).
% 0.79/0.95 tff(1682,plain,
% 0.79/0.95 (^[U: $i] : refl((hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(1683,plain,
% 0.79/0.96 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[1682])).
% 0.79/0.96 tff(1684,plain,
% 0.79/0.96 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1685,plain,
% 0.79/0.96 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp11) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp11))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp11) | hskp19) <=> ((hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp19))), rewrite(((hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp19) <=> (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp11) | hskp19) <=> (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(1686,plain,
% 0.79/0.96 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp11) | hskp19) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[1685])).
% 0.79/0.96 tff(1687,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp11) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 0.79/0.96 tff(1688,plain,
% 0.79/0.96 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1687, 1686])).
% 0.79/0.96 tff(1689,plain,
% 0.79/0.96 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1688, 1684])).
% 0.79/0.96 tff(1690,plain,(
% 0.79/0.96 ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.79/0.96 inference(skolemize,[status(sab)],[1689])).
% 0.79/0.96 tff(1691,plain,
% 0.79/0.96 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1690, 1683])).
% 0.79/0.96 tff(1692,plain,
% 0.79/0.96 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp19 | hskp11 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp19 | hskp11 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1693,plain,
% 0.79/0.96 ((hskp19 | hskp11 | (~ndr1_0) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13))) <=> (hskp19 | hskp11 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1694,plain,
% 0.79/0.96 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp19 | hskp11 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1693])).
% 0.79/0.96 tff(1695,plain,
% 0.79/0.96 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp19 | hskp11 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1694, 1692])).
% 0.79/0.96 tff(1696,plain,
% 0.79/0.96 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1697,plain,
% 0.79/0.96 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp19 | hskp11 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 0.79/0.96 tff(1698,plain,
% 0.79/0.96 (hskp19 | hskp11 | (~c1_1(a13)) | (~c3_1(a13))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1697, 108, 244, 1691])).
% 0.79/0.96 tff(1699,plain,
% 0.79/0.96 (hskp11),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1698, 1681, 1642, 1651])).
% 0.79/0.96 tff(1700,plain,
% 0.79/0.96 (~c3_1(a21)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[325, 1699])).
% 0.79/0.96 tff(1701,plain,
% 0.79/0.96 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1702,plain,
% 0.79/0.96 ((hskp30 | hskp8 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13))) <=> (hskp30 | hskp8 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1703,plain,
% 0.79/0.96 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13)))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1702])).
% 0.79/0.96 tff(1704,plain,
% 0.79/0.96 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1703, 1701])).
% 0.79/0.96 tff(1705,plain,
% 0.79/0.96 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1706,plain,
% 0.79/0.96 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1705, 1704])).
% 0.79/0.96 tff(1707,plain,
% 0.79/0.96 (hskp30 | hskp8 | (~c1_1(a13)) | c3_1(a13)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1706, 108, 244, 378])).
% 0.79/0.96 tff(1708,plain,
% 0.79/0.96 (c3_1(a13)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1707, 487, 1, 1642])).
% 0.79/0.96 tff(1709,plain,
% 0.79/0.96 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1710,plain,
% 0.79/0.96 ((hskp30 | hskp8 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35))) <=> (hskp30 | hskp8 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1711,plain,
% 0.79/0.96 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1710])).
% 0.79/0.96 tff(1712,plain,
% 0.79/0.96 (((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35)))) <=> ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1711, 1709])).
% 0.79/0.96 tff(1713,plain,
% 0.79/0.96 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp30 | hskp8 | (~ndr1_0) | c0_1(a35) | c3_1(a35) | (~c1_1(a35)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1714,plain,
% 0.79/0.96 ((~![U: $i] : (hskp30 | hskp8 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)))) | hskp30 | hskp8 | c0_1(a35) | c3_1(a35) | (~ndr1_0) | (~c1_1(a35))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1713, 1712])).
% 0.79/0.96 tff(1715,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1714, 108, 1, 487, 1672, 1664, 1658, 378])).
% 0.79/0.96 tff(1716,plain,((~hskp19) | hskp30 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(1717,plain,
% 0.79/0.96 (~hskp19),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1716, 487, 1])).
% 0.79/0.96 tff(1718,plain,
% 0.79/0.96 (hskp11),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1698, 1717, 1642, 1708])).
% 0.79/0.96 tff(1719,plain,
% 0.79/0.96 (~c3_1(a21)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[325, 1718])).
% 0.79/0.96 tff(1720,assumption,(c1_1(a13)), introduced(assumption)).
% 0.79/0.96 tff(1721,plain,
% 0.79/0.96 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1722,plain,
% 0.79/0.96 ((hskp16 | (~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13))) <=> (hskp16 | c2_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1723,plain,
% 0.79/0.96 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | c2_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1722])).
% 0.79/0.96 tff(1724,plain,
% 0.79/0.96 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1723, 1721])).
% 0.79/0.96 tff(1725,plain,
% 0.79/0.96 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1726,plain,
% 0.79/0.96 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | c2_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1725, 1724])).
% 0.79/0.96 tff(1727,plain,
% 0.79/0.96 (hskp16 | c2_1(a13) | (~c3_1(a13))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1726, 108, 1720, 180])).
% 0.79/0.96 tff(1728,plain,
% 0.79/0.96 (hskp16),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1727, 295, 1465])).
% 0.79/0.96 tff(1729,plain,
% 0.79/0.96 (~c1_1(a30)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[226, 1728])).
% 0.79/0.96 tff(1730,plain,
% 0.79/0.96 (c3_1(a30)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[242, 1728])).
% 0.79/0.96 tff(1731,plain,
% 0.79/0.96 (c2_1(a30)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[234, 1728])).
% 0.79/0.96 tff(1732,plain,
% 0.79/0.96 (~hskp21),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1546, 1731, 487, 1730, 1729])).
% 0.79/0.96 tff(1733,plain,
% 0.79/0.96 (~c0_1(a30)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[431, 108, 1732, 487, 1730, 1729, 21])).
% 0.79/0.96 tff(1734,plain,
% 0.79/0.96 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(1735,plain,
% 0.79/0.96 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[1734])).
% 0.79/0.96 tff(1736,plain,
% 0.79/0.96 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1737,plain,
% 0.79/0.96 (^[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))) | 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) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_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))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_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))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_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) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(1738,plain,
% 0.79/0.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[1737])).
% 0.79/0.96 tff(1739,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 0.79/0.96 tff(1740,plain,
% 0.79/0.96 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1739, 1738])).
% 0.79/0.96 tff(1741,plain,
% 0.79/0.96 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1740, 1736])).
% 0.79/0.96 tff(1742,plain,(
% 0.79/0.96 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.96 inference(skolemize,[status(sab)],[1741])).
% 0.79/0.96 tff(1743,plain,
% 0.79/0.96 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1742, 1735])).
% 0.79/0.96 tff(1744,plain,
% 0.79/0.96 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(1745,plain,
% 0.79/0.96 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[1744])).
% 0.79/0.96 tff(1746,plain,
% 0.79/0.96 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1747,plain,
% 0.79/0.96 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp8) <=> ((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8))), rewrite(((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.79/0.96 inference(bind,[status(th)],[])).
% 0.79/0.96 tff(1748,plain,
% 0.79/0.96 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp8) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.96 inference(quant_intro,[status(thm)],[1747])).
% 0.79/0.96 tff(1749,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp7) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.79/0.96 tff(1750,plain,
% 0.79/0.96 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 0.79/0.96 tff(1751,plain,
% 0.79/0.96 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1750, 1746])).
% 0.79/0.96 tff(1752,plain,(
% 0.79/0.96 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.96 inference(skolemize,[status(sab)],[1751])).
% 0.79/0.96 tff(1753,plain,
% 0.79/0.96 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1752, 1745])).
% 0.79/0.96 tff(1754,plain,
% 0.79/0.96 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1755,plain,
% 0.79/0.96 ((hskp8 | hskp7 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c1_1(a13))) <=> (hskp8 | hskp7 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1756,plain,
% 0.79/0.96 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1755])).
% 0.79/0.96 tff(1757,plain,
% 0.79/0.96 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c1_1(a13)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1756, 1754])).
% 0.79/0.96 tff(1758,plain,
% 0.79/0.96 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c2_1(a13) | c0_1(a13) | (~c1_1(a13)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1759,plain,
% 0.79/0.96 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp8 | hskp7 | c2_1(a13) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1758, 1757])).
% 0.79/0.96 tff(1760,plain,
% 0.79/0.96 (hskp8 | hskp7 | c2_1(a13) | (~c1_1(a13))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1759, 108, 244, 1753])).
% 0.79/0.96 tff(1761,plain,
% 0.79/0.96 (hskp7),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1760, 295, 1720, 487])).
% 0.79/0.96 tff(1762,plain,
% 0.79/0.96 (((~hskp7) | (~c3_1(a12))) <=> ((~hskp7) | (~c3_1(a12)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1763,plain,
% 0.79/0.96 (((~c3_1(a12)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a12)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1764,axiom,((~c3_1(a12)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.79/0.96 tff(1765,plain,
% 0.79/0.96 ((~hskp7) | (~c3_1(a12))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 0.79/0.96 tff(1766,plain,
% 0.79/0.96 ((~hskp7) | (~c3_1(a12))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1765, 1762])).
% 0.79/0.96 tff(1767,plain,
% 0.79/0.96 (~c3_1(a12)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1766, 1761])).
% 0.79/0.96 tff(1768,plain,
% 0.79/0.96 (((~hskp7) | c1_1(a12)) <=> ((~hskp7) | c1_1(a12))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1769,axiom,((~hskp7) | c1_1(a12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 0.79/0.96 tff(1770,plain,
% 0.79/0.96 ((~hskp7) | c1_1(a12)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1769, 1768])).
% 0.79/0.96 tff(1771,plain,
% 0.79/0.96 ((~hskp7) | c1_1(a12)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1770, 1768])).
% 0.79/0.96 tff(1772,plain,
% 0.79/0.96 ((~hskp7) | c1_1(a12)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1771, 1768])).
% 0.79/0.96 tff(1773,plain,
% 0.79/0.96 ((~hskp7) | c1_1(a12)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1772, 1768])).
% 0.79/0.96 tff(1774,plain,
% 0.79/0.96 ((~hskp7) | c1_1(a12)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1773, 1768])).
% 0.79/0.96 tff(1775,plain,
% 0.79/0.96 (c1_1(a12)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1774, 1761])).
% 0.79/0.96 tff(1776,plain,
% 0.79/0.96 (((~hskp7) | c0_1(a12)) <=> ((~hskp7) | c0_1(a12))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1777,axiom,((~hskp7) | c0_1(a12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.79/0.96 tff(1778,plain,
% 0.79/0.96 ((~hskp7) | c0_1(a12)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 0.79/0.96 tff(1779,plain,
% 0.79/0.96 ((~hskp7) | c0_1(a12)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1778, 1776])).
% 0.79/0.96 tff(1780,plain,
% 0.79/0.96 ((~hskp7) | c0_1(a12)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1779, 1776])).
% 0.79/0.96 tff(1781,plain,
% 0.79/0.96 ((~hskp7) | c0_1(a12)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1780, 1776])).
% 0.79/0.96 tff(1782,plain,
% 0.79/0.96 ((~hskp7) | c0_1(a12)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1781, 1776])).
% 0.79/0.96 tff(1783,plain,
% 0.79/0.96 (c0_1(a12)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1782, 1761])).
% 0.79/0.96 tff(1784,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a13) | c0_1(a13) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a12)) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a13) | c0_1(a13) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a12)) | (~c3_1(a13)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1785,plain,
% 0.79/0.96 ((hskp5 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c0_1(a13) | c2_1(a13) | (~c3_1(a13))) <=> (hskp5 | c2_1(a13) | c0_1(a13) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a12)) | (~c3_1(a13)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1786,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c0_1(a13) | c2_1(a13) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | c2_1(a13) | c0_1(a13) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a12)) | (~c3_1(a13))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[1785])).
% 0.79/0.96 tff(1787,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c0_1(a13) | c2_1(a13) | (~c3_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a13) | c0_1(a13) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a12)) | (~c3_1(a13)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[1786, 1784])).
% 0.79/0.96 tff(1788,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c0_1(a13) | c2_1(a13) | (~c3_1(a13)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(1789,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp5 | c2_1(a13) | c0_1(a13) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a12)) | (~c3_1(a13))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 0.79/0.96 tff(1790,plain,
% 0.79/0.96 (hskp5),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1789, 108, 295, 1783, 1775, 244, 1767, 1743, 1465])).
% 0.79/0.96 tff(1791,plain,
% 0.79/0.96 (~c2_1(a9)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1450, 1790])).
% 0.79/0.96 tff(1792,plain,
% 0.79/0.96 (~c1_1(a9)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1470, 1790])).
% 0.79/0.96 tff(1793,plain,
% 0.79/0.96 (~c0_1(a9)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1456, 1790])).
% 0.79/0.96 tff(1794,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a13) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a13) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(1795,plain,
% 0.79/0.96 (((~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9)) <=> (c2_1(a13) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1796,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a13) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1795])).
% 0.79/0.97 tff(1797,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a13) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1796, 1794])).
% 0.79/0.97 tff(1798,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1799,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a13) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 0.79/0.97 tff(1800,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1799, 108, 1731, 1730, 1720, 295, 1793, 1792, 1791, 443, 1465, 1733])).
% 0.79/0.97 tff(1801,plain,(c2_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a13) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(1802,plain,
% 0.79/0.97 (c2_1(a13)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1801, 1708, 1642, 244, 487])).
% 0.79/0.97 tff(1803,plain,
% 0.79/0.97 (c0_1(a21)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[356, 1718])).
% 0.79/0.97 tff(1804,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp30 | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp30 | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1805,plain,
% 0.79/0.97 ((hskp30 | (~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13))) <=> (hskp30 | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1806,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp30 | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1805])).
% 0.79/0.97 tff(1807,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp30 | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1806, 1804])).
% 0.79/0.97 tff(1808,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1809,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp30 | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 0.79/0.97 tff(1810,plain,
% 0.79/0.97 (~c1_1(a21)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1809, 108, 1, 1803, 1642, 1802, 1719, 244, 285])).
% 0.79/0.97 tff(1811,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21) | (~c0_1(a21)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1812,plain,
% 0.79/0.97 (((~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13))) <=> (c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21) | (~c0_1(a21)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1813,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21) | (~c0_1(a21))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1812])).
% 0.79/0.97 tff(1814,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21) | (~c0_1(a21)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1813, 1811])).
% 0.79/0.97 tff(1815,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a21) | c3_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c1_1(a13)) | (~c3_1(a13)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1816,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c1_1(a21) | (~c0_1(a21))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1815, 1814])).
% 0.79/0.97 tff(1817,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1816, 108, 1803, 1642, 1802, 1719, 244, 255, 1708, 1810])).
% 0.79/0.97 tff(1818,plain,(hskp8 | c0_1(a13) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(1819,plain,
% 0.79/0.97 (hskp8),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1818, 1, 244])).
% 0.79/0.97 tff(1820,plain,
% 0.79/0.97 (((~hskp8) | c2_1(a13)) <=> ((~hskp8) | c2_1(a13))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1821,axiom,((~hskp8) | c2_1(a13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.79/0.97 tff(1822,plain,
% 0.79/0.97 ((~hskp8) | c2_1(a13)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1821, 1820])).
% 0.79/0.97 tff(1823,plain,
% 0.79/0.97 ((~hskp8) | c2_1(a13)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1822, 1820])).
% 0.79/0.97 tff(1824,plain,
% 0.79/0.97 ((~hskp8) | c2_1(a13)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1823, 1820])).
% 0.79/0.97 tff(1825,plain,
% 0.79/0.97 ((~hskp8) | c2_1(a13)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1824, 1820])).
% 0.79/0.97 tff(1826,plain,
% 0.79/0.97 ((~hskp8) | c2_1(a13)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1825, 1820])).
% 0.79/0.97 tff(1827,plain,
% 0.79/0.97 (c2_1(a13)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1826, 1819])).
% 0.79/0.97 tff(1828,plain,
% 0.79/0.97 (c0_1(a21)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[356, 1699])).
% 0.79/0.97 tff(1829,plain,
% 0.79/0.97 (~c1_1(a21)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1809, 108, 1, 1828, 1642, 1827, 1700, 244, 285])).
% 0.79/0.97 tff(1830,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1816, 108, 1828, 1642, 1827, 1700, 244, 255, 1651, 1829])).
% 0.79/0.97 tff(1831,plain,(hskp12 | c0_1(a13) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(1832,plain,
% 0.79/0.97 (hskp12),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1831, 1, 244])).
% 0.79/0.97 tff(1833,plain,
% 0.79/0.97 (c3_1(a24)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[194, 1832])).
% 0.79/0.97 tff(1834,plain,
% 0.79/0.97 (~c2_1(a24)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[186, 1832])).
% 0.79/0.97 tff(1835,plain,
% 0.79/0.97 (c1_1(a24)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[202, 1832])).
% 0.79/0.97 tff(1836,plain,
% 0.79/0.97 (hskp16),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[211, 1832])).
% 0.79/0.97 tff(1837,plain,
% 0.79/0.97 (c3_1(a30)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[242, 1836])).
% 0.79/0.97 tff(1838,plain,
% 0.79/0.97 (~c1_1(a30)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[226, 1836])).
% 0.79/0.97 tff(1839,plain,
% 0.79/0.97 (c2_1(a30)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[234, 1836])).
% 0.79/0.97 tff(1840,assumption,(~c2_1(a24)), introduced(assumption)).
% 0.79/0.97 tff(1841,assumption,(c3_1(a24)), introduced(assumption)).
% 0.79/0.97 tff(1842,plain,
% 0.79/0.97 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c0_1(a24))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c0_1(a24))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1843,plain,
% 0.79/0.97 ((hskp30 | hskp11 | (~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24))) <=> (hskp30 | hskp11 | c2_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c0_1(a24))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1844,plain,
% 0.79/0.97 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | c2_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c0_1(a24)))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1843])).
% 0.79/0.97 tff(1845,plain,
% 0.79/0.97 (((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)))) <=> ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c0_1(a24))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1844, 1842])).
% 0.79/0.97 tff(1846,plain,
% 0.79/0.97 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp30 | hskp11 | (~ndr1_0) | c2_1(a24) | c0_1(a24) | (~c3_1(a24)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1847,plain,
% 0.79/0.97 ((~![U: $i] : (hskp30 | hskp11 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp30 | hskp11 | c2_1(a24) | (~ndr1_0) | (~c3_1(a24)) | c0_1(a24)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1846, 1845])).
% 0.79/0.97 tff(1848,plain,
% 0.79/0.97 (hskp11 | c0_1(a24)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1847, 108, 1, 1841, 1840, 41])).
% 0.79/0.97 tff(1849,plain,
% 0.79/0.97 (c0_1(a24)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1848, 1283])).
% 0.79/0.97 tff(1850,plain,
% 0.79/0.97 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W))))),
% 0.79/0.97 inference(bind,[status(th)],[])).
% 0.79/0.97 tff(1851,plain,
% 0.79/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_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)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.79/0.97 inference(quant_intro,[status(thm)],[1850])).
% 0.79/0.97 tff(1852,plain,
% 0.79/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_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)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1853,plain,
% 0.79/0.97 (^[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)) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_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)) | (~c0_1(V)) | (~c0_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_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)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_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)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_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)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_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)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))))),
% 0.79/0.97 inference(bind,[status(th)],[])).
% 0.79/0.97 tff(1854,plain,
% 0.79/0.97 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_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)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.79/0.97 inference(quant_intro,[status(thm)],[1853])).
% 0.79/0.97 tff(1855,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c3_1(W))) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.79/0.97 tff(1856,plain,
% 0.79/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1855, 1854])).
% 0.79/0.97 tff(1857,plain,
% 0.79/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1856, 1852])).
% 0.79/0.97 tff(1858,plain,(
% 0.79/0.97 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.79/0.97 inference(skolemize,[status(sab)],[1857])).
% 0.79/0.97 tff(1859,plain,
% 0.79/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1858, 1851])).
% 0.79/0.97 tff(1860,assumption,(c1_1(a24)), introduced(assumption)).
% 0.79/0.97 tff(1861,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a30) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a30) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1862,plain,
% 0.79/0.97 (((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30))) <=> (c1_1(a30) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1863,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a30) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1862])).
% 0.79/0.97 tff(1864,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a30) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1863, 1861])).
% 0.79/0.97 tff(1865,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1866,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a30) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1865, 1864])).
% 0.79/0.97 tff(1867,plain,
% 0.79/0.97 ((~c0_1(a24)) | (~c0_1(a30))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1866, 108, 303, 302, 1860, 1841, 301, 1859])).
% 0.79/0.97 tff(1868,plain,
% 0.79/0.97 (~c0_1(a30)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1867, 1849])).
% 0.79/0.97 tff(1869,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a30) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c0_1(a24)) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a30) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c0_1(a24)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1870,plain,
% 0.79/0.97 ((hskp15 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30))) <=> (hskp15 | c1_1(a30) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c0_1(a24)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1871,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | c1_1(a30) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c0_1(a24)) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1870])).
% 0.79/0.97 tff(1872,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a30) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c0_1(a24)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1871, 1869])).
% 0.79/0.97 tff(1873,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1874,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp15 | c1_1(a30) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c0_1(a24)) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1873, 1872])).
% 0.79/0.97 tff(1875,plain,
% 0.79/0.97 (hskp15 | (~c0_1(a24))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1874, 108, 303, 302, 1860, 301, 1840, 349])).
% 0.79/0.97 tff(1876,plain,
% 0.79/0.97 (hskp15),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1875, 1849])).
% 0.79/0.97 tff(1877,plain,
% 0.79/0.97 (c1_1(a29)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[124, 1876])).
% 0.79/0.97 tff(1878,plain,
% 0.79/0.97 (~c3_1(a29)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[130, 1876])).
% 0.79/0.97 tff(1879,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a24) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a24) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1880,plain,
% 0.79/0.97 (((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9)) <=> (c2_1(a24) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1881,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a24) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[1880])).
% 0.79/0.97 tff(1882,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a24) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[1881, 1879])).
% 0.79/0.97 tff(1883,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a9) | c0_1(a9) | c2_1(a9))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(1884,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c2_1(a24) | c0_1(a9) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 0.79/0.97 tff(1885,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1884, 108, 303, 302, 1860, 1841, 1840, 1457, 1471, 1451, 443, 1868])).
% 0.79/0.97 tff(1886,plain,(hskp11 | (~c2_1(a30)) | (~c3_1(a30)) | (~c1_1(a24)) | (~c3_1(a24)) | c2_1(a24) | c1_1(a30) | hskp21 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(1887,plain,
% 0.79/0.97 (hskp21),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1886, 1283, 302, 1860, 1841, 1840, 301, 303, 1])).
% 0.79/0.97 tff(1888,plain,
% 0.79/0.97 (~c2_1(a29)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[136, 1876])).
% 0.79/0.97 tff(1889,plain,
% 0.79/0.97 (~c0_1(a29)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[159, 1888, 1887, 1878, 1877])).
% 0.79/0.97 tff(1890,plain,
% 0.79/0.97 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.79/0.97 inference(bind,[status(th)],[])).
% 0.79/0.97 tff(1891,plain,
% 0.79/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.97 inference(quant_intro,[status(thm)],[1890])).
% 0.79/0.97 tff(1892,plain,
% 0.79/0.97 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(1893,plain,
% 0.79/0.97 (^[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(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | 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) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | 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) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(1894,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[1893])).
% 0.79/0.98 tff(1895,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 0.79/0.98 tff(1896,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 0.79/0.98 tff(1897,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1896, 1892])).
% 0.79/0.98 tff(1898,plain,(
% 0.79/0.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.98 inference(skolemize,[status(sab)],[1897])).
% 0.79/0.98 tff(1899,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1898, 1891])).
% 0.79/0.98 tff(1900,plain,
% 0.79/0.98 (~c3_1(a39)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[58, 1887])).
% 0.79/0.98 tff(1901,plain,
% 0.79/0.98 (~c0_1(a39)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[64, 1887])).
% 0.79/0.98 tff(1902,plain,
% 0.79/0.98 (c2_1(a39)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[72, 1887])).
% 0.79/0.98 tff(1903,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a39) | c3_1(a39) | c1_1(a30) | c2_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29) | c0_1(a30) | (~c2_1(a30)) | (~c2_1(a39)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a39) | c3_1(a39) | c1_1(a30) | c2_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29) | c0_1(a30) | (~c2_1(a30)) | (~c2_1(a39)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1904,plain,
% 0.79/0.98 (((~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)) | c0_1(a29) | c2_1(a29) | (~c1_1(a29)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30))) <=> (c0_1(a39) | c3_1(a39) | c1_1(a30) | c2_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29) | c0_1(a30) | (~c2_1(a30)) | (~c2_1(a39)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1905,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)) | c0_1(a29) | c2_1(a29) | (~c1_1(a29)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a39) | c3_1(a39) | c1_1(a30) | c2_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29) | c0_1(a30) | (~c2_1(a30)) | (~c2_1(a39))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1904])).
% 0.79/0.98 tff(1906,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)) | c0_1(a29) | c2_1(a29) | (~c1_1(a29)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a39) | c3_1(a39) | c1_1(a30) | c2_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29) | c0_1(a30) | (~c2_1(a30)) | (~c2_1(a39)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1905, 1903])).
% 0.79/0.98 tff(1907,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a39) | c3_1(a39) | (~c2_1(a39)) | c0_1(a29) | c2_1(a29) | (~c1_1(a29)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1908,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a39) | c3_1(a39) | c1_1(a30) | c2_1(a29) | (~ndr1_0) | (~c1_1(a29)) | c0_1(a29) | c0_1(a30) | (~c2_1(a30)) | (~c2_1(a39))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1907, 1906])).
% 0.79/0.98 tff(1909,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1908, 108, 1902, 303, 1877, 1901, 1900, 301, 1888, 1899, 1889, 1868])).
% 0.79/0.98 tff(1910,plain,(hskp11 | (~c2_1(a30)) | c1_1(a30) | (~c3_1(a30)) | (~c1_1(a24)) | c2_1(a24) | (~c3_1(a24)) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(1911,plain,
% 0.79/0.98 (hskp11),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1910, 1839, 1838, 1837, 1835, 1834, 1833, 1])).
% 0.79/0.98 tff(1912,plain,
% 0.79/0.98 (~c3_1(a21)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[325, 1911])).
% 0.79/0.98 tff(1913,plain,
% 0.79/0.98 (c0_1(a21)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[356, 1911])).
% 0.79/0.98 tff(1914,plain,
% 0.79/0.98 (~c1_1(a21)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1809, 108, 1, 1913, 1642, 1827, 1912, 244, 285])).
% 0.79/0.98 tff(1915,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c2_1(a21) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c2_1(a21) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1916,plain,
% 0.79/0.98 (((~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c2_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c2_1(a13)) | c3_1(a13)) <=> (c2_1(a21) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1917,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c2_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c2_1(a13)) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | (c2_1(a21) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1916])).
% 0.79/0.98 tff(1918,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c2_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c2_1(a13)) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c2_1(a21) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1917, 1915])).
% 0.79/0.98 tff(1919,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c2_1(a21) | (~c0_1(a21)) | c0_1(a13) | (~c2_1(a13)) | c3_1(a13))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1920,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | c3_1(W))) | c2_1(a21) | c3_1(a21) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a21)) | (~c0_1(a21))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1919, 1918])).
% 0.79/0.98 tff(1921,plain,
% 0.79/0.98 (~c1_1(a21)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1920, 108, 841, 1827, 839, 843, 244, 148, 300])).
% 0.79/0.98 tff(1922,plain,
% 0.79/0.98 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W)))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(1923,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_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) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[1922])).
% 0.79/0.98 tff(1924,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_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) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1925,plain,
% 0.79/0.98 (^[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)) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(1926,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) | c2_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) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[1925])).
% 0.79/0.98 tff(1927,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.79/0.98 tff(1928,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 0.79/0.98 tff(1929,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1928, 1924])).
% 0.79/0.98 tff(1930,plain,(
% 0.79/0.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 0.79/0.98 inference(skolemize,[status(sab)],[1929])).
% 0.79/0.98 tff(1931,plain,
% 0.79/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1930, 1923])).
% 0.79/0.98 tff(1932,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | (c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1933,plain,
% 0.79/0.98 (((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a30) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a21) | c2_1(a21) | c3_1(a21)) <=> (c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1934,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a30) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a21) | c2_1(a21) | c3_1(a21))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | (c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1933])).
% 0.79/0.98 tff(1935,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a30) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a21) | c2_1(a21) | c3_1(a21))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1934, 1932])).
% 0.79/0.98 tff(1936,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a30)) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a30) | (~c2_1(a30)) | (~c0_1(a30)) | c1_1(a21) | c2_1(a21) | c3_1(a21))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1937,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | c2_1(W) | c3_1(W))) | c1_1(a30) | c2_1(a21) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a30)) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 0.79/0.98 tff(1938,plain,
% 0.79/0.98 (~c0_1(a30)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1937, 108, 1839, 1837, 1838, 839, 843, 1931, 1921])).
% 0.79/0.98 tff(1939,plain,
% 0.79/0.98 (hskp23),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[857, 1921])).
% 0.79/0.98 tff(1940,plain,
% 0.79/0.98 (~c3_1(a42)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[762, 1939])).
% 0.79/0.98 tff(1941,plain,
% 0.79/0.98 (~c1_1(a42)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[768, 1939])).
% 0.79/0.98 tff(1942,plain,
% 0.79/0.98 (c0_1(a42)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[776, 1939])).
% 0.79/0.98 tff(1943,assumption,(~c3_1(a42)), introduced(assumption)).
% 0.79/0.98 tff(1944,assumption,(~c1_1(a42)), introduced(assumption)).
% 0.79/0.98 tff(1945,assumption,(c0_1(a42)), introduced(assumption)).
% 0.79/0.98 tff(1946,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a42) | c3_1(a42) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a42) | c3_1(a42) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24) | (~c0_1(a42)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1947,plain,
% 0.79/0.98 (((~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13))) <=> (c1_1(a42) | c3_1(a42) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24) | (~c0_1(a42)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1948,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a42) | c3_1(a42) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24) | (~c0_1(a42))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1947])).
% 0.79/0.98 tff(1949,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a42) | c3_1(a42) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24) | (~c0_1(a42)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1948, 1946])).
% 0.79/0.98 tff(1950,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a42) | c3_1(a42) | (~c0_1(a42)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1951,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a42) | c3_1(a42) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24) | (~c0_1(a42))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1950, 1949])).
% 0.79/0.98 tff(1952,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1951, 108, 1945, 1860, 1841, 1720, 1472, 1944, 1943, 244, 255, 245])).
% 0.79/0.98 tff(1953,plain,(c0_1(a24) | (~c0_1(a42)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c1_1(a13)) | (~c2_1(a13)) | c1_1(a42) | c3_1(a42) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(1954,plain,
% 0.79/0.98 (c0_1(a24)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1953, 1942, 1835, 1833, 1642, 1827, 1941, 1940, 244])).
% 0.79/0.98 tff(1955,plain,
% 0.79/0.98 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(1956,plain,
% 0.79/0.98 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[1955])).
% 0.79/0.98 tff(1957,plain,
% 0.79/0.98 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1958,plain,
% 0.79/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_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)) | hskp22) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_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)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(1959,plain,
% 0.79/0.98 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[1958])).
% 0.79/0.98 tff(1960,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.79/0.98 tff(1961,plain,
% 0.79/0.98 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1960, 1959])).
% 0.79/0.98 tff(1962,plain,
% 0.79/0.98 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1961, 1957])).
% 0.79/0.98 tff(1963,plain,(
% 0.79/0.98 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.98 inference(skolemize,[status(sab)],[1962])).
% 0.79/0.98 tff(1964,plain,
% 0.79/0.98 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1963, 1956])).
% 0.79/0.98 tff(1965,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1966,plain,
% 0.79/0.98 ((hskp22 | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a21) | c2_1(a21) | (~c0_1(a21))) <=> (hskp22 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1967,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a21) | c2_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[1966])).
% 0.79/0.98 tff(1968,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a21) | c2_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[1967, 1965])).
% 0.79/0.98 tff(1969,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a21) | c2_1(a21) | (~c0_1(a21)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(1970,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1969, 1968])).
% 0.79/0.98 tff(1971,plain,
% 0.79/0.98 (hskp22 | (~c0_1(a24))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1970, 108, 1835, 1833, 841, 839, 1964, 1921])).
% 0.79/0.98 tff(1972,plain,
% 0.79/0.98 (hskp22),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1971, 1954])).
% 0.79/0.98 tff(1973,plain,
% 0.79/0.98 (((~hskp22) | (~c2_1(a40))) <=> ((~hskp22) | (~c2_1(a40)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1974,plain,
% 0.79/0.98 (((~c2_1(a40)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a40)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1975,axiom,((~c2_1(a40)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.79/0.98 tff(1976,plain,
% 0.79/0.98 ((~hskp22) | (~c2_1(a40))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 0.79/0.98 tff(1977,plain,
% 0.79/0.98 ((~hskp22) | (~c2_1(a40))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1976, 1973])).
% 0.79/0.98 tff(1978,plain,
% 0.79/0.98 (~c2_1(a40)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1977, 1972])).
% 0.79/0.98 tff(1979,plain,
% 0.79/0.98 (((~hskp22) | (~c0_1(a40))) <=> ((~hskp22) | (~c0_1(a40)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1980,plain,
% 0.79/0.98 (((~c0_1(a40)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a40)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(1981,axiom,((~c0_1(a40)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.79/0.98 tff(1982,plain,
% 0.79/0.98 ((~hskp22) | (~c0_1(a40))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 0.79/0.98 tff(1983,plain,
% 0.79/0.98 ((~hskp22) | (~c0_1(a40))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[1982, 1979])).
% 0.79/0.98 tff(1984,plain,
% 0.79/0.98 (~c0_1(a40)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1983, 1972])).
% 0.79/0.98 tff(1985,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a40) | c2_1(a40) | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c1_1(a40)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a40) | c2_1(a40) | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c1_1(a40)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1986,plain,
% 0.79/0.99 (((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a40) | c2_1(a40) | (~c1_1(a40)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30))) <=> (c0_1(a40) | c2_1(a40) | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c1_1(a40)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1987,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a40) | c2_1(a40) | (~c1_1(a40)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a40) | c2_1(a40) | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c1_1(a40))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[1986])).
% 0.79/0.99 tff(1988,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a40) | c2_1(a40) | (~c1_1(a40)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a40) | c2_1(a40) | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c1_1(a40)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[1987, 1985])).
% 0.79/0.99 tff(1989,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a40) | c2_1(a40) | (~c1_1(a40)) | c1_1(a30) | c0_1(a30) | (~c2_1(a30)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(1990,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a40) | c2_1(a40) | c1_1(a30) | c0_1(a13) | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | c0_1(a30) | (~c2_1(a30)) | (~c1_1(a40))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 0.79/0.99 tff(1991,plain,
% 0.79/0.99 (~c1_1(a40)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1990, 108, 1839, 1827, 1984, 1978, 1838, 244, 1899, 300, 1938])).
% 0.79/0.99 tff(1992,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a40) | c2_1(a40) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a40))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a40) | c2_1(a40) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a40))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1993,plain,
% 0.79/0.99 (((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a40) | c0_1(a40) | c2_1(a40)) <=> (c0_1(a40) | c2_1(a40) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a40))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(1994,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a40) | c0_1(a40) | c2_1(a40))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a40) | c2_1(a40) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a40)))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[1993])).
% 0.79/0.99 tff(1995,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a40) | c0_1(a40) | c2_1(a40))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a40) | c2_1(a40) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a40))),
% 0.79/0.99 inference(transitivity,[status(thm)],[1994, 1992])).
% 0.79/0.99 tff(1996,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | c2_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c1_1(a40) | c0_1(a40) | c2_1(a40))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(1997,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a40) | c2_1(a40) | c2_1(a24) | (~ndr1_0) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a30) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a40)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[1996, 1995])).
% 0.79/0.99 tff(1998,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1997, 108, 1839, 1837, 1835, 1833, 1984, 1978, 1834, 443, 1938, 1991])).
% 0.79/0.99 tff(1999,plain,((~hskp11) | c0_1(a13) | c3_1(a13) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(2000,plain,
% 0.79/0.99 (c3_1(a13)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1999, 1911, 244, 1])).
% 0.79/0.99 tff(2001,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1816, 108, 1913, 1642, 1827, 1912, 244, 255, 2000, 1914])).
% 0.79/0.99 tff(2002,plain,(hskp30 | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(2003,plain,
% 0.79/0.99 (hskp30),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2002, 244])).
% 0.79/0.99 tff(2004,plain,
% 0.79/0.99 (((~hskp30) | c0_1(a20)) <=> ((~hskp30) | c0_1(a20))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2005,axiom,((~hskp30) | c0_1(a20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.79/0.99 tff(2006,plain,
% 0.79/0.99 ((~hskp30) | c0_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2005, 2004])).
% 0.79/0.99 tff(2007,plain,
% 0.79/0.99 ((~hskp30) | c0_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2006, 2004])).
% 0.79/0.99 tff(2008,plain,
% 0.79/0.99 ((~hskp30) | c0_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2007, 2004])).
% 0.79/0.99 tff(2009,plain,
% 0.79/0.99 ((~hskp30) | c0_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2008, 2004])).
% 0.79/0.99 tff(2010,plain,
% 0.79/0.99 ((~hskp30) | c0_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2009, 2004])).
% 0.79/0.99 tff(2011,plain,
% 0.79/0.99 (c0_1(a20)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2010, 2003])).
% 0.79/0.99 tff(2012,plain,
% 0.79/0.99 (((~hskp30) | c3_1(a20)) <=> ((~hskp30) | c3_1(a20))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2013,axiom,((~hskp30) | c3_1(a20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.79/0.99 tff(2014,plain,
% 0.79/0.99 ((~hskp30) | c3_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 0.79/0.99 tff(2015,plain,
% 0.79/0.99 ((~hskp30) | c3_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2014, 2012])).
% 0.79/0.99 tff(2016,plain,
% 0.79/0.99 ((~hskp30) | c3_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2015, 2012])).
% 0.79/0.99 tff(2017,plain,
% 0.79/0.99 ((~hskp30) | c3_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2016, 2012])).
% 0.79/0.99 tff(2018,plain,
% 0.79/0.99 ((~hskp30) | c3_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2017, 2012])).
% 0.79/0.99 tff(2019,plain,
% 0.79/0.99 (c3_1(a20)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2018, 2003])).
% 0.79/0.99 tff(2020,plain,
% 0.79/0.99 (((~hskp30) | c2_1(a20)) <=> ((~hskp30) | c2_1(a20))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2021,axiom,((~hskp30) | c2_1(a20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.79/0.99 tff(2022,plain,
% 0.79/0.99 ((~hskp30) | c2_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2021, 2020])).
% 0.79/0.99 tff(2023,plain,
% 0.79/0.99 ((~hskp30) | c2_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2022, 2020])).
% 0.79/0.99 tff(2024,plain,
% 0.79/0.99 ((~hskp30) | c2_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2023, 2020])).
% 0.79/0.99 tff(2025,plain,
% 0.79/0.99 ((~hskp30) | c2_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2024, 2020])).
% 0.79/0.99 tff(2026,plain,
% 0.79/0.99 ((~hskp30) | c2_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2025, 2020])).
% 0.79/0.99 tff(2027,plain,
% 0.79/0.99 (c2_1(a20)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2026, 2003])).
% 0.79/0.99 tff(2028,assumption,(c0_1(a20)), introduced(assumption)).
% 0.79/0.99 tff(2029,assumption,(c3_1(a20)), introduced(assumption)).
% 0.79/0.99 tff(2030,assumption,(c2_1(a20)), introduced(assumption)).
% 0.79/0.99 tff(2031,plain,
% 0.79/0.99 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | (~c0_1(a20)) | (~c3_1(a20)) | c1_1(a20))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | (~ndr1_0) | (~c0_1(a20)) | (~c3_1(a20)) | c1_1(a20))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2032,plain,
% 0.79/0.99 ((hskp21 | hskp8 | (~ndr1_0) | c1_1(a20) | (~c3_1(a20)) | (~c0_1(a20))) <=> (hskp21 | hskp8 | (~ndr1_0) | (~c0_1(a20)) | (~c3_1(a20)) | c1_1(a20))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2033,plain,
% 0.79/0.99 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a20) | (~c3_1(a20)) | (~c0_1(a20)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | (~c0_1(a20)) | (~c3_1(a20)) | c1_1(a20)))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[2032])).
% 0.79/0.99 tff(2034,plain,
% 0.79/0.99 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a20) | (~c3_1(a20)) | (~c0_1(a20)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | (~ndr1_0) | (~c0_1(a20)) | (~c3_1(a20)) | c1_1(a20))),
% 0.79/0.99 inference(transitivity,[status(thm)],[2033, 2031])).
% 0.79/0.99 tff(2035,plain,
% 0.79/0.99 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a20) | (~c3_1(a20)) | (~c0_1(a20)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(2036,plain,
% 0.79/0.99 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | (~ndr1_0) | (~c0_1(a20)) | (~c3_1(a20)) | c1_1(a20)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2035, 2034])).
% 0.79/0.99 tff(2037,plain,
% 0.79/0.99 (hskp21 | hskp8 | c1_1(a20)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2036, 108, 2028, 2029, 21])).
% 0.79/0.99 tff(2038,plain,
% 0.79/0.99 (c1_1(a20)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2037, 1358, 487])).
% 0.79/0.99 tff(2039,plain,
% 0.79/0.99 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))))),
% 0.79/0.99 inference(bind,[status(th)],[])).
% 0.79/0.99 tff(2040,plain,
% 0.79/0.99 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.99 inference(quant_intro,[status(thm)],[2039])).
% 0.79/0.99 tff(2041,plain,
% 0.79/0.99 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2042,plain,
% 0.79/0.99 (^[V: $i, U: $i] : 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)) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~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))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp21) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.79/0.99 inference(bind,[status(th)],[])).
% 0.79/0.99 tff(2043,plain,
% 0.79/0.99 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.99 inference(quant_intro,[status(thm)],[2042])).
% 0.79/0.99 tff(2044,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.79/0.99 tff(2045,plain,
% 0.79/0.99 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 0.79/0.99 tff(2046,plain,
% 0.79/0.99 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2045, 2041])).
% 0.79/0.99 tff(2047,plain,(
% 0.79/0.99 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.99 inference(skolemize,[status(sab)],[2046])).
% 0.79/0.99 tff(2048,plain,
% 0.79/0.99 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2047, 2040])).
% 0.79/0.99 tff(2049,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a20)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2050,plain,
% 0.79/0.99 ((hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a20)) | (~c3_1(a20)) | (~c0_1(a20))) <=> (hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a20)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2051,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a20)) | (~c3_1(a20)) | (~c0_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a20))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[2050])).
% 0.79/0.99 tff(2052,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a20)) | (~c3_1(a20)) | (~c0_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a20)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[2051, 2049])).
% 0.79/0.99 tff(2053,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a20)) | (~c3_1(a20)) | (~c0_1(a20)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(2054,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a20))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2053, 2052])).
% 0.79/0.99 tff(2055,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2054, 108, 1358, 2028, 2030, 2029, 2048, 2038])).
% 0.79/0.99 tff(2056,plain,(hskp21 | (~c0_1(a20)) | (~c2_1(a20)) | (~c3_1(a20)) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(2057,plain,
% 0.79/0.99 (hskp21),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2056, 487, 2030, 2029, 2028])).
% 0.79/0.99 tff(2058,plain,
% 0.79/0.99 (hskp16),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[220, 2057])).
% 0.79/0.99 tff(2059,plain,
% 0.79/0.99 (~c1_1(a30)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[226, 2058])).
% 0.79/0.99 tff(2060,plain,
% 0.79/0.99 (c2_1(a30)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[234, 2058])).
% 0.79/0.99 tff(2061,plain,
% 0.79/0.99 (c3_1(a30)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[242, 2058])).
% 0.79/0.99 tff(2062,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1546, 2061, 2060, 487, 2057, 2059])).
% 0.79/0.99 tff(2063,plain,(hskp8 | (~c2_1(a20)) | (~c3_1(a20)) | (~c0_1(a20))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(2064,plain,
% 0.79/0.99 (hskp8),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2063, 2027, 2019, 2011])).
% 0.79/0.99 tff(2065,plain,
% 0.79/0.99 (c1_1(a13)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[293, 2064])).
% 0.79/0.99 tff(2066,plain,
% 0.79/0.99 (c3_1(a13)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1650, 1643, 2065])).
% 0.79/0.99 tff(2067,plain,
% 0.79/0.99 (hskp11),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1698, 1681, 2065, 2066])).
% 0.79/0.99 tff(2068,plain,
% 0.79/0.99 (~c3_1(a21)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[325, 2067])).
% 0.79/0.99 tff(2069,plain,
% 0.79/0.99 (~c2_1(a21)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[331, 2067])).
% 0.79/0.99 tff(2070,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a21)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2071,plain,
% 0.79/0.99 ((hskp12 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | c3_1(a21) | c2_1(a21) | (~c1_1(a21))) <=> (hskp12 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a21)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2072,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | c3_1(a21) | c2_1(a21) | (~c1_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a21))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[2071])).
% 0.79/0.99 tff(2073,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | c3_1(a21) | c2_1(a21) | (~c1_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a21)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[2072, 2070])).
% 0.79/0.99 tff(2074,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | c3_1(a21) | c2_1(a21) | (~c1_1(a21)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(2075,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp12 | c2_1(a21) | c3_1(a21) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a21))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 0.79/0.99 tff(2076,plain,
% 0.79/0.99 (~c1_1(a21)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2075, 108, 1643, 2011, 2027, 2019, 2069, 2068, 275])).
% 0.79/0.99 tff(2077,plain,
% 0.79/0.99 (c2_1(a13)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1826, 2064])).
% 0.79/0.99 tff(2078,plain,
% 0.79/0.99 (c0_1(a21)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[356, 2067])).
% 0.79/0.99 tff(2079,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1816, 108, 2078, 2065, 2077, 2068, 244, 255, 2066, 2076])).
% 0.79/0.99 tff(2080,plain,(hskp12 | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.99 tff(2081,plain,
% 0.79/0.99 (hskp12),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2080, 244])).
% 0.79/0.99 tff(2082,plain,
% 0.79/0.99 (~c2_1(a24)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[186, 2081])).
% 0.79/0.99 tff(2083,plain,
% 0.79/0.99 (c3_1(a24)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[194, 2081])).
% 0.79/0.99 tff(2084,plain,
% 0.79/0.99 (((~![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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | (~c3_1(a24)) | c0_1(a24))) <=> ((~![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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | (~c3_1(a24)) | c0_1(a24))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2085,plain,
% 0.79/0.99 (((~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c3_1(a24))) <=> (c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | (~c3_1(a24)) | c0_1(a24))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2086,plain,
% 0.79/0.99 (((~![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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c3_1(a24)))) <=> ((~![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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | (~c3_1(a24)) | c0_1(a24)))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[2085])).
% 0.79/0.99 tff(2087,plain,
% 0.79/0.99 (((~![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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c3_1(a24)))) <=> ((~![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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | (~c3_1(a24)) | c0_1(a24))),
% 0.79/0.99 inference(transitivity,[status(thm)],[2086, 2084])).
% 0.79/0.99 tff(2088,plain,
% 0.79/0.99 ((~![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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c3_1(a24)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(2089,plain,
% 0.79/0.99 ((~![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)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | (~c3_1(a13)) | (~c2_1(a13)) | (~c3_1(a24)) | c0_1(a24)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2088, 2087])).
% 0.79/0.99 tff(2090,plain,
% 0.79/0.99 (~c3_1(a13)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2089, 108, 2083, 2065, 2077, 2082, 244, 265, 245])).
% 0.79/0.99 tff(2091,plain,
% 0.79/0.99 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.79/0.99 inference(bind,[status(th)],[])).
% 0.79/0.99 tff(2092,plain,
% 0.79/0.99 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.79/0.99 inference(quant_intro,[status(thm)],[2091])).
% 0.79/0.99 tff(2093,plain,
% 0.79/0.99 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2094,plain,
% 0.79/0.99 (^[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))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.79/1.00 inference(bind,[status(th)],[])).
% 0.79/1.00 tff(2095,plain,
% 0.79/1.00 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.79/1.00 inference(quant_intro,[status(thm)],[2094])).
% 0.79/1.00 tff(2096,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.79/1.00 tff(2097,plain,
% 0.79/1.00 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2096, 2095])).
% 0.79/1.00 tff(2098,plain,
% 0.79/1.00 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2097, 2093])).
% 0.79/1.00 tff(2099,plain,(
% 0.79/1.00 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.79/1.00 inference(skolemize,[status(sab)],[2098])).
% 0.79/1.00 tff(2100,plain,
% 0.79/1.00 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2099, 2092])).
% 0.79/1.00 tff(2101,plain,
% 0.79/1.00 (c1_1(a24)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[202, 2081])).
% 0.79/1.00 tff(2102,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13) | (~c1_1(a24)) | c0_1(a24))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13) | (~c1_1(a24)) | c0_1(a24))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2103,plain,
% 0.79/1.00 ((hskp6 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24))) <=> (hskp6 | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13) | (~c1_1(a24)) | c0_1(a24))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2104,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13) | (~c1_1(a24)) | c0_1(a24)))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2103])).
% 0.79/1.00 tff(2105,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13) | (~c1_1(a24)) | c0_1(a24))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2104, 2102])).
% 0.79/1.00 tff(2106,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c1_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2107,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a24) | c0_1(a13) | (~ndr1_0) | (~c1_1(a13)) | c3_1(a13) | (~c1_1(a24)) | c0_1(a24)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 0.79/1.00 tff(2108,plain,
% 0.79/1.00 (hskp6),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2107, 108, 2101, 2065, 2082, 244, 2100, 2090, 245])).
% 0.79/1.00 tff(2109,plain,
% 0.79/1.00 (((~hskp6) | (~c3_1(a10))) <=> ((~hskp6) | (~c3_1(a10)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2110,plain,
% 0.79/1.00 (((~c3_1(a10)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a10)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2111,axiom,((~c3_1(a10)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.79/1.00 tff(2112,plain,
% 0.79/1.00 ((~hskp6) | (~c3_1(a10))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2111, 2110])).
% 0.79/1.00 tff(2113,plain,
% 0.79/1.00 ((~hskp6) | (~c3_1(a10))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2112, 2109])).
% 0.79/1.00 tff(2114,plain,
% 0.79/1.00 (~c3_1(a10)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2113, 2108])).
% 0.79/1.00 tff(2115,plain,
% 0.79/1.00 (((~hskp6) | (~c1_1(a10))) <=> ((~hskp6) | (~c1_1(a10)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2116,plain,
% 0.79/1.00 (((~c1_1(a10)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a10)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2117,axiom,((~c1_1(a10)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.79/1.00 tff(2118,plain,
% 0.79/1.00 ((~hskp6) | (~c1_1(a10))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2117, 2116])).
% 0.79/1.00 tff(2119,plain,
% 0.79/1.00 ((~hskp6) | (~c1_1(a10))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2118, 2115])).
% 0.79/1.00 tff(2120,plain,
% 0.79/1.00 (~c1_1(a10)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2119, 2108])).
% 0.79/1.00 tff(2121,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a13) | c1_1(a10) | c3_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a13) | c1_1(a10) | c3_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2122,plain,
% 0.79/1.00 (((~ndr1_0) | c1_1(a10) | c3_1(a10) | (~c0_1(a10)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13))) <=> (c0_1(a13) | c1_1(a10) | c3_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2123,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a10) | c3_1(a10) | (~c0_1(a10)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a13) | c1_1(a10) | c3_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24)))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2122])).
% 0.79/1.00 tff(2124,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a10) | c3_1(a10) | (~c0_1(a10)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a13) | c1_1(a10) | c3_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2123, 2121])).
% 0.79/1.00 tff(2125,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a10) | c3_1(a10) | (~c0_1(a10)) | c0_1(a24) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a13) | (~c2_1(a13)) | (~c1_1(a13)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2126,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a13) | c1_1(a10) | c3_1(a10) | (~ndr1_0) | (~c0_1(a10)) | (~c1_1(a13)) | (~c2_1(a13)) | (~c1_1(a24)) | (~c3_1(a24)) | c0_1(a24)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2125, 2124])).
% 0.79/1.00 tff(2127,plain,
% 0.79/1.00 (~c0_1(a10)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2126, 108, 2101, 2083, 2065, 2077, 244, 2120, 2114, 255, 245])).
% 0.79/1.00 tff(2128,plain,
% 0.79/1.00 (((~hskp6) | c2_1(a10)) <=> ((~hskp6) | c2_1(a10))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2129,axiom,((~hskp6) | c2_1(a10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.79/1.00 tff(2130,plain,
% 0.79/1.00 ((~hskp6) | c2_1(a10)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2129, 2128])).
% 0.79/1.00 tff(2131,plain,
% 0.79/1.00 ((~hskp6) | c2_1(a10)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2130, 2128])).
% 0.79/1.00 tff(2132,plain,
% 0.79/1.00 ((~hskp6) | c2_1(a10)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2131, 2128])).
% 0.79/1.00 tff(2133,plain,
% 0.79/1.00 ((~hskp6) | c2_1(a10)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2132, 2128])).
% 0.79/1.00 tff(2134,plain,
% 0.79/1.00 ((~hskp6) | c2_1(a10)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2133, 2128])).
% 0.79/1.00 tff(2135,plain,
% 0.79/1.00 (c2_1(a10)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2134, 2108])).
% 0.79/1.00 tff(2136,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a24) | c0_1(a13) | c1_1(a10) | (~ndr1_0) | c0_1(a10) | (~c2_1(a10)) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a24)) | c0_1(a24))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a24) | c0_1(a13) | c1_1(a10) | (~ndr1_0) | c0_1(a10) | (~c2_1(a10)) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a24)) | c0_1(a24))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2137,plain,
% 0.79/1.00 (((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)) | c1_1(a10) | c0_1(a10) | (~c2_1(a10))) <=> (c2_1(a24) | c0_1(a13) | c1_1(a10) | (~ndr1_0) | c0_1(a10) | (~c2_1(a10)) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a24)) | c0_1(a24))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2138,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)) | c1_1(a10) | c0_1(a10) | (~c2_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a24) | c0_1(a13) | c1_1(a10) | (~ndr1_0) | c0_1(a10) | (~c2_1(a10)) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a24)) | c0_1(a24)))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2137])).
% 0.79/1.00 tff(2139,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)) | c1_1(a10) | c0_1(a10) | (~c2_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a24) | c0_1(a13) | c1_1(a10) | (~ndr1_0) | c0_1(a10) | (~c2_1(a10)) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a24)) | c0_1(a24))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2138, 2136])).
% 0.79/1.00 tff(2140,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a13) | c3_1(a13) | (~c2_1(a13)) | c0_1(a24) | c2_1(a24) | (~c1_1(a24)) | c1_1(a10) | c0_1(a10) | (~c2_1(a10)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2141,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a24) | c0_1(a13) | c1_1(a10) | (~ndr1_0) | c0_1(a10) | (~c2_1(a10)) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a24)) | c0_1(a24)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 0.79/1.00 tff(2142,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2141, 108, 2101, 2077, 2135, 2082, 244, 2120, 1899, 2090, 245, 2127])).
% 0.79/1.00 tff(2143,plain,(c0_1(a24) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(2144,plain,
% 0.79/1.00 (c0_1(a24)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2143, 244])).
% 0.79/1.00 tff(2145,plain,
% 0.79/1.00 (hskp16),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[211, 2081])).
% 0.79/1.00 tff(2146,plain,
% 0.79/1.00 (~c1_1(a30)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[226, 2145])).
% 0.79/1.00 tff(2147,plain,
% 0.79/1.00 (c3_1(a30)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[242, 2145])).
% 0.79/1.00 tff(2148,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a30) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c3_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a30) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c3_1(a30)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2149,plain,
% 0.79/1.00 (((~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30))) <=> (c1_1(a30) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c3_1(a30)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2150,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | (c1_1(a30) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c3_1(a30))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2149])).
% 0.79/1.00 tff(2151,plain,
% 0.79/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a30) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c3_1(a30)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2150, 2148])).
% 0.79/1.00 tff(2152,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | c1_1(a30) | (~c3_1(a30)) | (~c0_1(a30)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2153,plain,
% 0.79/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)) | (~c0_1(W)))) | c1_1(a30) | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)) | (~c0_1(a30)) | (~c3_1(a30))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2152, 2151])).
% 0.79/1.00 tff(2154,plain,
% 0.79/1.00 ((~c0_1(a24)) | (~c0_1(a30))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2153, 108, 2011, 2027, 2019, 2147, 2101, 2083, 2146, 1859])).
% 0.79/1.00 tff(2155,plain,
% 0.79/1.00 (~c0_1(a30)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2154, 2144])).
% 0.79/1.00 tff(2156,plain,
% 0.79/1.00 (c2_1(a30)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[234, 2145])).
% 0.79/1.00 tff(2157,plain,
% 0.79/1.00 (hskp15 | (~c0_1(a24))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1874, 108, 2156, 2147, 2101, 2146, 2082, 349])).
% 0.79/1.00 tff(2158,plain,
% 0.79/1.00 (hskp15),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2157, 2144])).
% 0.79/1.00 tff(2159,plain,
% 0.79/1.00 (c1_1(a29)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[124, 2158])).
% 0.79/1.00 tff(2160,plain,
% 0.79/1.00 (~c3_1(a29)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[130, 2158])).
% 0.79/1.00 tff(2161,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2162,plain,
% 0.79/1.00 ((hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24))) <=> (hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2163,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2162])).
% 0.79/1.00 tff(2164,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2163, 2161])).
% 0.79/1.00 tff(2165,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a20)) | (~c2_1(a20)) | (~c0_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2166,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c2_1(a20)) | (~c0_1(a20)) | (~c3_1(a20)) | (~c1_1(a24)) | (~c3_1(a24)) | (~c0_1(a24))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 0.79/1.00 tff(2167,plain,
% 0.79/1.00 (hskp21 | (~c0_1(a24))),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2166, 108, 2011, 2027, 2019, 2101, 2083, 2048])).
% 0.79/1.00 tff(2168,plain,
% 0.79/1.00 (hskp21),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2167, 2144])).
% 0.79/1.00 tff(2169,plain,
% 0.79/1.00 (~c2_1(a29)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[136, 2158])).
% 0.79/1.00 tff(2170,plain,
% 0.79/1.00 (~c0_1(a29)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[159, 2169, 2168, 2160, 2159])).
% 0.79/1.00 tff(2171,plain,
% 0.79/1.00 (~c3_1(a39)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[58, 2168])).
% 0.79/1.00 tff(2172,plain,
% 0.79/1.00 (~c0_1(a39)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[64, 2168])).
% 0.79/1.00 tff(2173,plain,
% 0.79/1.00 (c2_1(a39)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[72, 2168])).
% 0.79/1.00 tff(2174,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1908, 108, 2173, 2156, 2159, 2172, 2171, 2146, 2169, 1899, 2170, 2155])).
% 0.79/1.00 tff(2175,plain,(c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(2176,plain,
% 0.79/1.00 (((~hskp8) | (~c0_1(a13))) <=> ((~hskp8) | (~c0_1(a13)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2177,plain,
% 0.79/1.00 (((~c0_1(a13)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a13)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2178,axiom,((~c0_1(a13)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.79/1.00 tff(2179,plain,
% 0.79/1.00 ((~hskp8) | (~c0_1(a13))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 0.79/1.00 tff(2180,plain,
% 0.79/1.00 ((~hskp8) | (~c0_1(a13))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2179, 2176])).
% 0.79/1.00 tff(2181,plain,
% 0.79/1.00 (~hskp8),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2180, 2175])).
% 0.79/1.00 tff(2182,plain,
% 0.79/1.00 ((~hskp21) | (~c2_1(a30)) | (~c3_1(a30)) | c1_1(a30)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1546, 2181])).
% 0.79/1.00 tff(2183,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2182, 243, 235, 42, 227])).
% 0.79/1.00 tff(2184,plain,(~hskp21), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(2185,plain,
% 0.79/1.00 (hskp5),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1444, 1436, 2184])).
% 0.79/1.00 tff(2186,plain,
% 0.79/1.00 (~c2_1(a9)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1450, 2185])).
% 0.79/1.00 tff(2187,plain,
% 0.79/1.00 (~c0_1(a9)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1456, 2185])).
% 0.79/1.00 tff(2188,plain,
% 0.79/1.00 (~c3_1(a9)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1463, 108, 1, 1283, 2187, 2186, 41])).
% 0.79/1.00 tff(2189,plain,
% 0.79/1.00 (~c1_1(a9)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1470, 2185])).
% 0.79/1.00 tff(2190,assumption,(hskp31), introduced(assumption)).
% 0.79/1.00 tff(2191,plain,
% 0.79/1.00 (((~hskp31) | c3_1(a76)) <=> ((~hskp31) | c3_1(a76))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2192,axiom,((~hskp31) | c3_1(a76)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.79/1.00 tff(2193,plain,
% 0.79/1.00 ((~hskp31) | c3_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 0.79/1.00 tff(2194,plain,
% 0.79/1.00 ((~hskp31) | c3_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2193, 2191])).
% 0.79/1.00 tff(2195,plain,
% 0.79/1.00 ((~hskp31) | c3_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2194, 2191])).
% 0.79/1.00 tff(2196,plain,
% 0.79/1.00 ((~hskp31) | c3_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2195, 2191])).
% 0.79/1.00 tff(2197,plain,
% 0.79/1.00 ((~hskp31) | c3_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2196, 2191])).
% 0.79/1.00 tff(2198,plain,
% 0.79/1.00 (c3_1(a76)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2197, 2190])).
% 0.79/1.00 tff(2199,plain,
% 0.79/1.00 (((~hskp31) | c1_1(a76)) <=> ((~hskp31) | c1_1(a76))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2200,axiom,((~hskp31) | c1_1(a76)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.79/1.00 tff(2201,plain,
% 0.79/1.00 ((~hskp31) | c1_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2200, 2199])).
% 0.79/1.00 tff(2202,plain,
% 0.79/1.00 ((~hskp31) | c1_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2201, 2199])).
% 0.79/1.00 tff(2203,plain,
% 0.79/1.00 ((~hskp31) | c1_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2202, 2199])).
% 0.79/1.00 tff(2204,plain,
% 0.79/1.00 ((~hskp31) | c1_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2203, 2199])).
% 0.79/1.00 tff(2205,plain,
% 0.79/1.00 ((~hskp31) | c1_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2204, 2199])).
% 0.79/1.00 tff(2206,plain,
% 0.79/1.00 (c1_1(a76)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2205, 2190])).
% 0.79/1.00 tff(2207,plain,
% 0.79/1.00 (((~hskp31) | c0_1(a76)) <=> ((~hskp31) | c0_1(a76))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2208,axiom,((~hskp31) | c0_1(a76)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 0.79/1.00 tff(2209,plain,
% 0.79/1.00 ((~hskp31) | c0_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2208, 2207])).
% 0.79/1.00 tff(2210,plain,
% 0.79/1.00 ((~hskp31) | c0_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2209, 2207])).
% 0.79/1.00 tff(2211,plain,
% 0.79/1.00 ((~hskp31) | c0_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2210, 2207])).
% 0.79/1.00 tff(2212,plain,
% 0.79/1.00 ((~hskp31) | c0_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2211, 2207])).
% 0.79/1.00 tff(2213,plain,
% 0.79/1.00 ((~hskp31) | c0_1(a76)),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2212, 2207])).
% 0.79/1.00 tff(2214,plain,
% 0.79/1.00 (c0_1(a76)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2213, 2190])).
% 0.79/1.00 tff(2215,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c1_1(a76)) | (~c0_1(a76)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c1_1(a76)) | (~c0_1(a76)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2216,plain,
% 0.79/1.00 ((hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c0_1(a76)) | (~c1_1(a76)) | (~c3_1(a76)) | (~c0_1(a76))) <=> (hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c1_1(a76)) | (~c0_1(a76)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2217,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c0_1(a76)) | (~c1_1(a76)) | (~c3_1(a76)) | (~c0_1(a76)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c1_1(a76)) | (~c0_1(a76))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2216])).
% 0.79/1.00 tff(2218,plain,
% 0.79/1.00 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c0_1(a76)) | (~c1_1(a76)) | (~c3_1(a76)) | (~c0_1(a76)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c1_1(a76)) | (~c0_1(a76)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2217, 2215])).
% 0.79/1.00 tff(2219,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c0_1(a76)) | (~c1_1(a76)) | (~c3_1(a76)) | (~c0_1(a76)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2220,plain,
% 0.79/1.00 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | (~ndr1_0) | (~c3_1(a76)) | (~c2_1(a76)) | (~c1_1(a76)) | (~c0_1(a76))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2219, 2218])).
% 0.79/1.00 tff(2221,plain,
% 0.79/1.00 (~c2_1(a76)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2220, 108, 2184, 2214, 2206, 2198, 2048])).
% 0.79/1.00 tff(2222,plain,
% 0.79/1.00 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | (~c3_1(a76)) | c2_1(a76) | (~c1_1(a76)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | (~ndr1_0) | (~c3_1(a76)) | c2_1(a76) | (~c1_1(a76)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2223,plain,
% 0.79/1.00 ((hskp16 | (~ndr1_0) | c2_1(a76) | (~c1_1(a76)) | (~c3_1(a76))) <=> (hskp16 | (~ndr1_0) | (~c3_1(a76)) | c2_1(a76) | (~c1_1(a76)))),
% 0.79/1.00 inference(rewrite,[status(thm)],[])).
% 0.79/1.00 tff(2224,plain,
% 0.79/1.00 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a76) | (~c1_1(a76)) | (~c3_1(a76)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | (~c3_1(a76)) | c2_1(a76) | (~c1_1(a76))))),
% 0.79/1.00 inference(monotonicity,[status(thm)],[2223])).
% 0.79/1.00 tff(2225,plain,
% 0.79/1.00 (((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a76) | (~c1_1(a76)) | (~c3_1(a76)))) <=> ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | (~ndr1_0) | (~c3_1(a76)) | c2_1(a76) | (~c1_1(a76)))),
% 0.79/1.00 inference(transitivity,[status(thm)],[2224, 2222])).
% 0.79/1.00 tff(2226,plain,
% 0.79/1.00 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp16 | (~ndr1_0) | c2_1(a76) | (~c1_1(a76)) | (~c3_1(a76)))),
% 0.79/1.00 inference(quant_inst,[status(thm)],[])).
% 0.79/1.00 tff(2227,plain,
% 0.79/1.00 ((~![U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp16 | (~ndr1_0) | (~c3_1(a76)) | c2_1(a76) | (~c1_1(a76))),
% 0.79/1.00 inference(modus_ponens,[status(thm)],[2226, 2225])).
% 0.79/1.00 tff(2228,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2227, 108, 43, 2206, 2198, 180, 2221])).
% 0.79/1.00 tff(2229,plain,((~hskp31) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(2230,plain,
% 0.79/1.00 (~hskp31),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2229, 43])).
% 0.79/1.00 tff(2231,plain,
% 0.79/1.00 (hskp24),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[106, 2230, 212])).
% 0.79/1.00 tff(2232,plain,
% 0.79/1.00 (hskp11),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1435, 2231, 1])).
% 0.79/1.00 tff(2233,plain,
% 0.79/1.00 (~c3_1(a21)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[325, 2232])).
% 0.79/1.00 tff(2234,plain,
% 0.79/1.00 (~c2_1(a21)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[331, 2232])).
% 0.79/1.00 tff(2235,plain,
% 0.79/1.00 ((~hskp3) | hskp30 | hskp9 | hskp16),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1281, 2181])).
% 0.79/1.00 tff(2236,plain,
% 0.79/1.00 (hskp9),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2235, 1276, 1, 43])).
% 0.79/1.00 tff(2237,plain,
% 0.79/1.00 (~c3_1(a15)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[994, 2236])).
% 0.79/1.00 tff(2238,plain,
% 0.79/1.00 (~c2_1(a15)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[470, 2236])).
% 0.79/1.00 tff(2239,plain,
% 0.79/1.00 (~c1_1(a15)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[464, 2236])).
% 0.79/1.00 tff(2240,plain,
% 0.79/1.00 (hskp16 | hskp30 | hskp2 | (~c0_1(a6)) | (~c3_1(a6)) | c2_1(a6)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1249, 2181])).
% 0.79/1.00 tff(2241,plain,
% 0.79/1.00 (hskp2),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2240, 1279, 1, 43, 1278, 1277])).
% 0.79/1.00 tff(2242,plain,
% 0.79/1.00 (~c0_1(a5)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1193, 2241])).
% 0.79/1.00 tff(2243,plain,
% 0.79/1.00 (~c1_1(a5)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1074, 2241])).
% 0.79/1.00 tff(2244,plain,
% 0.79/1.00 (c3_1(a15) | hskp30 | c1_1(a15) | c2_1(a15) | c0_1(a5) | c1_1(a5)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[831, 2181])).
% 0.79/1.00 tff(2245,plain,
% 0.79/1.00 ($false),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2244, 2243, 2242, 2239, 2238, 2237, 1])).
% 0.79/1.00 tff(2246,plain,((~hskp3) | hskp30 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.79/1.00 tff(2247,plain,
% 0.79/1.00 (~hskp3),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2246, 43, 1])).
% 0.79/1.00 tff(2248,plain,
% 0.79/1.00 ((~hskp25) | hskp21),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1366, 2181])).
% 0.79/1.00 tff(2249,plain,
% 0.79/1.00 (~hskp25),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[2248, 2184])).
% 0.79/1.00 tff(2250,plain,
% 0.79/1.00 (~c1_1(a21)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[1373, 108, 2249, 2247, 2234, 2233, 1333])).
% 0.79/1.00 tff(2251,plain,
% 0.79/1.00 (~c2_1(a52)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[681, 2231])).
% 0.79/1.00 tff(2252,plain,
% 0.79/1.00 (~c0_1(a52)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[687, 2231])).
% 0.79/1.00 tff(2253,plain,
% 0.79/1.00 (c0_1(a21)),
% 0.79/1.00 inference(unit_resolution,[status(thm)],[356, 2232])).
% 0.79/1.01 tff(2254,plain,
% 0.79/1.01 (c3_1(a52)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[695, 2231])).
% 0.79/1.01 tff(2255,plain,
% 0.79/1.01 ((~hskp10) | hskp30 | hskp16),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[534, 2181])).
% 0.79/1.01 tff(2256,plain,
% 0.79/1.01 (~hskp10),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2255, 43, 1])).
% 0.79/1.01 tff(2257,plain,
% 0.79/1.01 ($false),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[702, 108, 2256, 2254, 2253, 2252, 2251, 2233, 658, 2250])).
% 0.79/1.01 tff(2258,plain,(hskp16 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.79/1.01 tff(2259,plain,
% 0.79/1.01 (hskp16),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2258, 1])).
% 0.79/1.01 tff(2260,plain,
% 0.79/1.01 (~c1_1(a30)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[226, 2259])).
% 0.79/1.01 tff(2261,plain,
% 0.79/1.01 (c3_1(a30)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[242, 2259])).
% 0.79/1.01 tff(2262,plain,
% 0.79/1.01 (c2_1(a30)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[234, 2259])).
% 0.79/1.01 tff(2263,plain,
% 0.79/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a30) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c2_1(a30)) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2264,plain,
% 0.79/1.01 ((hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a9) | c1_1(a9) | c2_1(a9)) <=> (hskp8 | c1_1(a30) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2265,plain,
% 0.79/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a9) | c1_1(a9) | c2_1(a9))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | c1_1(a30) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c2_1(a30)) | (~c3_1(a30))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2264])).
% 0.79/1.01 tff(2266,plain,
% 0.79/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a9) | c1_1(a9) | c2_1(a9))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c2_1(a30)) | (~c3_1(a30)))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2265, 2263])).
% 0.79/1.01 tff(2267,plain,
% 0.79/1.01 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp8 | (~ndr1_0) | c1_1(a30) | (~c3_1(a30)) | (~c2_1(a30)) | c3_1(a9) | c1_1(a9) | c2_1(a9))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(2268,plain,
% 0.79/1.01 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp8 | c1_1(a30) | c1_1(a9) | c2_1(a9) | (~ndr1_0) | c3_1(a9) | (~c2_1(a30)) | (~c3_1(a30))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 0.79/1.01 tff(2269,plain,
% 0.79/1.01 ($false),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2268, 108, 2181, 2262, 2261, 2260, 2189, 2186, 31, 2188])).
% 0.79/1.01 tff(2270,plain,(hskp11 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.79/1.01 tff(2271,plain,
% 0.79/1.01 (hskp11),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2270, 1])).
% 0.79/1.01 tff(2272,plain,
% 0.79/1.01 (~c3_1(a21)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[325, 2271])).
% 0.79/1.01 tff(2273,plain,
% 0.79/1.01 (~c2_1(a21)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[331, 2271])).
% 0.79/1.01 tff(2274,plain,
% 0.79/1.01 (c1_1(a21)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[338, 108, 2181, 2262, 2261, 2260, 2273, 2272, 31])).
% 0.79/1.01 tff(2275,plain,
% 0.79/1.01 (~c0_1(a30)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[431, 108, 2184, 2181, 2261, 2260, 21])).
% 0.79/1.01 tff(2276,plain,
% 0.79/1.01 (c0_1(a21)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[356, 2271])).
% 0.79/1.01 tff(2277,plain,
% 0.79/1.01 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a30) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a30) | (~c3_1(a30)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2278,plain,
% 0.79/1.01 ((hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | c0_1(a30) | (~c3_1(a30))) <=> (hskp3 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a30) | (~c3_1(a30)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2279,plain,
% 0.79/1.01 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | c0_1(a30) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a30) | (~c3_1(a30))))),
% 0.79/1.01 inference(monotonicity,[status(thm)],[2278])).
% 0.79/1.01 tff(2280,plain,
% 0.79/1.01 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | c0_1(a30) | (~c3_1(a30)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a30) | (~c3_1(a30)))),
% 0.79/1.01 inference(transitivity,[status(thm)],[2279, 2277])).
% 0.79/1.01 tff(2281,plain,
% 0.79/1.01 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a21) | (~c1_1(a21)) | (~c0_1(a21)) | c1_1(a30) | c0_1(a30) | (~c3_1(a30)))),
% 0.79/1.01 inference(quant_inst,[status(thm)],[])).
% 0.79/1.01 tff(2282,plain,
% 0.79/1.01 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a30) | c2_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | c0_1(a30) | (~c3_1(a30))),
% 0.79/1.01 inference(modus_ponens,[status(thm)],[2281, 2280])).
% 0.79/1.01 tff(2283,plain,
% 0.79/1.01 (hskp3 | (~c1_1(a21))),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2282, 108, 2261, 2276, 2260, 2273, 396, 2275])).
% 0.79/1.01 tff(2284,plain,
% 0.79/1.01 (hskp3),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[2283, 2274])).
% 0.79/1.01 tff(2285,plain,
% 0.79/1.01 (c3_1(a6)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[411, 2284])).
% 0.79/1.01 tff(2286,plain,
% 0.79/1.01 (c0_1(a6)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[419, 2284])).
% 0.79/1.01 tff(2287,plain,
% 0.79/1.01 (c1_1(a6)),
% 0.79/1.01 inference(unit_resolution,[status(thm)],[423, 108, 2184, 2181, 2286, 2285, 21])).
% 0.79/1.01 tff(2288,plain,
% 0.79/1.01 (^[U: $i] : refl((hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(2289,plain,
% 0.79/1.01 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[2288])).
% 0.79/1.01 tff(2290,plain,
% 0.79/1.01 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/1.01 inference(rewrite,[status(thm)],[])).
% 0.79/1.01 tff(2291,plain,
% 0.79/1.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp19) <=> ((hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp19))), rewrite(((hskp29 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp19) <=> (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.79/1.01 inference(bind,[status(th)],[])).
% 0.79/1.01 tff(2292,plain,
% 0.79/1.01 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp19) <=> ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/1.01 inference(quant_intro,[status(thm)],[2291])).
% 0.85/1.01 tff(2293,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp29) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.85/1.01 tff(2294,plain,
% 0.85/1.01 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 0.85/1.01 tff(2295,plain,
% 0.85/1.01 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2294, 2290])).
% 0.85/1.01 tff(2296,plain,(
% 0.85/1.01 ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.01 inference(skolemize,[status(sab)],[2295])).
% 0.85/1.01 tff(2297,plain,
% 0.85/1.01 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2296, 2289])).
% 0.85/1.01 tff(2298,plain,
% 0.85/1.01 ((~hskp19) | hskp30),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[1716, 2181])).
% 0.85/1.01 tff(2299,plain,
% 0.85/1.01 (~hskp19),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2298, 1])).
% 0.85/1.01 tff(2300,plain,
% 0.85/1.01 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2301,plain,
% 0.85/1.01 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(2302,plain,
% 0.85/1.01 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2301, 2300])).
% 0.85/1.01 tff(2303,plain,
% 0.85/1.01 (hskp29 | (~c1_1(a6))),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2302, 108, 2299, 2286, 2285, 2297])).
% 0.85/1.01 tff(2304,plain,
% 0.85/1.01 (hskp29),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2303, 2287])).
% 0.85/1.01 tff(2305,plain,
% 0.85/1.01 (((~hskp29) | c3_1(a8)) <=> ((~hskp29) | c3_1(a8))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2306,axiom,((~hskp29) | c3_1(a8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.85/1.01 tff(2307,plain,
% 0.85/1.01 ((~hskp29) | c3_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2306, 2305])).
% 0.85/1.01 tff(2308,plain,
% 0.85/1.01 ((~hskp29) | c3_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2307, 2305])).
% 0.85/1.01 tff(2309,plain,
% 0.85/1.01 ((~hskp29) | c3_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2308, 2305])).
% 0.85/1.01 tff(2310,plain,
% 0.85/1.01 ((~hskp29) | c3_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2309, 2305])).
% 0.85/1.01 tff(2311,plain,
% 0.85/1.01 ((~hskp29) | c3_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2310, 2305])).
% 0.85/1.01 tff(2312,plain,
% 0.85/1.01 (c3_1(a8)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2311, 2304])).
% 0.85/1.01 tff(2313,plain,
% 0.85/1.01 (((~hskp29) | c2_1(a8)) <=> ((~hskp29) | c2_1(a8))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2314,axiom,((~hskp29) | c2_1(a8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.85/1.01 tff(2315,plain,
% 0.85/1.01 ((~hskp29) | c2_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 0.85/1.01 tff(2316,plain,
% 0.85/1.01 ((~hskp29) | c2_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2315, 2313])).
% 0.85/1.01 tff(2317,plain,
% 0.85/1.01 ((~hskp29) | c2_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2316, 2313])).
% 0.85/1.01 tff(2318,plain,
% 0.85/1.01 ((~hskp29) | c2_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2317, 2313])).
% 0.85/1.01 tff(2319,plain,
% 0.85/1.01 ((~hskp29) | c2_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2318, 2313])).
% 0.85/1.01 tff(2320,plain,
% 0.85/1.01 (c2_1(a8)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2319, 2304])).
% 0.85/1.01 tff(2321,plain,
% 0.85/1.01 (((~hskp29) | c1_1(a8)) <=> ((~hskp29) | c1_1(a8))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2322,axiom,((~hskp29) | c1_1(a8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.85/1.01 tff(2323,plain,
% 0.85/1.01 ((~hskp29) | c1_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 0.85/1.01 tff(2324,plain,
% 0.85/1.01 ((~hskp29) | c1_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2323, 2321])).
% 0.85/1.01 tff(2325,plain,
% 0.85/1.01 ((~hskp29) | c1_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2324, 2321])).
% 0.85/1.01 tff(2326,plain,
% 0.85/1.01 ((~hskp29) | c1_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2325, 2321])).
% 0.85/1.01 tff(2327,plain,
% 0.85/1.01 ((~hskp29) | c1_1(a8)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2326, 2321])).
% 0.85/1.01 tff(2328,plain,
% 0.85/1.01 (c1_1(a8)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2327, 2304])).
% 0.85/1.01 tff(2329,plain,
% 0.85/1.01 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | (~c2_1(a8)) | (~c1_1(a8)) | (~c3_1(a8)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp25 | hskp9 | (~ndr1_0) | (~c2_1(a8)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2330,plain,
% 0.85/1.01 ((hskp25 | hskp9 | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c2_1(a8))) <=> (hskp25 | hskp9 | (~ndr1_0) | (~c2_1(a8)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2331,plain,
% 0.85/1.01 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c2_1(a8)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | (~c2_1(a8)) | (~c1_1(a8)) | (~c3_1(a8))))),
% 0.85/1.01 inference(monotonicity,[status(thm)],[2330])).
% 0.85/1.01 tff(2332,plain,
% 0.85/1.01 (((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c2_1(a8)))) <=> ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp25 | hskp9 | (~ndr1_0) | (~c2_1(a8)) | (~c1_1(a8)) | (~c3_1(a8)))),
% 0.85/1.01 inference(transitivity,[status(thm)],[2331, 2329])).
% 0.85/1.01 tff(2333,plain,
% 0.85/1.01 ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(a8)) | (~c3_1(a8)) | (~c2_1(a8)))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(2334,plain,
% 0.85/1.01 ((~![U: $i] : (hskp25 | hskp9 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))) | hskp25 | hskp9 | (~ndr1_0) | (~c2_1(a8)) | (~c1_1(a8)) | (~c3_1(a8))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2333, 2332])).
% 0.85/1.01 tff(2335,plain,
% 0.85/1.01 (hskp9),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2334, 108, 2249, 2328, 2320, 2312, 11])).
% 0.85/1.01 tff(2336,plain,
% 0.85/1.01 (~c3_1(a15)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[994, 2335])).
% 0.85/1.01 tff(2337,plain,
% 0.85/1.01 (hskp15 | (~c1_1(a21))),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[363, 108, 2262, 2261, 2276, 2260, 2273, 349])).
% 0.85/1.01 tff(2338,plain,
% 0.85/1.01 (hskp15),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2337, 2274])).
% 0.85/1.01 tff(2339,plain,
% 0.85/1.01 (c1_1(a29)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[124, 2338])).
% 0.85/1.01 tff(2340,plain,
% 0.85/1.01 (~c3_1(a29)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[130, 2338])).
% 0.85/1.01 tff(2341,plain,
% 0.85/1.01 (c0_1(a29)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[384, 108, 1, 2181, 2339, 2340, 378])).
% 0.85/1.01 tff(2342,assumption,(hskp0), introduced(assumption)).
% 0.85/1.01 tff(2343,plain,
% 0.85/1.01 (~c1_1(a1)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[1153, 2342])).
% 0.85/1.01 tff(2344,plain,
% 0.85/1.01 (c0_1(a1)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[1161, 2342])).
% 0.85/1.01 tff(2345,plain,
% 0.85/1.01 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c0_1(a1)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2346,plain,
% 0.85/1.01 ((hskp21 | hskp8 | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a1))) <=> (hskp21 | hskp8 | c1_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c0_1(a1)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2347,plain,
% 0.85/1.01 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | c1_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c0_1(a1))))),
% 0.85/1.01 inference(monotonicity,[status(thm)],[2346])).
% 0.85/1.01 tff(2348,plain,
% 0.85/1.01 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c0_1(a1)))),
% 0.85/1.01 inference(transitivity,[status(thm)],[2347, 2345])).
% 0.85/1.01 tff(2349,plain,
% 0.85/1.01 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp8 | (~ndr1_0) | c1_1(a1) | (~c3_1(a1)) | (~c0_1(a1)))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(2350,plain,
% 0.85/1.01 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp8 | c1_1(a1) | (~ndr1_0) | (~c3_1(a1)) | (~c0_1(a1))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2349, 2348])).
% 0.85/1.01 tff(2351,plain,
% 0.85/1.01 (~c3_1(a1)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2350, 108, 1358, 487, 2344, 2343, 21])).
% 0.85/1.01 tff(2352,plain,
% 0.85/1.01 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 0.85/1.01 inference(bind,[status(th)],[])).
% 0.85/1.01 tff(2353,plain,
% 0.85/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.85/1.01 inference(quant_intro,[status(thm)],[2352])).
% 0.85/1.01 tff(2354,plain,
% 0.85/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2355,plain,
% 0.85/1.01 (^[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(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) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | 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))) | (~ndr1_0)) | c3_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))) | (~ndr1_0)) | c3_1(U)) | 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)) | c1_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 0.85/1.01 inference(bind,[status(th)],[])).
% 0.85/1.01 tff(2356,plain,
% 0.85/1.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.85/1.01 inference(quant_intro,[status(thm)],[2355])).
% 0.85/1.01 tff(2357,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.85/1.01 tff(2358,plain,
% 0.85/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 0.85/1.01 tff(2359,plain,
% 0.85/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2358, 2354])).
% 0.85/1.01 tff(2360,plain,(
% 0.85/1.01 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.85/1.01 inference(skolemize,[status(sab)],[2359])).
% 0.85/1.01 tff(2361,plain,
% 0.85/1.01 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2360, 2353])).
% 0.85/1.01 tff(2362,plain,
% 0.85/1.01 (~c2_1(a1)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[1147, 2342])).
% 0.85/1.01 tff(2363,plain,
% 0.85/1.01 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp21 | c3_1(a29) | c1_1(a1) | c2_1(a1) | (~ndr1_0) | c3_1(a1) | (~c1_1(a29)) | (~c0_1(a29)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp21 | c3_1(a29) | c1_1(a1) | c2_1(a1) | (~ndr1_0) | c3_1(a1) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2364,plain,
% 0.85/1.01 ((hskp21 | (~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a1) | c1_1(a1) | c2_1(a1)) <=> (hskp21 | c3_1(a29) | c1_1(a1) | c2_1(a1) | (~ndr1_0) | c3_1(a1) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2365,plain,
% 0.85/1.01 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a1) | c1_1(a1) | c2_1(a1))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp21 | c3_1(a29) | c1_1(a1) | c2_1(a1) | (~ndr1_0) | c3_1(a1) | (~c1_1(a29)) | (~c0_1(a29))))),
% 0.85/1.01 inference(monotonicity,[status(thm)],[2364])).
% 0.85/1.01 tff(2366,plain,
% 0.85/1.01 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a1) | c1_1(a1) | c2_1(a1))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp21 | c3_1(a29) | c1_1(a1) | c2_1(a1) | (~ndr1_0) | c3_1(a1) | (~c1_1(a29)) | (~c0_1(a29)))),
% 0.85/1.01 inference(transitivity,[status(thm)],[2365, 2363])).
% 0.85/1.01 tff(2367,plain,
% 0.85/1.01 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp21 | (~ndr1_0) | c3_1(a29) | (~c1_1(a29)) | (~c0_1(a29)) | c3_1(a1) | c1_1(a1) | c2_1(a1))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(2368,plain,
% 0.85/1.01 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp21 | c3_1(a29) | c1_1(a1) | c2_1(a1) | (~ndr1_0) | c3_1(a1) | (~c1_1(a29)) | (~c0_1(a29))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2367, 2366])).
% 0.85/1.01 tff(2369,plain,
% 0.85/1.01 ($false),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2368, 108, 1358, 151, 149, 2343, 2362, 2361, 138, 2351])).
% 0.85/1.01 tff(2370,plain,((~hskp0) | hskp21 | (~c1_1(a29)) | c3_1(a29) | (~c0_1(a29)) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.85/1.01 tff(2371,plain,
% 0.85/1.01 ((~hskp0) | hskp21 | (~c1_1(a29)) | c3_1(a29) | (~c0_1(a29))),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2370, 2181])).
% 0.85/1.01 tff(2372,plain,
% 0.85/1.01 (~hskp0),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[2371, 2341, 2184, 2340, 2339])).
% 0.85/1.01 tff(2373,plain,
% 0.85/1.01 (^[U: $i] : refl((hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 0.85/1.01 inference(bind,[status(th)],[])).
% 0.85/1.01 tff(2374,plain,
% 0.85/1.01 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.01 inference(quant_intro,[status(thm)],[2373])).
% 0.85/1.01 tff(2375,plain,
% 0.85/1.01 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2376,plain,
% 0.85/1.01 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp2) <=> ((hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp2))), rewrite(((hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp2) <=> (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp2) <=> (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.85/1.01 inference(bind,[status(th)],[])).
% 0.85/1.01 tff(2377,plain,
% 0.85/1.01 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp2) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.01 inference(quant_intro,[status(thm)],[2376])).
% 0.85/1.01 tff(2378,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp0) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.85/1.01 tff(2379,plain,
% 0.85/1.01 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2378, 2377])).
% 0.85/1.01 tff(2380,plain,
% 0.85/1.01 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2379, 2375])).
% 0.85/1.01 tff(2381,plain,(
% 0.85/1.01 ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.01 inference(skolemize,[status(sab)],[2380])).
% 0.85/1.01 tff(2382,plain,
% 0.85/1.01 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[2381, 2374])).
% 0.85/1.01 tff(2383,plain,
% 0.85/1.01 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp2 | hskp0 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(2384,plain,
% 0.85/1.01 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(2385,plain,
% 0.85/1.02 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp2 | hskp0 | (~ndr1_0) | (~c1_1(a6)) | (~c3_1(a6)) | (~c0_1(a6))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 0.85/1.02 tff(2386,plain,
% 0.85/1.02 (hskp2 | hskp0 | (~c1_1(a6))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2385, 108, 2286, 2285, 2382])).
% 0.85/1.02 tff(2387,plain,
% 0.85/1.02 (hskp2),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2386, 2372, 2287])).
% 0.85/1.02 tff(2388,plain,
% 0.85/1.02 (~c1_1(a5)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1074, 2387])).
% 0.85/1.02 tff(2389,plain,
% 0.85/1.02 (~c0_1(a5)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[1193, 2387])).
% 0.85/1.02 tff(2390,plain,
% 0.85/1.02 (~c1_1(a15)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[464, 2335])).
% 0.85/1.02 tff(2391,plain,
% 0.85/1.02 (~c2_1(a15)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[470, 2335])).
% 0.85/1.02 tff(2392,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2244, 2391, 2390, 2389, 2388, 2336, 1])).
% 0.85/1.02 tff(2393,plain,(hskp30), inference(lemma,lemma(discharge,[]))).
% 0.85/1.02 tff(2394,plain,
% 0.85/1.02 (c0_1(a20)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2010, 2393])).
% 0.85/1.02 tff(2395,plain,
% 0.85/1.02 (c2_1(a20)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2026, 2393])).
% 0.85/1.02 tff(2396,plain,
% 0.85/1.02 (c3_1(a20)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2018, 2393])).
% 0.85/1.02 tff(2397,plain,
% 0.85/1.02 ((~c2_1(a20)) | (~c3_1(a20)) | (~c0_1(a20))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2063, 2181])).
% 0.85/1.02 tff(2398,plain,
% 0.85/1.02 ($false),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[2397, 2396, 2395, 2394])).
% 0.85/1.02 % SZS output end Proof
% 0.85/1.02 % E exiting
%------------------------------------------------------------------------------