%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN498-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:39:21 AM UTC 2025
% Result : Unsatisfiable 1.29s 1.47s
% Output : Proof 1.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SYN498-1 : TPTP v9.0.0. Released v2.1.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:37:17 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.29/1.47 % SZS status Unsatisfiable
% 1.29/1.47 % SZS output start Proof
% 1.29/1.47 tff(c0_1_type, type, (
% 1.29/1.47 c0_1: $i > $o)).
% 1.29/1.47 tff(a20_type, type, (
% 1.29/1.47 a20: $i)).
% 1.29/1.47 tff(c2_1_type, type, (
% 1.29/1.47 c2_1: $i > $o)).
% 1.29/1.47 tff(a16_type, type, (
% 1.29/1.47 a16: $i)).
% 1.29/1.47 tff(a3_type, type, (
% 1.29/1.47 a3: $i)).
% 1.29/1.47 tff(a37_type, type, (
% 1.29/1.47 a37: $i)).
% 1.29/1.47 tff(c1_1_type, type, (
% 1.29/1.47 c1_1: $i > $o)).
% 1.29/1.47 tff(c3_1_type, type, (
% 1.29/1.47 c3_1: $i > $o)).
% 1.29/1.47 tff(ndr1_0_type, type, (
% 1.29/1.47 ndr1_0: $o)).
% 1.29/1.47 tff(hskp3_type, type, (
% 1.29/1.47 hskp3: $o)).
% 1.29/1.47 tff(hskp24_type, type, (
% 1.29/1.47 hskp24: $o)).
% 1.29/1.47 tff(hskp20_type, type, (
% 1.29/1.47 hskp20: $o)).
% 1.29/1.47 tff(hskp28_type, type, (
% 1.29/1.47 hskp28: $o)).
% 1.29/1.47 tff(hskp0_type, type, (
% 1.29/1.47 hskp0: $o)).
% 1.29/1.47 tff(a21_type, type, (
% 1.29/1.47 a21: $i)).
% 1.29/1.47 tff(hskp13_type, type, (
% 1.29/1.47 hskp13: $o)).
% 1.29/1.47 tff(hskp21_type, type, (
% 1.29/1.47 hskp21: $o)).
% 1.29/1.47 tff(hskp6_type, type, (
% 1.29/1.47 hskp6: $o)).
% 1.29/1.47 tff(hskp1_type, type, (
% 1.29/1.47 hskp1: $o)).
% 1.29/1.47 tff(a2_type, type, (
% 1.29/1.47 a2: $i)).
% 1.29/1.47 tff(a13_type, type, (
% 1.29/1.47 a13: $i)).
% 1.29/1.47 tff(a58_type, type, (
% 1.29/1.47 a58: $i)).
% 1.29/1.47 tff(a7_type, type, (
% 1.29/1.47 a7: $i)).
% 1.29/1.47 tff(hskp2_type, type, (
% 1.29/1.47 hskp2: $o)).
% 1.29/1.47 tff(a1_type, type, (
% 1.29/1.47 a1: $i)).
% 1.29/1.47 tff(hskp14_type, type, (
% 1.29/1.47 hskp14: $o)).
% 1.29/1.47 tff(hskp29_type, type, (
% 1.29/1.47 hskp29: $o)).
% 1.29/1.47 tff(hskp26_type, type, (
% 1.29/1.47 hskp26: $o)).
% 1.29/1.47 tff(a11_type, type, (
% 1.29/1.47 a11: $i)).
% 1.29/1.47 tff(hskp5_type, type, (
% 1.29/1.47 hskp5: $o)).
% 1.29/1.47 tff(a31_type, type, (
% 1.29/1.47 a31: $i)).
% 1.29/1.47 tff(hskp18_type, type, (
% 1.29/1.47 hskp18: $o)).
% 1.29/1.47 tff(a38_type, type, (
% 1.29/1.47 a38: $i)).
% 1.29/1.47 tff(a15_type, type, (
% 1.29/1.47 a15: $i)).
% 1.29/1.47 tff(a18_type, type, (
% 1.29/1.47 a18: $i)).
% 1.29/1.47 tff(a25_type, type, (
% 1.29/1.47 a25: $i)).
% 1.29/1.47 tff(hskp27_type, type, (
% 1.29/1.47 hskp27: $o)).
% 1.29/1.47 tff(a12_type, type, (
% 1.29/1.47 a12: $i)).
% 1.29/1.47 tff(hskp10_type, type, (
% 1.29/1.47 hskp10: $o)).
% 1.29/1.47 tff(hskp9_type, type, (
% 1.29/1.47 hskp9: $o)).
% 1.29/1.47 tff(hskp12_type, type, (
% 1.29/1.47 hskp12: $o)).
% 1.29/1.47 tff(a14_type, type, (
% 1.29/1.47 a14: $i)).
% 1.29/1.47 tff(hskp7_type, type, (
% 1.29/1.47 hskp7: $o)).
% 1.29/1.47 tff(hskp8_type, type, (
% 1.29/1.47 hskp8: $o)).
% 1.29/1.47 tff(a42_type, type, (
% 1.29/1.47 a42: $i)).
% 1.29/1.47 tff(hskp22_type, type, (
% 1.29/1.47 hskp22: $o)).
% 1.29/1.47 tff(a28_type, type, (
% 1.29/1.47 a28: $i)).
% 1.29/1.47 tff(hskp17_type, type, (
% 1.29/1.47 hskp17: $o)).
% 1.29/1.47 tff(1,plain,
% 1.29/1.47 (^[U: $i] : refl((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(2,plain,
% 1.29/1.47 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[1])).
% 1.29/1.47 tff(3,plain,
% 1.29/1.47 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(4,plain,
% 1.29/1.47 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp3) | hskp24) <=> ((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp24))), rewrite(((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp3) | hskp24) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(5,plain,
% 1.29/1.47 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp3) | hskp24) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[4])).
% 1.29/1.47 tff(6,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp3) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.29/1.47 tff(7,plain,
% 1.29/1.47 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.29/1.47 tff(8,plain,
% 1.29/1.47 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.29/1.47 tff(9,plain,(
% 1.29/1.47 ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.47 inference(skolemize,[status(sab)],[8])).
% 1.29/1.47 tff(10,plain,
% 1.29/1.47 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.29/1.47 tff(11,assumption,(~hskp0), introduced(assumption)).
% 1.29/1.47 tff(12,assumption,(~c3_1(a2)), introduced(assumption)).
% 1.29/1.47 tff(13,assumption,(~c2_1(a2)), introduced(assumption)).
% 1.29/1.47 tff(14,assumption,(~c0_1(a2)), introduced(assumption)).
% 1.29/1.47 tff(15,plain,
% 1.29/1.47 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(16,plain,
% 1.29/1.47 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[15])).
% 1.29/1.47 tff(17,plain,
% 1.29/1.47 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(18,plain,
% 1.29/1.47 (^[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) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(19,plain,
% 1.29/1.47 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[18])).
% 1.29/1.47 tff(20,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 1.29/1.47 tff(21,plain,
% 1.29/1.47 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[20, 19])).
% 1.29/1.47 tff(22,plain,
% 1.29/1.47 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[21, 17])).
% 1.29/1.47 tff(23,plain,(
% 1.29/1.47 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.47 inference(skolemize,[status(sab)],[22])).
% 1.29/1.47 tff(24,plain,
% 1.29/1.47 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[23, 16])).
% 1.29/1.47 tff(25,assumption,(~hskp6), introduced(assumption)).
% 1.29/1.47 tff(26,assumption,(~c1_1(a58)), introduced(assumption)).
% 1.29/1.47 tff(27,plain,
% 1.29/1.47 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(28,plain,
% 1.29/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[27])).
% 1.29/1.47 tff(29,plain,
% 1.29/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(30,plain,
% 1.29/1.47 (^[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) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(31,plain,
% 1.29/1.47 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[30])).
% 1.29/1.47 tff(32,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 1.29/1.47 tff(33,plain,
% 1.29/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.29/1.47 tff(34,plain,
% 1.29/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[33, 29])).
% 1.29/1.47 tff(35,plain,(
% 1.29/1.47 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.47 inference(skolemize,[status(sab)],[34])).
% 1.29/1.47 tff(36,plain,
% 1.29/1.47 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[35, 28])).
% 1.29/1.47 tff(37,assumption,(~c0_1(a58)), introduced(assumption)).
% 1.29/1.47 tff(38,plain,
% 1.29/1.47 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(39,plain,
% 1.29/1.47 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[38])).
% 1.29/1.47 tff(40,plain,
% 1.29/1.47 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(41,plain,
% 1.29/1.47 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp1) <=> ((hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp1) <=> (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(42,plain,
% 1.29/1.47 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp1) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[41])).
% 1.29/1.47 tff(43,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.29/1.47 tff(44,plain,
% 1.29/1.47 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.29/1.47 tff(45,plain,
% 1.29/1.47 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.29/1.47 tff(46,plain,(
% 1.29/1.47 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.29/1.47 inference(skolemize,[status(sab)],[45])).
% 1.29/1.47 tff(47,plain,
% 1.29/1.47 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[46, 39])).
% 1.29/1.47 tff(48,assumption,(~hskp3), introduced(assumption)).
% 1.29/1.47 tff(49,plain,
% 1.29/1.47 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(50,plain,
% 1.29/1.47 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[49])).
% 1.29/1.47 tff(51,plain,
% 1.29/1.47 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(52,plain,
% 1.29/1.47 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_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)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_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)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(53,plain,
% 1.29/1.47 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[52])).
% 1.29/1.47 tff(54,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.29/1.47 tff(55,plain,
% 1.29/1.47 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.29/1.47 tff(56,plain,
% 1.29/1.47 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[55, 51])).
% 1.29/1.47 tff(57,plain,(
% 1.29/1.47 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.29/1.47 inference(skolemize,[status(sab)],[56])).
% 1.29/1.47 tff(58,plain,
% 1.29/1.47 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[57, 50])).
% 1.29/1.47 tff(59,assumption,(c2_1(a58)), introduced(assumption)).
% 1.29/1.47 tff(60,plain,
% 1.29/1.47 (^[U: $i] : refl((hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(61,plain,
% 1.29/1.47 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[60])).
% 1.29/1.47 tff(62,plain,
% 1.29/1.47 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(63,plain,
% 1.29/1.47 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp0) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp0))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp0) <=> (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp0) <=> (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.29/1.47 inference(bind,[status(th)],[])).
% 1.29/1.47 tff(64,plain,
% 1.29/1.47 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp0) <=> ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.47 inference(quant_intro,[status(thm)],[63])).
% 1.29/1.47 tff(65,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp3) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.29/1.47 tff(66,plain,
% 1.29/1.47 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[65, 64])).
% 1.29/1.47 tff(67,plain,
% 1.29/1.47 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[66, 62])).
% 1.29/1.47 tff(68,plain,(
% 1.29/1.47 ![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.47 inference(skolemize,[status(sab)],[67])).
% 1.29/1.47 tff(69,plain,
% 1.29/1.47 (![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[68, 61])).
% 1.29/1.47 tff(70,assumption,(~ndr1_0), introduced(assumption)).
% 1.29/1.47 tff(71,plain,
% 1.29/1.47 ((ndr1_0 | (~hskp14)) <=> (ndr1_0 | (~hskp14))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(72,plain,
% 1.29/1.47 (((~hskp14) | ndr1_0) <=> (ndr1_0 | (~hskp14))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(73,axiom,((~hskp14) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause17')).
% 1.29/1.47 tff(74,plain,
% 1.29/1.47 (ndr1_0 | (~hskp14)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.29/1.47 tff(75,plain,
% 1.29/1.47 (ndr1_0 | (~hskp14)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[74, 71])).
% 1.29/1.47 tff(76,plain,
% 1.29/1.47 (~hskp14),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[75, 70])).
% 1.29/1.47 tff(77,plain,
% 1.29/1.47 ((ndr1_0 | (~hskp29)) <=> (ndr1_0 | (~hskp29))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(78,plain,
% 1.29/1.47 (((~hskp29) | ndr1_0) <=> (ndr1_0 | (~hskp29))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(79,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 1.29/1.47 tff(80,plain,
% 1.29/1.47 (ndr1_0 | (~hskp29)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.29/1.47 tff(81,plain,
% 1.29/1.47 (ndr1_0 | (~hskp29)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[80, 77])).
% 1.29/1.47 tff(82,plain,
% 1.29/1.47 (~hskp29),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[81, 70])).
% 1.29/1.47 tff(83,plain,
% 1.29/1.47 ((ndr1_0 | (~hskp26)) <=> (ndr1_0 | (~hskp26))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(84,plain,
% 1.29/1.47 (((~hskp26) | ndr1_0) <=> (ndr1_0 | (~hskp26))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(85,axiom,((~hskp26) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 1.29/1.47 tff(86,plain,
% 1.29/1.47 (ndr1_0 | (~hskp26)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[85, 84])).
% 1.29/1.47 tff(87,plain,
% 1.29/1.47 (ndr1_0 | (~hskp26)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[86, 83])).
% 1.29/1.47 tff(88,plain,
% 1.29/1.47 (~hskp26),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[87, 70])).
% 1.29/1.47 tff(89,plain,
% 1.29/1.47 ((hskp29 | hskp26 | hskp14) <=> (hskp29 | hskp26 | hskp14)),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(90,plain,
% 1.29/1.47 (((hskp29 | hskp26) | hskp14) <=> (hskp29 | hskp26 | hskp14)),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(91,plain,
% 1.29/1.47 ((hskp29 | hskp26) <=> (hskp29 | hskp26)),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(92,plain,
% 1.29/1.47 (((hskp29 | hskp26) | hskp14) <=> ((hskp29 | hskp26) | hskp14)),
% 1.29/1.47 inference(monotonicity,[status(thm)],[91])).
% 1.29/1.47 tff(93,plain,
% 1.29/1.47 (((hskp29 | hskp26) | hskp14) <=> (hskp29 | hskp26 | hskp14)),
% 1.29/1.47 inference(transitivity,[status(thm)],[92, 90])).
% 1.29/1.47 tff(94,axiom,((hskp29 | hskp26) | hskp14), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 1.29/1.47 tff(95,plain,
% 1.29/1.47 (hskp29 | hskp26 | hskp14),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.29/1.47 tff(96,plain,
% 1.29/1.47 (hskp29 | hskp26 | hskp14),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[95, 89])).
% 1.29/1.47 tff(97,plain,
% 1.29/1.47 (hskp29 | hskp26 | hskp14),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[96, 89])).
% 1.29/1.47 tff(98,plain,
% 1.29/1.47 (hskp29 | hskp26 | hskp14),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[97, 89])).
% 1.29/1.47 tff(99,plain,
% 1.29/1.47 (hskp29 | hskp26 | hskp14),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[98, 89])).
% 1.29/1.47 tff(100,plain,
% 1.29/1.47 ($false),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[99, 88, 82, 76])).
% 1.29/1.47 tff(101,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.29/1.47 tff(102,plain,
% 1.29/1.47 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(103,plain,
% 1.29/1.47 ((hskp3 | hskp0 | (~ndr1_0) | c1_1(a58) | c0_1(a58) | (~c2_1(a58))) <=> (hskp3 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(104,plain,
% 1.29/1.47 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a58) | c0_1(a58) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | (~c2_1(a58))))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[103])).
% 1.29/1.47 tff(105,plain,
% 1.29/1.47 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a58) | c0_1(a58) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)))),
% 1.29/1.47 inference(transitivity,[status(thm)],[104, 102])).
% 1.29/1.47 tff(106,plain,
% 1.29/1.47 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a58) | c0_1(a58) | (~c2_1(a58)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(107,plain,
% 1.29/1.47 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | (~c2_1(a58))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.29/1.47 tff(108,plain,
% 1.29/1.47 (hskp0 | c1_1(a58) | (~c2_1(a58))),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[107, 101, 48, 37, 69])).
% 1.29/1.47 tff(109,plain,
% 1.29/1.47 (hskp0),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[108, 59, 26])).
% 1.29/1.47 tff(110,plain,
% 1.29/1.47 (((~hskp0) | (~c3_1(a1))) <=> ((~hskp0) | (~c3_1(a1)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(111,plain,
% 1.29/1.47 (((~c3_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a1)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(112,axiom,((~c3_1(a1)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.29/1.47 tff(113,plain,
% 1.29/1.47 ((~hskp0) | (~c3_1(a1))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.29/1.47 tff(114,plain,
% 1.29/1.47 ((~hskp0) | (~c3_1(a1))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[113, 110])).
% 1.29/1.47 tff(115,plain,
% 1.29/1.47 (~c3_1(a1)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[114, 109])).
% 1.29/1.47 tff(116,plain,
% 1.29/1.47 (((~hskp0) | c2_1(a1)) <=> ((~hskp0) | c2_1(a1))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(117,axiom,((~hskp0) | c2_1(a1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.29/1.47 tff(118,plain,
% 1.29/1.47 ((~hskp0) | c2_1(a1)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.29/1.47 tff(119,plain,
% 1.29/1.47 ((~hskp0) | c2_1(a1)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[118, 116])).
% 1.29/1.47 tff(120,plain,
% 1.29/1.47 ((~hskp0) | c2_1(a1)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[119, 116])).
% 1.29/1.47 tff(121,plain,
% 1.29/1.47 ((~hskp0) | c2_1(a1)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[120, 116])).
% 1.29/1.47 tff(122,plain,
% 1.29/1.47 ((~hskp0) | c2_1(a1)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[121, 116])).
% 1.29/1.47 tff(123,plain,
% 1.29/1.47 (c2_1(a1)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[122, 109])).
% 1.29/1.47 tff(124,plain,
% 1.29/1.47 (((~hskp0) | c1_1(a1)) <=> ((~hskp0) | c1_1(a1))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(125,axiom,((~hskp0) | c1_1(a1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.29/1.47 tff(126,plain,
% 1.29/1.47 ((~hskp0) | c1_1(a1)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.29/1.47 tff(127,plain,
% 1.29/1.47 ((~hskp0) | c1_1(a1)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[126, 124])).
% 1.29/1.47 tff(128,plain,
% 1.29/1.47 ((~hskp0) | c1_1(a1)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[127, 124])).
% 1.29/1.47 tff(129,plain,
% 1.29/1.47 ((~hskp0) | c1_1(a1)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[128, 124])).
% 1.29/1.48 tff(130,plain,
% 1.29/1.48 ((~hskp0) | c1_1(a1)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[129, 124])).
% 1.29/1.48 tff(131,plain,
% 1.29/1.48 (c1_1(a1)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[130, 109])).
% 1.29/1.48 tff(132,plain,
% 1.29/1.48 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.29/1.48 inference(bind,[status(th)],[])).
% 1.29/1.48 tff(133,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.29/1.48 inference(quant_intro,[status(thm)],[132])).
% 1.29/1.48 tff(134,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(135,plain,
% 1.29/1.48 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.29/1.48 inference(bind,[status(th)],[])).
% 1.29/1.48 tff(136,plain,
% 1.29/1.48 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.29/1.48 inference(quant_intro,[status(thm)],[135])).
% 1.29/1.48 tff(137,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.29/1.48 tff(138,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.29/1.48 tff(139,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[138, 134])).
% 1.29/1.48 tff(140,plain,(
% 1.29/1.48 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.29/1.48 inference(skolemize,[status(sab)],[139])).
% 1.29/1.48 tff(141,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[140, 133])).
% 1.29/1.48 tff(142,assumption,(~c3_1(a1)), introduced(assumption)).
% 1.29/1.48 tff(143,assumption,(c2_1(a1)), introduced(assumption)).
% 1.29/1.48 tff(144,assumption,(c1_1(a1)), introduced(assumption)).
% 1.29/1.48 tff(145,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(146,plain,
% 1.29/1.48 ((hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | (~c2_1(a1)) | (~c0_1(a1))) <=> (hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(147,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | (~c2_1(a1)) | (~c0_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1))))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[146])).
% 1.29/1.48 tff(148,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | (~c2_1(a1)) | (~c0_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)))),
% 1.29/1.48 inference(transitivity,[status(thm)],[147, 145])).
% 1.29/1.48 tff(149,plain,
% 1.29/1.48 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | (~c2_1(a1)) | (~c0_1(a1)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(150,plain,
% 1.29/1.48 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.29/1.48 tff(151,plain,
% 1.29/1.48 (hskp6 | (~c0_1(a1))),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[150, 101, 144, 143, 142, 141])).
% 1.29/1.48 tff(152,plain,
% 1.29/1.48 (~c0_1(a1)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[151, 25])).
% 1.29/1.48 tff(153,plain,
% 1.29/1.48 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.29/1.48 inference(bind,[status(th)],[])).
% 1.29/1.48 tff(154,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.29/1.48 inference(quant_intro,[status(thm)],[153])).
% 1.29/1.48 tff(155,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(156,plain,
% 1.29/1.48 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | 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) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.29/1.48 inference(bind,[status(th)],[])).
% 1.29/1.48 tff(157,plain,
% 1.29/1.48 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.29/1.48 inference(quant_intro,[status(thm)],[156])).
% 1.29/1.48 tff(158,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.29/1.48 tff(159,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[158, 157])).
% 1.29/1.48 tff(160,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[159, 155])).
% 1.29/1.48 tff(161,plain,(
% 1.29/1.48 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.29/1.48 inference(skolemize,[status(sab)],[160])).
% 1.29/1.48 tff(162,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[161, 154])).
% 1.29/1.48 tff(163,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a1))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a1))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(164,plain,
% 1.29/1.48 ((hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1))) <=> (hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a1))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(165,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a1)))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[164])).
% 1.29/1.48 tff(166,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a1))),
% 1.29/1.48 inference(transitivity,[status(thm)],[165, 163])).
% 1.29/1.48 tff(167,plain,
% 1.29/1.48 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(168,plain,
% 1.29/1.48 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a1)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.29/1.48 tff(169,plain,
% 1.29/1.48 (hskp6 | c0_1(a1)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[168, 101, 144, 143, 142, 162])).
% 1.29/1.48 tff(170,plain,
% 1.29/1.48 ($false),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[169, 152, 25])).
% 1.29/1.48 tff(171,plain,(hskp6 | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.48 tff(172,plain,
% 1.29/1.48 (hskp6),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[171, 131, 123, 115])).
% 1.29/1.48 tff(173,plain,
% 1.29/1.48 (((~hskp6) | (~c3_1(a13))) <=> ((~hskp6) | (~c3_1(a13)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(174,plain,
% 1.29/1.48 (((~c3_1(a13)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a13)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(175,axiom,((~c3_1(a13)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.29/1.48 tff(176,plain,
% 1.29/1.48 ((~hskp6) | (~c3_1(a13))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.29/1.48 tff(177,plain,
% 1.29/1.48 ((~hskp6) | (~c3_1(a13))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[176, 173])).
% 1.29/1.48 tff(178,plain,
% 1.29/1.48 (~c3_1(a13)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[177, 172])).
% 1.29/1.48 tff(179,plain,
% 1.29/1.48 (((~hskp6) | (~c1_1(a13))) <=> ((~hskp6) | (~c1_1(a13)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(180,plain,
% 1.29/1.48 (((~c1_1(a13)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a13)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(181,axiom,((~c1_1(a13)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 1.29/1.48 tff(182,plain,
% 1.29/1.48 ((~hskp6) | (~c1_1(a13))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[181, 180])).
% 1.29/1.48 tff(183,plain,
% 1.29/1.48 ((~hskp6) | (~c1_1(a13))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[182, 179])).
% 1.29/1.48 tff(184,plain,
% 1.29/1.48 (~c1_1(a13)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[183, 172])).
% 1.29/1.48 tff(185,plain,
% 1.29/1.48 (((~hskp6) | (~c0_1(a13))) <=> ((~hskp6) | (~c0_1(a13)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(186,plain,
% 1.29/1.48 (((~c0_1(a13)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a13)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(187,axiom,((~c0_1(a13)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 1.29/1.48 tff(188,plain,
% 1.29/1.48 ((~hskp6) | (~c0_1(a13))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[187, 186])).
% 1.29/1.48 tff(189,plain,
% 1.29/1.48 ((~hskp6) | (~c0_1(a13))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[188, 185])).
% 1.29/1.48 tff(190,plain,
% 1.29/1.48 (~c0_1(a13)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[189, 172])).
% 1.29/1.48 tff(191,assumption,(~hskp1), introduced(assumption)).
% 1.29/1.48 tff(192,assumption,(hskp2), introduced(assumption)).
% 1.29/1.48 tff(193,plain,
% 1.29/1.48 (((~hskp2) | (~c2_1(a3))) <=> ((~hskp2) | (~c2_1(a3)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(194,plain,
% 1.29/1.48 (((~c2_1(a3)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a3)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(195,axiom,((~c2_1(a3)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.29/1.48 tff(196,plain,
% 1.29/1.48 ((~hskp2) | (~c2_1(a3))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[195, 194])).
% 1.29/1.48 tff(197,plain,
% 1.29/1.48 ((~hskp2) | (~c2_1(a3))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[196, 193])).
% 1.29/1.48 tff(198,plain,
% 1.29/1.48 (~c2_1(a3)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[197, 192])).
% 1.29/1.48 tff(199,plain,
% 1.29/1.48 (((~hskp2) | c3_1(a3)) <=> ((~hskp2) | c3_1(a3))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(200,axiom,((~hskp2) | c3_1(a3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.29/1.48 tff(201,plain,
% 1.29/1.48 ((~hskp2) | c3_1(a3)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.29/1.48 tff(202,plain,
% 1.29/1.48 ((~hskp2) | c3_1(a3)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[201, 199])).
% 1.29/1.48 tff(203,plain,
% 1.29/1.48 ((~hskp2) | c3_1(a3)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[202, 199])).
% 1.29/1.48 tff(204,plain,
% 1.29/1.48 ((~hskp2) | c3_1(a3)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[203, 199])).
% 1.29/1.48 tff(205,plain,
% 1.29/1.48 ((~hskp2) | c3_1(a3)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[204, 199])).
% 1.29/1.48 tff(206,plain,
% 1.29/1.48 (c3_1(a3)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[205, 192])).
% 1.29/1.48 tff(207,plain,
% 1.29/1.48 (((~hskp2) | c1_1(a3)) <=> ((~hskp2) | c1_1(a3))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(208,axiom,((~hskp2) | c1_1(a3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.29/1.48 tff(209,plain,
% 1.29/1.48 ((~hskp2) | c1_1(a3)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[208, 207])).
% 1.29/1.48 tff(210,plain,
% 1.29/1.48 ((~hskp2) | c1_1(a3)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[209, 207])).
% 1.29/1.48 tff(211,plain,
% 1.29/1.48 ((~hskp2) | c1_1(a3)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[210, 207])).
% 1.29/1.48 tff(212,plain,
% 1.29/1.48 ((~hskp2) | c1_1(a3)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[211, 207])).
% 1.29/1.48 tff(213,plain,
% 1.29/1.48 ((~hskp2) | c1_1(a3)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[212, 207])).
% 1.29/1.48 tff(214,plain,
% 1.29/1.48 (c1_1(a3)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[213, 192])).
% 1.29/1.48 tff(215,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a58)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(216,plain,
% 1.29/1.48 ((hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58))) <=> (hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a58)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(217,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a58))))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[216])).
% 1.29/1.48 tff(218,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a58)))),
% 1.29/1.48 inference(transitivity,[status(thm)],[217, 215])).
% 1.29/1.48 tff(219,plain,
% 1.29/1.48 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(220,plain,
% 1.29/1.48 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a58))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[219, 218])).
% 1.29/1.48 tff(221,plain,
% 1.29/1.48 ($false),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[220, 101, 191, 59, 214, 206, 37, 26, 198, 58])).
% 1.29/1.48 tff(222,plain,((~hskp2) | hskp1 | (~c2_1(a58)) | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.48 tff(223,plain,
% 1.29/1.48 (~hskp2),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[222, 191, 59, 37, 26])).
% 1.29/1.48 tff(224,assumption,(~c3_1(a13)), introduced(assumption)).
% 1.29/1.48 tff(225,assumption,(~c1_1(a13)), introduced(assumption)).
% 1.29/1.48 tff(226,assumption,(~c0_1(a13)), introduced(assumption)).
% 1.29/1.48 tff(227,plain,
% 1.29/1.48 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(228,plain,
% 1.29/1.48 ((hskp2 | hskp1 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13)) <=> (hskp2 | hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(229,plain,
% 1.29/1.48 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0)))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[228])).
% 1.29/1.48 tff(230,plain,
% 1.29/1.48 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))),
% 1.29/1.48 inference(transitivity,[status(thm)],[229, 227])).
% 1.29/1.48 tff(231,plain,
% 1.29/1.48 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(232,plain,
% 1.29/1.48 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[231, 230])).
% 1.29/1.48 tff(233,plain,
% 1.29/1.48 (hskp2 | hskp1),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[232, 101, 226, 225, 224, 47])).
% 1.29/1.48 tff(234,plain,
% 1.29/1.48 ($false),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[233, 223, 191])).
% 1.29/1.48 tff(235,plain,(hskp1 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~c2_1(a58)) | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.48 tff(236,plain,
% 1.29/1.48 (hskp1),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[235, 190, 184, 178, 59, 37, 26])).
% 1.29/1.48 tff(237,plain,
% 1.29/1.48 (((~hskp1) | (~c3_1(a2))) <=> ((~hskp1) | (~c3_1(a2)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(238,plain,
% 1.29/1.48 (((~c3_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a2)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(239,axiom,((~c3_1(a2)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.29/1.48 tff(240,plain,
% 1.29/1.48 ((~hskp1) | (~c3_1(a2))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[239, 238])).
% 1.29/1.48 tff(241,plain,
% 1.29/1.48 ((~hskp1) | (~c3_1(a2))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[240, 237])).
% 1.29/1.48 tff(242,plain,
% 1.29/1.48 (~c3_1(a2)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[241, 236])).
% 1.29/1.48 tff(243,plain,
% 1.29/1.48 (((~hskp1) | (~c2_1(a2))) <=> ((~hskp1) | (~c2_1(a2)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(244,plain,
% 1.29/1.48 (((~c2_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a2)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(245,axiom,((~c2_1(a2)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.29/1.48 tff(246,plain,
% 1.29/1.48 ((~hskp1) | (~c2_1(a2))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[245, 244])).
% 1.29/1.48 tff(247,plain,
% 1.29/1.48 ((~hskp1) | (~c2_1(a2))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[246, 243])).
% 1.29/1.48 tff(248,plain,
% 1.29/1.48 (~c2_1(a2)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[247, 236])).
% 1.29/1.48 tff(249,plain,
% 1.29/1.48 (((~hskp1) | (~c0_1(a2))) <=> ((~hskp1) | (~c0_1(a2)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(250,plain,
% 1.29/1.48 (((~c0_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a2)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(251,axiom,((~c0_1(a2)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.29/1.48 tff(252,plain,
% 1.29/1.48 ((~hskp1) | (~c0_1(a2))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[251, 250])).
% 1.29/1.48 tff(253,plain,
% 1.29/1.48 ((~hskp1) | (~c0_1(a2))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[252, 249])).
% 1.29/1.48 tff(254,plain,
% 1.29/1.48 (~c0_1(a2)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[253, 236])).
% 1.29/1.48 tff(255,plain,
% 1.29/1.48 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 1.29/1.48 inference(bind,[status(th)],[])).
% 1.29/1.48 tff(256,plain,
% 1.29/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.29/1.48 inference(quant_intro,[status(thm)],[255])).
% 1.29/1.48 tff(257,plain,
% 1.29/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(258,plain,
% 1.29/1.48 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 1.29/1.48 inference(bind,[status(th)],[])).
% 1.29/1.48 tff(259,plain,
% 1.29/1.48 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.29/1.48 inference(quant_intro,[status(thm)],[258])).
% 1.29/1.48 tff(260,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause201')).
% 1.29/1.48 tff(261,plain,
% 1.29/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[260, 259])).
% 1.29/1.48 tff(262,plain,
% 1.29/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[261, 257])).
% 1.29/1.48 tff(263,plain,(
% 1.29/1.48 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.29/1.48 inference(skolemize,[status(sab)],[262])).
% 1.29/1.48 tff(264,plain,
% 1.29/1.48 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[263, 256])).
% 1.29/1.48 tff(265,assumption,(c2_1(a13)), introduced(assumption)).
% 1.29/1.48 tff(266,plain,
% 1.29/1.48 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.29/1.48 inference(bind,[status(th)],[])).
% 1.29/1.48 tff(267,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.48 inference(quant_intro,[status(thm)],[266])).
% 1.29/1.48 tff(268,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(269,plain,
% 1.29/1.48 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.29/1.49 inference(bind,[status(th)],[])).
% 1.29/1.49 tff(270,plain,
% 1.29/1.49 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.49 inference(quant_intro,[status(thm)],[269])).
% 1.29/1.49 tff(271,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 1.29/1.49 tff(272,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[271, 270])).
% 1.29/1.49 tff(273,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[272, 268])).
% 1.29/1.49 tff(274,plain,(
% 1.29/1.49 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.49 inference(skolemize,[status(sab)],[273])).
% 1.29/1.49 tff(275,plain,
% 1.29/1.49 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[274, 267])).
% 1.29/1.49 tff(276,plain,
% 1.29/1.49 (hskp6),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[171, 144, 143, 142])).
% 1.29/1.49 tff(277,plain,
% 1.29/1.49 (~c3_1(a13)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[177, 276])).
% 1.29/1.49 tff(278,plain,
% 1.29/1.49 (~c1_1(a13)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[183, 276])).
% 1.29/1.49 tff(279,plain,
% 1.29/1.49 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a13)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(280,plain,
% 1.29/1.49 ((hskp5 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp5 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a13)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(281,plain,
% 1.29/1.49 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a13))))),
% 1.29/1.49 inference(monotonicity,[status(thm)],[280])).
% 1.29/1.49 tff(282,plain,
% 1.29/1.49 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a13)))),
% 1.29/1.49 inference(transitivity,[status(thm)],[281, 279])).
% 1.29/1.49 tff(283,plain,
% 1.29/1.49 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.29/1.49 inference(quant_inst,[status(thm)],[])).
% 1.29/1.49 tff(284,plain,
% 1.29/1.49 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a13))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[283, 282])).
% 1.29/1.49 tff(285,plain,
% 1.29/1.49 (hskp5 | (~c2_1(a13))),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[284, 101, 278, 277, 14, 13, 12, 275])).
% 1.29/1.49 tff(286,plain,
% 1.29/1.49 (hskp5),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[285, 265])).
% 1.29/1.49 tff(287,plain,
% 1.29/1.49 (((~hskp5) | (~c2_1(a11))) <=> ((~hskp5) | (~c2_1(a11)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(288,plain,
% 1.29/1.49 (((~c2_1(a11)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a11)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(289,axiom,((~c2_1(a11)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.29/1.49 tff(290,plain,
% 1.29/1.49 ((~hskp5) | (~c2_1(a11))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.29/1.49 tff(291,plain,
% 1.29/1.49 ((~hskp5) | (~c2_1(a11))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[290, 287])).
% 1.29/1.49 tff(292,plain,
% 1.29/1.49 (~c2_1(a11)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[291, 286])).
% 1.29/1.49 tff(293,plain,
% 1.29/1.49 (((~hskp5) | (~c1_1(a11))) <=> ((~hskp5) | (~c1_1(a11)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(294,plain,
% 1.29/1.49 (((~c1_1(a11)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a11)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(295,axiom,((~c1_1(a11)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.29/1.49 tff(296,plain,
% 1.29/1.49 ((~hskp5) | (~c1_1(a11))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[295, 294])).
% 1.29/1.49 tff(297,plain,
% 1.29/1.49 ((~hskp5) | (~c1_1(a11))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[296, 293])).
% 1.29/1.49 tff(298,plain,
% 1.29/1.49 (~c1_1(a11)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[297, 286])).
% 1.29/1.49 tff(299,plain,
% 1.29/1.49 (((~hskp5) | c0_1(a11)) <=> ((~hskp5) | c0_1(a11))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(300,axiom,((~hskp5) | c0_1(a11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.29/1.49 tff(301,plain,
% 1.29/1.49 ((~hskp5) | c0_1(a11)),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[300, 299])).
% 1.29/1.49 tff(302,plain,
% 1.29/1.49 ((~hskp5) | c0_1(a11)),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[301, 299])).
% 1.29/1.49 tff(303,plain,
% 1.29/1.49 ((~hskp5) | c0_1(a11)),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[302, 299])).
% 1.29/1.49 tff(304,plain,
% 1.29/1.49 ((~hskp5) | c0_1(a11)),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[303, 299])).
% 1.29/1.49 tff(305,plain,
% 1.29/1.49 ((~hskp5) | c0_1(a11)),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[304, 299])).
% 1.29/1.49 tff(306,plain,
% 1.29/1.49 (c0_1(a11)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[305, 286])).
% 1.29/1.49 tff(307,plain,
% 1.29/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a11) | c2_1(a11) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a11)) | (~c0_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a11) | c2_1(a11) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a11)) | (~c0_1(a11)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(308,plain,
% 1.29/1.49 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11))) <=> (c1_1(a11) | c2_1(a11) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a11)) | (~c0_1(a11)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(309,plain,
% 1.29/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a11) | c2_1(a11) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a11)) | (~c0_1(a11))))),
% 1.29/1.49 inference(monotonicity,[status(thm)],[308])).
% 1.29/1.49 tff(310,plain,
% 1.29/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a11) | c2_1(a11) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a11)) | (~c0_1(a11)))),
% 1.29/1.49 inference(transitivity,[status(thm)],[309, 307])).
% 1.29/1.49 tff(311,plain,
% 1.29/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11)))),
% 1.29/1.49 inference(quant_inst,[status(thm)],[])).
% 1.29/1.49 tff(312,plain,
% 1.29/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a11) | c2_1(a11) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a11)) | (~c0_1(a11))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[311, 310])).
% 1.29/1.49 tff(313,plain,
% 1.29/1.49 (~c3_1(a11)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[312, 101, 306, 144, 143, 298, 292, 142, 264])).
% 1.29/1.49 tff(314,plain,
% 1.29/1.49 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))),
% 1.29/1.49 inference(bind,[status(th)],[])).
% 1.29/1.49 tff(315,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_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) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.29/1.49 inference(quant_intro,[status(thm)],[314])).
% 1.29/1.49 tff(316,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_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) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(317,plain,
% 1.29/1.49 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c1_1(W))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))))),
% 1.29/1.49 inference(bind,[status(th)],[])).
% 1.29/1.49 tff(318,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.29/1.49 inference(quant_intro,[status(thm)],[317])).
% 1.29/1.49 tff(319,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.29/1.49 tff(320,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[319, 318])).
% 1.29/1.49 tff(321,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[320, 316])).
% 1.29/1.49 tff(322,plain,(
% 1.29/1.49 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.29/1.49 inference(skolemize,[status(sab)],[321])).
% 1.29/1.49 tff(323,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[322, 315])).
% 1.29/1.49 tff(324,plain,
% 1.29/1.49 (~c0_1(a13)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[189, 276])).
% 1.29/1.49 tff(325,plain,
% 1.29/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a13) | c3_1(a13) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a13) | c3_1(a13) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a13)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(326,plain,
% 1.29/1.49 (((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a11) | c1_1(a11) | c3_1(a11)) <=> (c0_1(a13) | c3_1(a13) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a13)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(327,plain,
% 1.29/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a11) | c1_1(a11) | c3_1(a11))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a13) | c3_1(a13) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a13))))),
% 1.29/1.49 inference(monotonicity,[status(thm)],[326])).
% 1.29/1.49 tff(328,plain,
% 1.29/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a11) | c1_1(a11) | c3_1(a11))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a13) | c3_1(a13) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a13)))),
% 1.29/1.49 inference(transitivity,[status(thm)],[327, 325])).
% 1.29/1.49 tff(329,plain,
% 1.29/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a11) | c1_1(a11) | c3_1(a11))),
% 1.29/1.49 inference(quant_inst,[status(thm)],[])).
% 1.29/1.49 tff(330,plain,
% 1.29/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a13) | c3_1(a13) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a13))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[329, 328])).
% 1.29/1.49 tff(331,plain,
% 1.29/1.49 ($false),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[330, 101, 306, 324, 277, 298, 292, 323, 265, 313])).
% 1.29/1.49 tff(332,plain,((~c2_1(a13)) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.49 tff(333,plain,
% 1.29/1.49 (~c2_1(a13)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[332, 254, 123, 115, 131, 248, 242])).
% 1.29/1.49 tff(334,assumption,(~c2_1(a13)), introduced(assumption)).
% 1.29/1.49 tff(335,plain,
% 1.29/1.49 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.29/1.49 inference(bind,[status(th)],[])).
% 1.29/1.49 tff(336,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.49 inference(quant_intro,[status(thm)],[335])).
% 1.29/1.49 tff(337,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(338,plain,
% 1.29/1.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_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) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | 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) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_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) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_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) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.29/1.49 inference(bind,[status(th)],[])).
% 1.29/1.49 tff(339,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.49 inference(quant_intro,[status(thm)],[338])).
% 1.29/1.49 tff(340,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 1.29/1.49 tff(341,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[340, 339])).
% 1.29/1.49 tff(342,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[341, 337])).
% 1.29/1.49 tff(343,plain,(
% 1.29/1.49 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.49 inference(skolemize,[status(sab)],[342])).
% 1.29/1.49 tff(344,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[343, 336])).
% 1.29/1.49 tff(345,plain,
% 1.29/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(346,plain,
% 1.29/1.49 (((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a58) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(347,plain,
% 1.29/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58))))),
% 1.29/1.49 inference(monotonicity,[status(thm)],[346])).
% 1.29/1.49 tff(348,plain,
% 1.29/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.29/1.49 inference(transitivity,[status(thm)],[347, 345])).
% 1.29/1.49 tff(349,plain,
% 1.29/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 1.29/1.49 inference(quant_inst,[status(thm)],[])).
% 1.29/1.49 tff(350,plain,
% 1.29/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58))),
% 1.29/1.49 inference(modus_ponens,[status(thm)],[349, 348])).
% 1.29/1.49 tff(351,plain,
% 1.29/1.49 (c0_1(a2) | c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58))),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[350, 101, 26, 225, 224, 13, 12, 344])).
% 1.29/1.49 tff(352,plain,
% 1.29/1.49 (~c3_1(a58)),
% 1.29/1.49 inference(unit_resolution,[status(thm)],[351, 59, 334, 14])).
% 1.29/1.49 tff(353,plain,
% 1.29/1.49 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.29/1.49 inference(bind,[status(th)],[])).
% 1.29/1.49 tff(354,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.49 inference(quant_intro,[status(thm)],[353])).
% 1.29/1.49 tff(355,plain,
% 1.29/1.49 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.49 inference(rewrite,[status(thm)],[])).
% 1.29/1.49 tff(356,plain,
% 1.29/1.49 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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) | c3_1(U) | 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) | c3_1(U) | c2_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) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(U) | c2_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) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_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) | c3_1(U) | c2_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)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.29/1.50 inference(bind,[status(th)],[])).
% 1.29/1.50 tff(357,plain,
% 1.29/1.50 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.50 inference(quant_intro,[status(thm)],[356])).
% 1.29/1.50 tff(358,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.29/1.50 tff(359,plain,
% 1.29/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.50 inference(modus_ponens,[status(thm)],[358, 357])).
% 1.29/1.50 tff(360,plain,
% 1.29/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.50 inference(modus_ponens,[status(thm)],[359, 355])).
% 1.29/1.50 tff(361,plain,(
% 1.29/1.50 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.50 inference(skolemize,[status(sab)],[360])).
% 1.29/1.50 tff(362,plain,
% 1.29/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.29/1.50 inference(modus_ponens,[status(thm)],[361, 354])).
% 1.29/1.50 tff(363,plain,
% 1.29/1.50 (^[U: $i] : refl((hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.29/1.50 inference(bind,[status(th)],[])).
% 1.29/1.50 tff(364,plain,
% 1.29/1.50 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.50 inference(quant_intro,[status(thm)],[363])).
% 1.29/1.50 tff(365,plain,
% 1.29/1.50 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.50 inference(rewrite,[status(thm)],[])).
% 1.29/1.50 tff(366,plain,
% 1.29/1.50 (^[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) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp3) | hskp18) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp18))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp18) <=> (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp3) | hskp18) <=> (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.29/1.50 inference(bind,[status(th)],[])).
% 1.29/1.50 tff(367,plain,
% 1.29/1.50 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp3) | hskp18) <=> ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.50 inference(quant_intro,[status(thm)],[366])).
% 1.29/1.50 tff(368,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp3) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.29/1.50 tff(369,plain,
% 1.29/1.50 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.50 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.29/1.50 tff(370,plain,
% 1.29/1.50 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.50 inference(modus_ponens,[status(thm)],[369, 365])).
% 1.29/1.50 tff(371,plain,(
% 1.29/1.50 ![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.50 inference(skolemize,[status(sab)],[370])).
% 1.29/1.50 tff(372,plain,
% 1.29/1.50 (![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.29/1.50 inference(modus_ponens,[status(thm)],[371, 364])).
% 1.29/1.50 tff(373,plain,
% 1.29/1.50 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 1.29/1.50 inference(rewrite,[status(thm)],[])).
% 1.29/1.50 tff(374,plain,
% 1.29/1.50 ((hskp18 | hskp3 | (~ndr1_0) | c3_1(a58) | c0_1(a58) | (~c2_1(a58))) <=> (hskp18 | hskp3 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 1.29/1.50 inference(rewrite,[status(thm)],[])).
% 1.29/1.50 tff(375,plain,
% 1.29/1.50 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)))),
% 1.29/1.50 inference(monotonicity,[status(thm)],[374])).
% 1.29/1.50 tff(376,plain,
% 1.29/1.50 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 1.29/1.50 inference(transitivity,[status(thm)],[375, 373])).
% 1.29/1.50 tff(377,plain,
% 1.29/1.50 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(378,plain,
% 1.33/1.50 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.33/1.50 tff(379,plain,
% 1.33/1.50 (hskp18 | (~c2_1(a58)) | c3_1(a58)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[378, 101, 48, 37, 372])).
% 1.33/1.50 tff(380,plain,
% 1.33/1.50 (hskp18),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[379, 59, 352])).
% 1.33/1.50 tff(381,plain,
% 1.33/1.50 (((~hskp18) | (~c3_1(a31))) <=> ((~hskp18) | (~c3_1(a31)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(382,plain,
% 1.33/1.50 (((~c3_1(a31)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a31)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(383,axiom,((~c3_1(a31)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.33/1.50 tff(384,plain,
% 1.33/1.50 ((~hskp18) | (~c3_1(a31))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.33/1.50 tff(385,plain,
% 1.33/1.50 ((~hskp18) | (~c3_1(a31))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[384, 381])).
% 1.33/1.50 tff(386,plain,
% 1.33/1.50 (~c3_1(a31)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[385, 380])).
% 1.33/1.50 tff(387,plain,
% 1.33/1.50 (((~hskp18) | c1_1(a31)) <=> ((~hskp18) | c1_1(a31))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(388,axiom,((~hskp18) | c1_1(a31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.33/1.50 tff(389,plain,
% 1.33/1.50 ((~hskp18) | c1_1(a31)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.33/1.50 tff(390,plain,
% 1.33/1.50 ((~hskp18) | c1_1(a31)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[389, 387])).
% 1.33/1.50 tff(391,plain,
% 1.33/1.50 ((~hskp18) | c1_1(a31)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[390, 387])).
% 1.33/1.50 tff(392,plain,
% 1.33/1.50 ((~hskp18) | c1_1(a31)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[391, 387])).
% 1.33/1.50 tff(393,plain,
% 1.33/1.50 ((~hskp18) | c1_1(a31)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[392, 387])).
% 1.33/1.50 tff(394,plain,
% 1.33/1.50 (c1_1(a31)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[393, 380])).
% 1.33/1.50 tff(395,plain,
% 1.33/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a58) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(396,plain,
% 1.33/1.50 (((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13)) <=> (c1_1(a58) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(397,plain,
% 1.33/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a58) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58)))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[396])).
% 1.33/1.50 tff(398,plain,
% 1.33/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))),
% 1.33/1.50 inference(transitivity,[status(thm)],[397, 395])).
% 1.33/1.50 tff(399,plain,
% 1.33/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(400,plain,
% 1.33/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[399, 398])).
% 1.33/1.50 tff(401,plain,
% 1.33/1.50 (c2_1(a31)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[400, 101, 59, 394, 26, 386, 226, 225, 362, 334, 352])).
% 1.33/1.50 tff(402,plain,
% 1.33/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(403,plain,
% 1.33/1.50 ((hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a13) | c2_1(a13) | c0_1(a13)) <=> (hskp5 | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(404,plain,
% 1.33/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a13) | c2_1(a13) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58)))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[403])).
% 1.33/1.50 tff(405,plain,
% 1.33/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a13) | c2_1(a13) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))),
% 1.33/1.50 inference(transitivity,[status(thm)],[404, 402])).
% 1.33/1.50 tff(406,plain,
% 1.33/1.50 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a13) | c2_1(a13) | c0_1(a13))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(407,plain,
% 1.33/1.50 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[406, 405])).
% 1.33/1.50 tff(408,plain,
% 1.33/1.50 (hskp5),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[407, 101, 59, 26, 226, 224, 275, 334, 352])).
% 1.33/1.50 tff(409,plain,
% 1.33/1.50 (~c2_1(a11)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[291, 408])).
% 1.33/1.50 tff(410,plain,
% 1.33/1.50 (~c1_1(a11)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[297, 408])).
% 1.33/1.50 tff(411,plain,
% 1.33/1.50 (c0_1(a11)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[305, 408])).
% 1.33/1.50 tff(412,plain,
% 1.33/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c1_1(a31)) | (~c2_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(413,plain,
% 1.33/1.50 (((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11))) <=> (c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(414,plain,
% 1.33/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c1_1(a31)) | (~c2_1(a31))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[413])).
% 1.33/1.50 tff(415,plain,
% 1.33/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[414, 412])).
% 1.33/1.50 tff(416,plain,
% 1.33/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a11) | (~c3_1(a11)) | (~c0_1(a11)) | c2_1(a11) | c1_1(a11) | (~c3_1(a11)))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(417,plain,
% 1.33/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c1_1(a31)) | (~c2_1(a31))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[416, 415])).
% 1.33/1.50 tff(418,plain,
% 1.33/1.50 (~c3_1(a11)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[417, 101, 394, 411, 386, 410, 409, 264, 401])).
% 1.33/1.50 tff(419,plain,
% 1.33/1.50 (((~hskp18) | (~c0_1(a31))) <=> ((~hskp18) | (~c0_1(a31)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(420,plain,
% 1.33/1.50 (((~c0_1(a31)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a31)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(421,axiom,((~c0_1(a31)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.33/1.50 tff(422,plain,
% 1.33/1.50 ((~hskp18) | (~c0_1(a31))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[421, 420])).
% 1.33/1.50 tff(423,plain,
% 1.33/1.50 ((~hskp18) | (~c0_1(a31))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[422, 419])).
% 1.33/1.50 tff(424,plain,
% 1.33/1.50 (~c0_1(a31)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[423, 380])).
% 1.33/1.50 tff(425,plain,
% 1.33/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a31) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a31) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(426,plain,
% 1.33/1.50 (((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a11) | c1_1(a11) | c3_1(a11)) <=> (c0_1(a31) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(427,plain,
% 1.33/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a11) | c1_1(a11) | c3_1(a11))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a31) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[426])).
% 1.33/1.50 tff(428,plain,
% 1.33/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a11) | c1_1(a11) | c3_1(a11))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a31) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[427, 425])).
% 1.33/1.50 tff(429,plain,
% 1.33/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a11) | c1_1(a11) | c3_1(a11))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.50 tff(430,plain,
% 1.33/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a31) | c3_1(a31) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31))),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[429, 428])).
% 1.33/1.50 tff(431,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[430, 101, 411, 424, 386, 410, 409, 323, 401, 418])).
% 1.33/1.50 tff(432,plain,((~c2_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c2_1(a13) | c1_1(a13) | hskp3 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(433,plain,
% 1.33/1.50 ($false),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[432, 333, 254, 59, 178, 26, 184, 48, 37, 190, 248, 242])).
% 1.33/1.50 tff(434,plain,((~c2_1(a58)) | c1_1(a58) | hskp3 | c0_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.50 tff(435,plain,
% 1.33/1.50 (~c2_1(a58)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[434, 48, 26, 37])).
% 1.33/1.50 tff(436,plain,
% 1.33/1.50 (((~hskp24) | c2_1(a58)) <=> ((~hskp24) | c2_1(a58))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(437,axiom,((~hskp24) | c2_1(a58)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.33/1.50 tff(438,plain,
% 1.33/1.50 ((~hskp24) | c2_1(a58)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[437, 436])).
% 1.33/1.50 tff(439,plain,
% 1.33/1.50 ((~hskp24) | c2_1(a58)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[438, 436])).
% 1.33/1.50 tff(440,plain,
% 1.33/1.50 ((~hskp24) | c2_1(a58)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[439, 436])).
% 1.33/1.50 tff(441,plain,
% 1.33/1.50 ((~hskp24) | c2_1(a58)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[440, 436])).
% 1.33/1.50 tff(442,plain,
% 1.33/1.50 ((~hskp24) | c2_1(a58)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[441, 436])).
% 1.33/1.50 tff(443,plain,
% 1.33/1.50 (~hskp24),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[442, 435])).
% 1.33/1.50 tff(444,assumption,(~c3_1(a15)), introduced(assumption)).
% 1.33/1.50 tff(445,assumption,(hskp6), introduced(assumption)).
% 1.33/1.50 tff(446,plain,
% 1.33/1.50 (~c0_1(a13)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[189, 445])).
% 1.33/1.50 tff(447,plain,
% 1.33/1.50 (~c3_1(a13)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[177, 445])).
% 1.33/1.50 tff(448,plain,
% 1.33/1.50 (~c2_1(a58)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[434, 26, 48, 37])).
% 1.33/1.50 tff(449,plain,
% 1.33/1.50 (~hskp24),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[442, 448])).
% 1.33/1.50 tff(450,assumption,(~c2_1(a38)), introduced(assumption)).
% 1.33/1.50 tff(451,assumption,(~c1_1(a15)), introduced(assumption)).
% 1.33/1.50 tff(452,plain,
% 1.33/1.50 (~c2_1(a58)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[108, 11, 26])).
% 1.33/1.50 tff(453,assumption,(hskp28), introduced(assumption)).
% 1.33/1.50 tff(454,plain,
% 1.33/1.50 (((~hskp28) | c3_1(a25)) <=> ((~hskp28) | c3_1(a25))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(455,axiom,((~hskp28) | c3_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.33/1.50 tff(456,plain,
% 1.33/1.50 ((~hskp28) | c3_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[455, 454])).
% 1.33/1.50 tff(457,plain,
% 1.33/1.50 ((~hskp28) | c3_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[456, 454])).
% 1.33/1.50 tff(458,plain,
% 1.33/1.50 ((~hskp28) | c3_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[457, 454])).
% 1.33/1.50 tff(459,plain,
% 1.33/1.50 ((~hskp28) | c3_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[458, 454])).
% 1.33/1.50 tff(460,plain,
% 1.33/1.50 ((~hskp28) | c3_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[459, 454])).
% 1.33/1.50 tff(461,plain,
% 1.33/1.50 (c3_1(a25)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[460, 453])).
% 1.33/1.50 tff(462,plain,
% 1.33/1.50 (((~hskp28) | c1_1(a25)) <=> ((~hskp28) | c1_1(a25))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(463,axiom,((~hskp28) | c1_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.33/1.50 tff(464,plain,
% 1.33/1.50 ((~hskp28) | c1_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[463, 462])).
% 1.33/1.50 tff(465,plain,
% 1.33/1.50 ((~hskp28) | c1_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[464, 462])).
% 1.33/1.50 tff(466,plain,
% 1.33/1.50 ((~hskp28) | c1_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[465, 462])).
% 1.33/1.50 tff(467,plain,
% 1.33/1.50 ((~hskp28) | c1_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[466, 462])).
% 1.33/1.50 tff(468,plain,
% 1.33/1.50 ((~hskp28) | c1_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[467, 462])).
% 1.33/1.50 tff(469,plain,
% 1.33/1.50 (c1_1(a25)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[468, 453])).
% 1.33/1.50 tff(470,plain,
% 1.33/1.50 (((~hskp28) | c2_1(a25)) <=> ((~hskp28) | c2_1(a25))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(471,axiom,((~hskp28) | c2_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.33/1.50 tff(472,plain,
% 1.33/1.50 ((~hskp28) | c2_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[471, 470])).
% 1.33/1.50 tff(473,plain,
% 1.33/1.50 ((~hskp28) | c2_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[472, 470])).
% 1.33/1.50 tff(474,plain,
% 1.33/1.50 ((~hskp28) | c2_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[473, 470])).
% 1.33/1.50 tff(475,plain,
% 1.33/1.50 ((~hskp28) | c2_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[474, 470])).
% 1.33/1.50 tff(476,plain,
% 1.33/1.50 ((~hskp28) | c2_1(a25)),
% 1.33/1.50 inference(modus_ponens,[status(thm)],[475, 470])).
% 1.33/1.50 tff(477,plain,
% 1.33/1.50 (c2_1(a25)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[476, 453])).
% 1.33/1.50 tff(478,assumption,(ndr1_0), introduced(assumption)).
% 1.33/1.50 tff(479,plain,
% 1.33/1.50 (hskp3 | hskp0 | c0_1(a58) | (~ndr1_0) | (~c2_1(a58))),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[107, 26, 69])).
% 1.33/1.50 tff(480,plain,
% 1.33/1.50 (~c2_1(a58)),
% 1.33/1.50 inference(unit_resolution,[status(thm)],[479, 48, 11, 478, 37])).
% 1.33/1.50 tff(481,assumption,(c3_1(a25)), introduced(assumption)).
% 1.33/1.50 tff(482,assumption,(c2_1(a25)), introduced(assumption)).
% 1.33/1.50 tff(483,assumption,(c1_1(a25)), introduced(assumption)).
% 1.33/1.50 tff(484,plain,
% 1.33/1.50 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(485,plain,
% 1.33/1.50 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.33/1.50 inference(rewrite,[status(thm)],[])).
% 1.33/1.50 tff(486,plain,
% 1.33/1.50 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c2_1(a25))))),
% 1.33/1.50 inference(monotonicity,[status(thm)],[485])).
% 1.33/1.50 tff(487,plain,
% 1.33/1.50 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)))),
% 1.33/1.50 inference(transitivity,[status(thm)],[486, 484])).
% 1.33/1.50 tff(488,plain,
% 1.33/1.50 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)))),
% 1.33/1.50 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(489,plain,
% 1.33/1.51 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c2_1(a25))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[488, 487])).
% 1.33/1.51 tff(490,plain,
% 1.33/1.51 (hskp24 | hskp3),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[489, 478, 483, 482, 481, 10])).
% 1.33/1.51 tff(491,plain,
% 1.33/1.51 (hskp24),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[490, 48])).
% 1.33/1.51 tff(492,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[442, 491, 480])).
% 1.33/1.51 tff(493,plain,(hskp3 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | (~c3_1(a25)) | hskp0 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(494,plain,
% 1.33/1.51 (hskp3 | (~c1_1(a25)) | (~c2_1(a25)) | (~c3_1(a25)) | hskp0 | c0_1(a58) | c1_1(a58)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[493, 101])).
% 1.33/1.51 tff(495,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[494, 477, 469, 48, 461, 11, 37, 26])).
% 1.33/1.51 tff(496,plain,((~hskp28) | hskp3 | hskp0 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(497,plain,
% 1.33/1.51 (~hskp28),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[496, 11, 48, 37, 26])).
% 1.33/1.51 tff(498,plain,
% 1.33/1.51 ((hskp28 | hskp20 | hskp1) <=> (hskp28 | hskp20 | hskp1)),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(499,plain,
% 1.33/1.51 (((hskp28 | hskp20) | hskp1) <=> (hskp28 | hskp20 | hskp1)),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(500,plain,
% 1.33/1.51 ((hskp28 | hskp20) <=> (hskp28 | hskp20)),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(501,plain,
% 1.33/1.51 (((hskp28 | hskp20) | hskp1) <=> ((hskp28 | hskp20) | hskp1)),
% 1.33/1.51 inference(monotonicity,[status(thm)],[500])).
% 1.33/1.51 tff(502,plain,
% 1.33/1.51 (((hskp28 | hskp20) | hskp1) <=> (hskp28 | hskp20 | hskp1)),
% 1.33/1.51 inference(transitivity,[status(thm)],[501, 499])).
% 1.33/1.51 tff(503,axiom,((hskp28 | hskp20) | hskp1), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 1.33/1.51 tff(504,plain,
% 1.33/1.51 (hskp28 | hskp20 | hskp1),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[503, 502])).
% 1.33/1.51 tff(505,plain,
% 1.33/1.51 (hskp28 | hskp20 | hskp1),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[504, 498])).
% 1.33/1.51 tff(506,plain,
% 1.33/1.51 (hskp28 | hskp20 | hskp1),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[505, 498])).
% 1.33/1.51 tff(507,plain,
% 1.33/1.51 (hskp28 | hskp20 | hskp1),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[506, 498])).
% 1.33/1.51 tff(508,plain,
% 1.33/1.51 (hskp28 | hskp20 | hskp1),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[507, 498])).
% 1.33/1.51 tff(509,plain,
% 1.33/1.51 (hskp20),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[508, 497, 191])).
% 1.33/1.51 tff(510,plain,
% 1.33/1.51 (((~hskp20) | c3_1(a37)) <=> ((~hskp20) | c3_1(a37))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(511,axiom,((~hskp20) | c3_1(a37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.33/1.51 tff(512,plain,
% 1.33/1.51 ((~hskp20) | c3_1(a37)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[511, 510])).
% 1.33/1.51 tff(513,plain,
% 1.33/1.51 ((~hskp20) | c3_1(a37)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[512, 510])).
% 1.33/1.51 tff(514,plain,
% 1.33/1.51 ((~hskp20) | c3_1(a37)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[513, 510])).
% 1.33/1.51 tff(515,plain,
% 1.33/1.51 ((~hskp20) | c3_1(a37)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[514, 510])).
% 1.33/1.51 tff(516,plain,
% 1.33/1.51 ((~hskp20) | c3_1(a37)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[515, 510])).
% 1.33/1.51 tff(517,plain,
% 1.33/1.51 (c3_1(a37)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[516, 509])).
% 1.33/1.51 tff(518,plain,
% 1.33/1.51 (((~hskp20) | c1_1(a37)) <=> ((~hskp20) | c1_1(a37))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(519,axiom,((~hskp20) | c1_1(a37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.33/1.51 tff(520,plain,
% 1.33/1.51 ((~hskp20) | c1_1(a37)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[519, 518])).
% 1.33/1.51 tff(521,plain,
% 1.33/1.51 ((~hskp20) | c1_1(a37)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[520, 518])).
% 1.33/1.51 tff(522,plain,
% 1.33/1.51 ((~hskp20) | c1_1(a37)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[521, 518])).
% 1.33/1.51 tff(523,plain,
% 1.33/1.51 ((~hskp20) | c1_1(a37)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[522, 518])).
% 1.33/1.51 tff(524,plain,
% 1.33/1.51 ((~hskp20) | c1_1(a37)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[523, 518])).
% 1.33/1.51 tff(525,plain,
% 1.33/1.51 (c1_1(a37)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[524, 509])).
% 1.33/1.51 tff(526,assumption,(~hskp24), introduced(assumption)).
% 1.33/1.51 tff(527,plain,
% 1.33/1.51 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(528,plain,
% 1.33/1.51 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(529,plain,
% 1.33/1.51 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)) | (~c1_1(a37))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[528, 527])).
% 1.33/1.51 tff(530,plain,
% 1.33/1.51 (~c2_1(a37)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[529, 101, 526, 48, 525, 517, 10])).
% 1.33/1.51 tff(531,plain,
% 1.33/1.51 (^[U: $i] : refl((hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.33/1.51 inference(bind,[status(th)],[])).
% 1.33/1.51 tff(532,plain,
% 1.33/1.51 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.33/1.51 inference(quant_intro,[status(thm)],[531])).
% 1.33/1.51 tff(533,plain,
% 1.33/1.51 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(534,plain,
% 1.33/1.51 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp0) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0) <=> (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp0) <=> (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.33/1.51 inference(bind,[status(th)],[])).
% 1.33/1.51 tff(535,plain,
% 1.33/1.51 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp0) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.33/1.51 inference(quant_intro,[status(thm)],[534])).
% 1.33/1.51 tff(536,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 1.33/1.51 tff(537,plain,
% 1.33/1.51 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.33/1.51 tff(538,plain,
% 1.33/1.51 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[537, 533])).
% 1.33/1.51 tff(539,plain,(
% 1.33/1.51 ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.33/1.51 inference(skolemize,[status(sab)],[538])).
% 1.33/1.51 tff(540,plain,
% 1.33/1.51 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[539, 532])).
% 1.33/1.51 tff(541,plain,
% 1.33/1.51 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(542,plain,
% 1.33/1.51 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(543,plain,
% 1.33/1.51 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[542, 541])).
% 1.33/1.51 tff(544,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[543, 101, 497, 11, 525, 517, 540, 530])).
% 1.33/1.51 tff(545,plain,(hskp0 | hskp24 | hskp3 | hskp1 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(546,plain,
% 1.33/1.51 (hskp24),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[545, 11, 48, 191, 37, 26])).
% 1.33/1.51 tff(547,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[442, 546, 452])).
% 1.33/1.51 tff(548,plain,(hskp0 | hskp3 | hskp1 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(549,plain,
% 1.33/1.51 (hskp1),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[548, 11, 48, 37, 26])).
% 1.33/1.51 tff(550,plain,
% 1.33/1.51 (~c0_1(a2)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[253, 549])).
% 1.33/1.51 tff(551,plain,
% 1.33/1.51 (~c2_1(a2)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[247, 549])).
% 1.33/1.51 tff(552,plain,
% 1.33/1.51 (~hskp24),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[442, 452])).
% 1.33/1.51 tff(553,assumption,(hskp27), introduced(assumption)).
% 1.33/1.51 tff(554,plain,
% 1.33/1.51 (((~hskp27) | c3_1(a12)) <=> ((~hskp27) | c3_1(a12))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(555,axiom,((~hskp27) | c3_1(a12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.33/1.51 tff(556,plain,
% 1.33/1.51 ((~hskp27) | c3_1(a12)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[555, 554])).
% 1.33/1.51 tff(557,plain,
% 1.33/1.51 ((~hskp27) | c3_1(a12)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[556, 554])).
% 1.33/1.51 tff(558,plain,
% 1.33/1.51 ((~hskp27) | c3_1(a12)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[557, 554])).
% 1.33/1.51 tff(559,plain,
% 1.33/1.51 ((~hskp27) | c3_1(a12)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[558, 554])).
% 1.33/1.51 tff(560,plain,
% 1.33/1.51 ((~hskp27) | c3_1(a12)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[559, 554])).
% 1.33/1.51 tff(561,plain,
% 1.33/1.51 (c3_1(a12)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[560, 553])).
% 1.33/1.51 tff(562,plain,
% 1.33/1.51 (((~hskp27) | c1_1(a12)) <=> ((~hskp27) | c1_1(a12))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(563,axiom,((~hskp27) | c1_1(a12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 1.33/1.51 tff(564,plain,
% 1.33/1.51 ((~hskp27) | c1_1(a12)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[563, 562])).
% 1.33/1.51 tff(565,plain,
% 1.33/1.51 ((~hskp27) | c1_1(a12)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[564, 562])).
% 1.33/1.51 tff(566,plain,
% 1.33/1.51 ((~hskp27) | c1_1(a12)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[565, 562])).
% 1.33/1.51 tff(567,plain,
% 1.33/1.51 ((~hskp27) | c1_1(a12)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[566, 562])).
% 1.33/1.51 tff(568,plain,
% 1.33/1.51 ((~hskp27) | c1_1(a12)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[567, 562])).
% 1.33/1.51 tff(569,plain,
% 1.33/1.51 (c1_1(a12)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[568, 553])).
% 1.33/1.51 tff(570,plain,
% 1.33/1.51 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c2_1(a12)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c2_1(a12)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(571,plain,
% 1.33/1.51 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a12)) | (~c3_1(a12)) | (~c1_1(a12))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c2_1(a12)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(572,plain,
% 1.33/1.51 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a12)) | (~c3_1(a12)) | (~c1_1(a12)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c2_1(a12))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[571])).
% 1.33/1.51 tff(573,plain,
% 1.33/1.51 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a12)) | (~c3_1(a12)) | (~c1_1(a12)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c2_1(a12)))),
% 1.33/1.51 inference(transitivity,[status(thm)],[572, 570])).
% 1.33/1.51 tff(574,plain,
% 1.33/1.51 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a12)) | (~c3_1(a12)) | (~c1_1(a12)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(575,plain,
% 1.33/1.51 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c2_1(a12))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[574, 573])).
% 1.33/1.51 tff(576,plain,
% 1.33/1.51 (~c2_1(a12)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[575, 101, 526, 48, 569, 561, 10])).
% 1.33/1.51 tff(577,assumption,(~hskp28), introduced(assumption)).
% 1.33/1.51 tff(578,plain,
% 1.33/1.51 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | c2_1(a12))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | c2_1(a12))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(579,plain,
% 1.33/1.51 ((hskp28 | hskp0 | (~ndr1_0) | c2_1(a12) | (~c3_1(a12)) | (~c1_1(a12))) <=> (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | c2_1(a12))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(580,plain,
% 1.33/1.51 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a12) | (~c3_1(a12)) | (~c1_1(a12)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | c2_1(a12)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[579])).
% 1.33/1.51 tff(581,plain,
% 1.33/1.51 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a12) | (~c3_1(a12)) | (~c1_1(a12)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | c2_1(a12))),
% 1.33/1.51 inference(transitivity,[status(thm)],[580, 578])).
% 1.33/1.51 tff(582,plain,
% 1.33/1.51 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a12) | (~c3_1(a12)) | (~c1_1(a12)))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(583,plain,
% 1.33/1.51 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | c2_1(a12)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[582, 581])).
% 1.33/1.51 tff(584,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[583, 101, 577, 11, 569, 561, 540, 576])).
% 1.33/1.51 tff(585,plain,((~hskp27) | hskp28 | hskp0 | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(586,plain,
% 1.33/1.51 (~hskp27),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[585, 497, 552, 11, 48])).
% 1.33/1.51 tff(587,assumption,(~hskp27), introduced(assumption)).
% 1.33/1.51 tff(588,assumption,(hskp21), introduced(assumption)).
% 1.33/1.51 tff(589,plain,
% 1.33/1.51 (((~hskp21) | c0_1(a38)) <=> ((~hskp21) | c0_1(a38))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(590,axiom,((~hskp21) | c0_1(a38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.33/1.51 tff(591,plain,
% 1.33/1.51 ((~hskp21) | c0_1(a38)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[590, 589])).
% 1.33/1.51 tff(592,plain,
% 1.33/1.51 ((~hskp21) | c0_1(a38)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[591, 589])).
% 1.33/1.51 tff(593,plain,
% 1.33/1.51 ((~hskp21) | c0_1(a38)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[592, 589])).
% 1.33/1.51 tff(594,plain,
% 1.33/1.51 ((~hskp21) | c0_1(a38)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[593, 589])).
% 1.33/1.51 tff(595,plain,
% 1.33/1.51 ((~hskp21) | c0_1(a38)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[594, 589])).
% 1.33/1.51 tff(596,plain,
% 1.33/1.51 (c0_1(a38)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[595, 588])).
% 1.33/1.51 tff(597,plain,
% 1.33/1.51 (((~hskp21) | c1_1(a38)) <=> ((~hskp21) | c1_1(a38))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(598,axiom,((~hskp21) | c1_1(a38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.33/1.51 tff(599,plain,
% 1.33/1.51 ((~hskp21) | c1_1(a38)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[598, 597])).
% 1.33/1.51 tff(600,plain,
% 1.33/1.51 ((~hskp21) | c1_1(a38)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[599, 597])).
% 1.33/1.51 tff(601,plain,
% 1.33/1.51 ((~hskp21) | c1_1(a38)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[600, 597])).
% 1.33/1.51 tff(602,plain,
% 1.33/1.51 ((~hskp21) | c1_1(a38)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[601, 597])).
% 1.33/1.51 tff(603,plain,
% 1.33/1.51 ((~hskp21) | c1_1(a38)),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[602, 597])).
% 1.33/1.51 tff(604,plain,
% 1.33/1.51 (c1_1(a38)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[603, 588])).
% 1.33/1.51 tff(605,plain,
% 1.33/1.51 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.33/1.51 inference(bind,[status(th)],[])).
% 1.33/1.51 tff(606,plain,
% 1.33/1.51 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.33/1.51 inference(quant_intro,[status(thm)],[605])).
% 1.33/1.51 tff(607,plain,
% 1.33/1.51 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(608,plain,
% 1.33/1.51 (^[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(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)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.33/1.51 inference(bind,[status(th)],[])).
% 1.33/1.51 tff(609,plain,
% 1.33/1.51 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.33/1.51 inference(quant_intro,[status(thm)],[608])).
% 1.33/1.51 tff(610,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 1.33/1.51 tff(611,plain,
% 1.33/1.51 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[610, 609])).
% 1.33/1.51 tff(612,plain,
% 1.33/1.51 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[611, 607])).
% 1.33/1.51 tff(613,plain,(
% 1.33/1.51 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.33/1.51 inference(skolemize,[status(sab)],[612])).
% 1.33/1.51 tff(614,plain,
% 1.33/1.51 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[613, 606])).
% 1.33/1.51 tff(615,plain,
% 1.33/1.51 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(616,plain,
% 1.33/1.51 ((hskp27 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(617,plain,
% 1.33/1.51 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[616])).
% 1.33/1.51 tff(618,plain,
% 1.33/1.51 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.33/1.51 inference(transitivity,[status(thm)],[617, 615])).
% 1.33/1.51 tff(619,plain,
% 1.33/1.51 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(620,plain,
% 1.33/1.51 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[619, 618])).
% 1.33/1.51 tff(621,plain,
% 1.33/1.51 (hskp27 | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38))),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[620, 450, 14, 13, 12, 614])).
% 1.33/1.51 tff(622,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[621, 604, 596, 478, 587])).
% 1.33/1.51 tff(623,plain,((~hskp21) | (~ndr1_0) | hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(624,plain,
% 1.33/1.51 ((~hskp21) | hskp27 | c2_1(a38) | c0_1(a2) | c2_1(a2) | c3_1(a2)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[623, 101])).
% 1.33/1.51 tff(625,plain,
% 1.33/1.51 (~hskp21),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[624, 586, 450, 551, 12, 550])).
% 1.33/1.51 tff(626,assumption,(hskp20), introduced(assumption)).
% 1.33/1.51 tff(627,plain,
% 1.33/1.51 (((~hskp20) | (~c0_1(a37))) <=> ((~hskp20) | (~c0_1(a37)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(628,plain,
% 1.33/1.51 (((~c0_1(a37)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a37)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(629,axiom,((~c0_1(a37)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.33/1.51 tff(630,plain,
% 1.33/1.51 ((~hskp20) | (~c0_1(a37))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[629, 628])).
% 1.33/1.51 tff(631,plain,
% 1.33/1.51 ((~hskp20) | (~c0_1(a37))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[630, 627])).
% 1.33/1.51 tff(632,plain,
% 1.33/1.51 (~c0_1(a37)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[631, 626])).
% 1.33/1.51 tff(633,plain,
% 1.33/1.51 (c3_1(a37)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[516, 626])).
% 1.33/1.51 tff(634,plain,
% 1.33/1.51 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(635,plain,
% 1.33/1.51 ((hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp0 | c0_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(636,plain,
% 1.33/1.51 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37))))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[635])).
% 1.33/1.51 tff(637,plain,
% 1.33/1.51 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37)))),
% 1.33/1.51 inference(transitivity,[status(thm)],[636, 634])).
% 1.33/1.51 tff(638,plain,
% 1.33/1.51 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.33/1.51 inference(quant_inst,[status(thm)],[])).
% 1.33/1.51 tff(639,plain,
% 1.33/1.51 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a37)) | (~c3_1(a37))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[638, 637])).
% 1.33/1.51 tff(640,plain,
% 1.33/1.51 (~c2_1(a37)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[639, 101, 11, 633, 632, 14, 13, 12, 24])).
% 1.33/1.51 tff(641,plain,
% 1.33/1.51 (c1_1(a37)),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[524, 626])).
% 1.33/1.51 tff(642,plain,
% 1.33/1.51 ($false),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[543, 101, 577, 11, 641, 633, 540, 640])).
% 1.33/1.51 tff(643,plain,((~hskp20) | hskp28 | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.33/1.51 tff(644,plain,
% 1.33/1.51 (~hskp20),
% 1.33/1.51 inference(unit_resolution,[status(thm)],[643, 551, 12, 11, 550, 497])).
% 1.33/1.51 tff(645,plain,
% 1.33/1.51 (^[U: $i] : refl((hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))),
% 1.33/1.51 inference(bind,[status(th)],[])).
% 1.33/1.51 tff(646,plain,
% 1.33/1.51 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.33/1.51 inference(quant_intro,[status(thm)],[645])).
% 1.33/1.51 tff(647,plain,
% 1.33/1.51 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(648,plain,
% 1.33/1.51 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp20) <=> ((hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp20))), rewrite(((hskp21 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp20) <=> (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp20) <=> (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))))),
% 1.33/1.51 inference(bind,[status(th)],[])).
% 1.33/1.51 tff(649,plain,
% 1.33/1.51 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp20) <=> ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.33/1.51 inference(quant_intro,[status(thm)],[648])).
% 1.33/1.51 tff(650,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp21) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.33/1.51 tff(651,plain,
% 1.33/1.51 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[650, 649])).
% 1.33/1.51 tff(652,plain,
% 1.33/1.51 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[651, 647])).
% 1.33/1.51 tff(653,plain,(
% 1.33/1.51 ![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.33/1.51 inference(skolemize,[status(sab)],[652])).
% 1.33/1.51 tff(654,plain,
% 1.33/1.51 (![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 1.33/1.51 inference(modus_ponens,[status(thm)],[653, 646])).
% 1.33/1.51 tff(655,plain,
% 1.33/1.51 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(656,plain,
% 1.33/1.51 ((hskp21 | hskp20 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c2_1(a2)) <=> (hskp21 | hskp20 | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 1.33/1.51 inference(rewrite,[status(thm)],[])).
% 1.33/1.51 tff(657,plain,
% 1.33/1.51 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c2_1(a2))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2)))),
% 1.33/1.51 inference(monotonicity,[status(thm)],[656])).
% 1.33/1.51 tff(658,plain,
% 1.33/1.51 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c2_1(a2))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 1.33/1.52 inference(transitivity,[status(thm)],[657, 655])).
% 1.33/1.52 tff(659,plain,
% 1.33/1.52 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c2_1(a2))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(660,plain,
% 1.33/1.52 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[659, 658])).
% 1.33/1.52 tff(661,plain,
% 1.33/1.52 (hskp21 | hskp20 | c2_1(a2) | c1_1(a2)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[660, 101, 12, 654])).
% 1.33/1.52 tff(662,plain,
% 1.33/1.52 (c1_1(a2)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[661, 644, 551, 625])).
% 1.33/1.52 tff(663,plain,
% 1.33/1.52 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(664,plain,
% 1.33/1.52 ((hskp21 | hskp20 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c2_1(a58)) <=> (hskp21 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(665,plain,
% 1.33/1.52 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c2_1(a58))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58)))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[664])).
% 1.33/1.52 tff(666,plain,
% 1.33/1.52 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c2_1(a58))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))),
% 1.33/1.52 inference(transitivity,[status(thm)],[665, 663])).
% 1.33/1.52 tff(667,plain,
% 1.33/1.52 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c2_1(a58))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(668,plain,
% 1.33/1.52 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[667, 666])).
% 1.33/1.52 tff(669,plain,
% 1.33/1.52 (hskp21 | hskp20 | c2_1(a58) | c3_1(a58)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[668, 101, 26, 654])).
% 1.33/1.52 tff(670,plain,
% 1.33/1.52 (c3_1(a58)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[669, 625, 452, 644])).
% 1.33/1.52 tff(671,plain,
% 1.33/1.52 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.33/1.52 inference(bind,[status(th)],[])).
% 1.33/1.52 tff(672,plain,
% 1.33/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(quant_intro,[status(thm)],[671])).
% 1.33/1.52 tff(673,plain,
% 1.33/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(674,plain,
% 1.33/1.52 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.33/1.52 inference(bind,[status(th)],[])).
% 1.33/1.52 tff(675,plain,
% 1.33/1.52 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(quant_intro,[status(thm)],[674])).
% 1.33/1.52 tff(676,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 1.33/1.52 tff(677,plain,
% 1.33/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[676, 675])).
% 1.33/1.52 tff(678,plain,
% 1.33/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[677, 673])).
% 1.33/1.52 tff(679,plain,(
% 1.33/1.52 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(skolemize,[status(sab)],[678])).
% 1.33/1.52 tff(680,plain,
% 1.33/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[679, 672])).
% 1.33/1.52 tff(681,plain,
% 1.33/1.52 (hskp1),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[545, 552, 48, 11, 37, 26])).
% 1.33/1.52 tff(682,plain,
% 1.33/1.52 (~c0_1(a2)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[253, 681])).
% 1.33/1.52 tff(683,plain,
% 1.33/1.52 (~c2_1(a2)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[247, 681])).
% 1.33/1.52 tff(684,plain,
% 1.33/1.52 (~hskp20),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[643, 683, 11, 12, 682, 497])).
% 1.33/1.52 tff(685,plain,
% 1.33/1.52 (~hskp27),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[585, 552, 497, 11, 48])).
% 1.33/1.52 tff(686,plain,
% 1.33/1.52 (~hskp21),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[624, 683, 450, 685, 12, 682])).
% 1.33/1.52 tff(687,plain,
% 1.33/1.52 (c3_1(a58)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[669, 686, 452, 684])).
% 1.33/1.52 tff(688,plain,
% 1.33/1.52 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.33/1.52 inference(bind,[status(th)],[])).
% 1.33/1.52 tff(689,plain,
% 1.33/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(quant_intro,[status(thm)],[688])).
% 1.33/1.52 tff(690,plain,
% 1.33/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(691,plain,
% 1.33/1.52 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.33/1.52 inference(bind,[status(th)],[])).
% 1.33/1.52 tff(692,plain,
% 1.33/1.52 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(quant_intro,[status(thm)],[691])).
% 1.33/1.52 tff(693,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 1.33/1.52 tff(694,plain,
% 1.33/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[693, 692])).
% 1.33/1.52 tff(695,plain,
% 1.33/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[694, 690])).
% 1.33/1.52 tff(696,plain,(
% 1.33/1.52 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(skolemize,[status(sab)],[695])).
% 1.33/1.52 tff(697,plain,
% 1.33/1.52 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[696, 689])).
% 1.33/1.52 tff(698,assumption,(~c2_1(a15)), introduced(assumption)).
% 1.33/1.52 tff(699,plain,
% 1.33/1.52 (~hskp27),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[585, 497, 11, 552, 48])).
% 1.33/1.52 tff(700,plain,
% 1.33/1.52 (^[U: $i] : refl((hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.33/1.52 inference(bind,[status(th)],[])).
% 1.33/1.52 tff(701,plain,
% 1.33/1.52 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.33/1.52 inference(quant_intro,[status(thm)],[700])).
% 1.33/1.52 tff(702,plain,
% 1.33/1.52 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(703,plain,
% 1.33/1.52 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1) <=> ((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1) <=> (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.33/1.52 inference(bind,[status(th)],[])).
% 1.33/1.52 tff(704,plain,
% 1.33/1.52 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.33/1.52 inference(quant_intro,[status(thm)],[703])).
% 1.33/1.52 tff(705,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp0) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.33/1.52 tff(706,plain,
% 1.33/1.52 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[705, 704])).
% 1.33/1.52 tff(707,plain,
% 1.33/1.52 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[706, 702])).
% 1.33/1.52 tff(708,plain,(
% 1.33/1.52 ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.33/1.52 inference(skolemize,[status(sab)],[707])).
% 1.33/1.52 tff(709,plain,
% 1.33/1.52 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[708, 701])).
% 1.33/1.52 tff(710,plain,
% 1.33/1.52 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(711,plain,
% 1.33/1.52 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c0_1(a58)) <=> (hskp1 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(712,plain,
% 1.33/1.52 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58)))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[711])).
% 1.33/1.52 tff(713,plain,
% 1.33/1.52 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58))),
% 1.33/1.52 inference(transitivity,[status(thm)],[712, 710])).
% 1.33/1.52 tff(714,plain,
% 1.33/1.52 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | c0_1(a58))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(715,plain,
% 1.33/1.52 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a58) | c1_1(a58) | (~ndr1_0) | c3_1(a58)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[714, 713])).
% 1.33/1.52 tff(716,plain,
% 1.33/1.52 (hskp1 | hskp0 | c1_1(a58) | c3_1(a58)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[715, 101, 37, 709])).
% 1.33/1.52 tff(717,plain,
% 1.33/1.52 (c3_1(a58)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[716, 191, 26, 11])).
% 1.33/1.52 tff(718,plain,
% 1.33/1.52 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(719,plain,
% 1.33/1.52 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15)) <=> (hskp1 | hskp0 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(720,plain,
% 1.33/1.52 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15)))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[719])).
% 1.33/1.52 tff(721,plain,
% 1.33/1.52 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))),
% 1.33/1.52 inference(transitivity,[status(thm)],[720, 718])).
% 1.33/1.52 tff(722,plain,
% 1.33/1.52 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(723,plain,
% 1.33/1.52 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[722, 721])).
% 1.33/1.52 tff(724,plain,
% 1.33/1.52 (hskp1 | hskp0 | c3_1(a15) | c0_1(a15)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[723, 101, 451, 709])).
% 1.33/1.52 tff(725,plain,
% 1.33/1.52 (c0_1(a15)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[724, 191, 444, 11])).
% 1.33/1.52 tff(726,assumption,(~c2_1(a58)), introduced(assumption)).
% 1.33/1.52 tff(727,plain,
% 1.33/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a58)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(728,plain,
% 1.33/1.52 (((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a58)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(729,plain,
% 1.33/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a58))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[728])).
% 1.33/1.52 tff(730,plain,
% 1.33/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a58)))),
% 1.33/1.52 inference(transitivity,[status(thm)],[729, 727])).
% 1.33/1.52 tff(731,plain,
% 1.33/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(732,plain,
% 1.33/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a58))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[731, 730])).
% 1.33/1.52 tff(733,plain,
% 1.33/1.52 ((~c0_1(a15)) | (~c3_1(a58))),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[732, 101, 726, 37, 26, 451, 698, 697])).
% 1.33/1.52 tff(734,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[733, 725, 717])).
% 1.33/1.52 tff(735,plain,(hskp1 | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(736,plain,
% 1.33/1.52 (hskp1),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[735, 452, 37, 26, 451, 698, 444, 11])).
% 1.33/1.52 tff(737,plain,
% 1.33/1.52 (~c3_1(a2)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[241, 736])).
% 1.33/1.52 tff(738,plain,
% 1.33/1.52 (~c0_1(a2)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[253, 736])).
% 1.33/1.52 tff(739,plain,
% 1.33/1.52 (~c2_1(a2)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[247, 736])).
% 1.33/1.52 tff(740,plain,
% 1.33/1.52 (~hskp21),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[624, 13, 450, 587, 14, 12])).
% 1.33/1.52 tff(741,plain,
% 1.33/1.52 (~hskp20),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[643, 13, 11, 12, 14, 577])).
% 1.33/1.52 tff(742,plain,
% 1.33/1.52 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(743,plain,
% 1.33/1.52 ((hskp21 | hskp20 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c2_1(a15)) <=> (hskp21 | hskp20 | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(744,plain,
% 1.33/1.52 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0)))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[743])).
% 1.33/1.52 tff(745,plain,
% 1.33/1.52 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c2_1(a15))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0))),
% 1.33/1.52 inference(transitivity,[status(thm)],[744, 742])).
% 1.33/1.52 tff(746,plain,
% 1.33/1.52 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c2_1(a15))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(747,plain,
% 1.33/1.52 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[746, 745])).
% 1.33/1.52 tff(748,plain,
% 1.33/1.52 (hskp21 | hskp20 | c2_1(a15) | c3_1(a15)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[747, 101, 451, 654])).
% 1.33/1.52 tff(749,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[748, 741, 740, 698, 444])).
% 1.33/1.52 tff(750,plain,(c2_1(a2) | c2_1(a15) | c3_1(a15) | c1_1(a15) | hskp0 | c3_1(a2) | c0_1(a2) | hskp28 | c2_1(a38) | hskp27), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(751,plain,
% 1.33/1.52 ($false),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[750, 739, 738, 444, 451, 11, 737, 698, 497, 450, 699])).
% 1.33/1.52 tff(752,plain,(hskp0 | c3_1(a15) | c1_1(a15) | c2_1(a15) | c2_1(a38) | c0_1(a58) | c1_1(a58) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.33/1.52 tff(753,plain,
% 1.33/1.52 (hskp0),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[752, 444, 451, 698, 450, 37, 26, 48])).
% 1.33/1.52 tff(754,plain,
% 1.33/1.52 (c1_1(a1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[130, 753])).
% 1.33/1.52 tff(755,plain,
% 1.33/1.52 (~c3_1(a1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[114, 753])).
% 1.33/1.52 tff(756,plain,
% 1.33/1.52 (c2_1(a1)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[122, 753])).
% 1.33/1.52 tff(757,assumption,(~hskp21), introduced(assumption)).
% 1.33/1.52 tff(758,plain,
% 1.33/1.52 ((hskp24 | hskp21 | hskp13) <=> (hskp24 | hskp21 | hskp13)),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(759,plain,
% 1.33/1.52 (((hskp21 | hskp13) | hskp24) <=> (hskp24 | hskp21 | hskp13)),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(760,plain,
% 1.33/1.52 ((hskp21 | hskp13) <=> (hskp21 | hskp13)),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(761,plain,
% 1.33/1.52 (((hskp21 | hskp13) | hskp24) <=> ((hskp21 | hskp13) | hskp24)),
% 1.33/1.52 inference(monotonicity,[status(thm)],[760])).
% 1.33/1.52 tff(762,plain,
% 1.33/1.52 (((hskp21 | hskp13) | hskp24) <=> (hskp24 | hskp21 | hskp13)),
% 1.33/1.52 inference(transitivity,[status(thm)],[761, 759])).
% 1.33/1.52 tff(763,axiom,((hskp21 | hskp13) | hskp24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.33/1.52 tff(764,plain,
% 1.33/1.52 (hskp24 | hskp21 | hskp13),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[763, 762])).
% 1.33/1.52 tff(765,plain,
% 1.33/1.52 (hskp24 | hskp21 | hskp13),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[764, 758])).
% 1.33/1.52 tff(766,plain,
% 1.33/1.52 (hskp24 | hskp21 | hskp13),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[765, 758])).
% 1.33/1.52 tff(767,plain,
% 1.33/1.52 (hskp24 | hskp21 | hskp13),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[766, 758])).
% 1.33/1.52 tff(768,plain,
% 1.33/1.52 (hskp24 | hskp21 | hskp13),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[767, 758])).
% 1.33/1.52 tff(769,plain,
% 1.33/1.52 (hskp13),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[768, 757, 526])).
% 1.33/1.52 tff(770,plain,
% 1.33/1.52 (((~hskp13) | (~c3_1(a21))) <=> ((~hskp13) | (~c3_1(a21)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(771,plain,
% 1.33/1.52 (((~c3_1(a21)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a21)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(772,axiom,((~c3_1(a21)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.33/1.52 tff(773,plain,
% 1.33/1.52 ((~hskp13) | (~c3_1(a21))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.33/1.52 tff(774,plain,
% 1.33/1.52 ((~hskp13) | (~c3_1(a21))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[773, 770])).
% 1.33/1.52 tff(775,plain,
% 1.33/1.52 (~c3_1(a21)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[774, 769])).
% 1.33/1.52 tff(776,plain,
% 1.33/1.52 (((~hskp13) | c2_1(a21)) <=> ((~hskp13) | c2_1(a21))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(777,axiom,((~hskp13) | c2_1(a21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.33/1.52 tff(778,plain,
% 1.33/1.52 ((~hskp13) | c2_1(a21)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[777, 776])).
% 1.33/1.52 tff(779,plain,
% 1.33/1.52 ((~hskp13) | c2_1(a21)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[778, 776])).
% 1.33/1.52 tff(780,plain,
% 1.33/1.52 ((~hskp13) | c2_1(a21)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[779, 776])).
% 1.33/1.52 tff(781,plain,
% 1.33/1.52 ((~hskp13) | c2_1(a21)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[780, 776])).
% 1.33/1.52 tff(782,plain,
% 1.33/1.52 ((~hskp13) | c2_1(a21)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[781, 776])).
% 1.33/1.52 tff(783,plain,
% 1.33/1.52 (c2_1(a21)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[782, 769])).
% 1.33/1.52 tff(784,plain,
% 1.33/1.52 (((~hskp13) | c0_1(a21)) <=> ((~hskp13) | c0_1(a21))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(785,axiom,((~hskp13) | c0_1(a21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.33/1.52 tff(786,plain,
% 1.33/1.52 ((~hskp13) | c0_1(a21)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[785, 784])).
% 1.33/1.52 tff(787,plain,
% 1.33/1.52 ((~hskp13) | c0_1(a21)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[786, 784])).
% 1.33/1.52 tff(788,plain,
% 1.33/1.52 ((~hskp13) | c0_1(a21)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[787, 784])).
% 1.33/1.52 tff(789,plain,
% 1.33/1.52 ((~hskp13) | c0_1(a21)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[788, 784])).
% 1.33/1.52 tff(790,plain,
% 1.33/1.52 ((~hskp13) | c0_1(a21)),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[789, 784])).
% 1.33/1.52 tff(791,plain,
% 1.33/1.52 (c0_1(a21)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[790, 769])).
% 1.33/1.52 tff(792,plain,
% 1.33/1.52 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a21) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a21)) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a21) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(793,plain,
% 1.33/1.52 ((hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21))) <=> (hskp6 | c3_1(a21) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.33/1.52 inference(rewrite,[status(thm)],[])).
% 1.33/1.52 tff(794,plain,
% 1.33/1.52 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a21) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a21)) | (~c2_1(a21))))),
% 1.33/1.52 inference(monotonicity,[status(thm)],[793])).
% 1.33/1.52 tff(795,plain,
% 1.33/1.52 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a21) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.33/1.52 inference(transitivity,[status(thm)],[794, 792])).
% 1.33/1.52 tff(796,plain,
% 1.33/1.52 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))),
% 1.33/1.52 inference(quant_inst,[status(thm)],[])).
% 1.33/1.52 tff(797,plain,
% 1.33/1.52 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a21) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a21)) | (~c2_1(a21))),
% 1.33/1.52 inference(modus_ponens,[status(thm)],[796, 795])).
% 1.33/1.52 tff(798,plain,
% 1.33/1.52 (hskp6),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[797, 101, 791, 783, 144, 143, 775, 142, 141])).
% 1.33/1.52 tff(799,plain,
% 1.33/1.52 (~c3_1(a13)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[177, 798])).
% 1.33/1.52 tff(800,plain,
% 1.33/1.52 (~c1_1(a13)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[183, 798])).
% 1.33/1.52 tff(801,plain,
% 1.33/1.52 (~c0_1(a13)),
% 1.33/1.52 inference(unit_resolution,[status(thm)],[189, 798])).
% 1.33/1.53 tff(802,plain,
% 1.33/1.53 (hskp2),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[232, 101, 191, 801, 800, 799, 47])).
% 1.33/1.53 tff(803,plain,
% 1.33/1.53 (~c2_1(a3)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[197, 802])).
% 1.33/1.53 tff(804,plain,
% 1.33/1.53 (^[U: $i] : refl((hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.33/1.53 inference(bind,[status(th)],[])).
% 1.33/1.53 tff(805,plain,
% 1.33/1.53 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.33/1.53 inference(quant_intro,[status(thm)],[804])).
% 1.33/1.53 tff(806,plain,
% 1.33/1.53 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(807,plain,
% 1.33/1.53 (^[U: $i] : 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)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp10) <=> ((hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp21 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp10) <=> (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.33/1.53 inference(bind,[status(th)],[])).
% 1.33/1.53 tff(808,plain,
% 1.33/1.53 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp10) <=> ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.33/1.53 inference(quant_intro,[status(thm)],[807])).
% 1.33/1.53 tff(809,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp21) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.33/1.53 tff(810,plain,
% 1.33/1.53 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[809, 808])).
% 1.33/1.53 tff(811,plain,
% 1.33/1.53 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[810, 806])).
% 1.33/1.53 tff(812,plain,(
% 1.33/1.53 ![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.33/1.53 inference(skolemize,[status(sab)],[811])).
% 1.33/1.53 tff(813,plain,
% 1.33/1.53 (![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[812, 805])).
% 1.33/1.53 tff(814,plain,
% 1.33/1.53 (hskp20),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[748, 757, 698, 444])).
% 1.33/1.53 tff(815,plain,
% 1.33/1.53 (c3_1(a37)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[516, 814])).
% 1.33/1.53 tff(816,plain,
% 1.33/1.53 (c1_1(a37)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[524, 814])).
% 1.33/1.53 tff(817,plain,
% 1.33/1.53 (~c2_1(a37)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[529, 101, 526, 48, 816, 815, 10])).
% 1.33/1.53 tff(818,plain,
% 1.33/1.53 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.33/1.53 inference(bind,[status(th)],[])).
% 1.33/1.53 tff(819,plain,
% 1.33/1.53 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.33/1.53 inference(quant_intro,[status(thm)],[818])).
% 1.33/1.53 tff(820,plain,
% 1.33/1.53 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(821,plain,
% 1.33/1.53 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.33/1.53 inference(bind,[status(th)],[])).
% 1.33/1.53 tff(822,plain,
% 1.33/1.53 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.33/1.53 inference(quant_intro,[status(thm)],[821])).
% 1.33/1.53 tff(823,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.33/1.53 tff(824,plain,
% 1.33/1.53 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[823, 822])).
% 1.33/1.53 tff(825,plain,
% 1.33/1.53 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[824, 820])).
% 1.33/1.53 tff(826,plain,(
% 1.33/1.53 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.33/1.53 inference(skolemize,[status(sab)],[825])).
% 1.33/1.53 tff(827,plain,
% 1.33/1.53 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[826, 819])).
% 1.33/1.53 tff(828,plain,
% 1.33/1.53 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(829,plain,
% 1.33/1.53 ((hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))) <=> (hskp9 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(830,plain,
% 1.33/1.53 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[829])).
% 1.33/1.53 tff(831,plain,
% 1.33/1.53 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[830, 828])).
% 1.33/1.53 tff(832,plain,
% 1.33/1.53 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(833,plain,
% 1.33/1.53 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[832, 831])).
% 1.33/1.53 tff(834,plain,
% 1.33/1.53 (hskp9),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[833, 101, 816, 815, 144, 143, 142, 827, 817])).
% 1.33/1.53 tff(835,plain,
% 1.33/1.53 (((~hskp9) | (~c3_1(a16))) <=> ((~hskp9) | (~c3_1(a16)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(836,plain,
% 1.33/1.53 (((~c3_1(a16)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a16)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(837,axiom,((~c3_1(a16)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.33/1.53 tff(838,plain,
% 1.33/1.53 ((~hskp9) | (~c3_1(a16))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[837, 836])).
% 1.33/1.53 tff(839,plain,
% 1.33/1.53 ((~hskp9) | (~c3_1(a16))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[838, 835])).
% 1.33/1.53 tff(840,plain,
% 1.33/1.53 (~c3_1(a16)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[839, 834])).
% 1.33/1.53 tff(841,plain,
% 1.33/1.53 (((~hskp9) | c1_1(a16)) <=> ((~hskp9) | c1_1(a16))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(842,axiom,((~hskp9) | c1_1(a16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.33/1.53 tff(843,plain,
% 1.33/1.53 ((~hskp9) | c1_1(a16)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[842, 841])).
% 1.33/1.53 tff(844,plain,
% 1.33/1.53 ((~hskp9) | c1_1(a16)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[843, 841])).
% 1.33/1.53 tff(845,plain,
% 1.33/1.53 ((~hskp9) | c1_1(a16)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[844, 841])).
% 1.33/1.53 tff(846,plain,
% 1.33/1.53 ((~hskp9) | c1_1(a16)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[845, 841])).
% 1.33/1.53 tff(847,plain,
% 1.33/1.53 ((~hskp9) | c1_1(a16)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[846, 841])).
% 1.33/1.53 tff(848,plain,
% 1.33/1.53 (c1_1(a16)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[847, 834])).
% 1.33/1.53 tff(849,plain,
% 1.33/1.53 (((~hskp9) | c0_1(a16)) <=> ((~hskp9) | c0_1(a16))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(850,axiom,((~hskp9) | c0_1(a16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.33/1.53 tff(851,plain,
% 1.33/1.53 ((~hskp9) | c0_1(a16)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[850, 849])).
% 1.33/1.53 tff(852,plain,
% 1.33/1.53 ((~hskp9) | c0_1(a16)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[851, 849])).
% 1.33/1.53 tff(853,plain,
% 1.33/1.53 ((~hskp9) | c0_1(a16)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[852, 849])).
% 1.33/1.53 tff(854,plain,
% 1.33/1.53 ((~hskp9) | c0_1(a16)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[853, 849])).
% 1.33/1.53 tff(855,plain,
% 1.33/1.53 ((~hskp9) | c0_1(a16)),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[854, 849])).
% 1.33/1.53 tff(856,plain,
% 1.33/1.53 (c0_1(a16)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[855, 834])).
% 1.33/1.53 tff(857,plain,
% 1.33/1.53 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp10 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(858,plain,
% 1.33/1.53 ((hskp21 | hskp10 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16))) <=> (hskp21 | hskp10 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(859,plain,
% 1.33/1.53 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[858])).
% 1.33/1.53 tff(860,plain,
% 1.33/1.53 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp10 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[859, 857])).
% 1.33/1.53 tff(861,plain,
% 1.33/1.53 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(862,plain,
% 1.33/1.53 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp10 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[861, 860])).
% 1.33/1.53 tff(863,plain,
% 1.33/1.53 (hskp10),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[862, 101, 757, 856, 848, 840, 813])).
% 1.33/1.53 tff(864,plain,
% 1.33/1.53 (((~hskp10) | (~c1_1(a18))) <=> ((~hskp10) | (~c1_1(a18)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(865,plain,
% 1.33/1.53 (((~c1_1(a18)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a18)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(866,axiom,((~c1_1(a18)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.33/1.53 tff(867,plain,
% 1.33/1.53 ((~hskp10) | (~c1_1(a18))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[866, 865])).
% 1.33/1.53 tff(868,plain,
% 1.33/1.53 ((~hskp10) | (~c1_1(a18))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[867, 864])).
% 1.33/1.53 tff(869,plain,
% 1.33/1.53 (~c1_1(a18)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[868, 863])).
% 1.33/1.53 tff(870,plain,
% 1.33/1.53 (((~hskp10) | (~c0_1(a18))) <=> ((~hskp10) | (~c0_1(a18)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(871,plain,
% 1.33/1.53 (((~c0_1(a18)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a18)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(872,axiom,((~c0_1(a18)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.33/1.53 tff(873,plain,
% 1.33/1.53 ((~hskp10) | (~c0_1(a18))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[872, 871])).
% 1.33/1.53 tff(874,plain,
% 1.33/1.53 ((~hskp10) | (~c0_1(a18))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[873, 870])).
% 1.33/1.53 tff(875,plain,
% 1.33/1.53 (~c0_1(a18)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[874, 863])).
% 1.33/1.53 tff(876,plain,
% 1.33/1.53 (c3_1(a3)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[205, 802])).
% 1.33/1.53 tff(877,plain,
% 1.33/1.53 (c1_1(a3)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[213, 802])).
% 1.33/1.53 tff(878,plain,
% 1.33/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a18) | c1_1(a18) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a18) | c1_1(a18) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a18)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(879,plain,
% 1.33/1.53 ((hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (hskp1 | c0_1(a18) | c1_1(a18) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a18)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(880,plain,
% 1.33/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a18) | c1_1(a18) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a18))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[879])).
% 1.33/1.53 tff(881,plain,
% 1.33/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a18) | c1_1(a18) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a18)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[880, 878])).
% 1.33/1.53 tff(882,plain,
% 1.33/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(883,plain,
% 1.33/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a18) | c1_1(a18) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a18))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[882, 881])).
% 1.33/1.53 tff(884,plain,
% 1.33/1.53 (~c2_1(a18)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[883, 101, 191, 877, 876, 875, 869, 803, 58])).
% 1.33/1.53 tff(885,plain,
% 1.33/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(886,plain,
% 1.33/1.53 ((hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13))) <=> (hskp1 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(887,plain,
% 1.33/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[886])).
% 1.33/1.53 tff(888,plain,
% 1.33/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[887, 885])).
% 1.33/1.53 tff(889,plain,
% 1.33/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(890,plain,
% 1.33/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[889, 888])).
% 1.33/1.53 tff(891,plain,
% 1.33/1.53 (~c2_1(a13)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[890, 101, 191, 816, 815, 801, 800, 58, 817])).
% 1.33/1.53 tff(892,plain,
% 1.33/1.53 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W))))),
% 1.33/1.53 inference(bind,[status(th)],[])).
% 1.33/1.53 tff(893,plain,
% 1.33/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.33/1.53 inference(quant_intro,[status(thm)],[892])).
% 1.33/1.53 tff(894,plain,
% 1.33/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(895,plain,
% 1.33/1.53 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))))),
% 1.33/1.53 inference(bind,[status(th)],[])).
% 1.33/1.53 tff(896,plain,
% 1.33/1.53 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.33/1.53 inference(quant_intro,[status(thm)],[895])).
% 1.33/1.53 tff(897,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause203')).
% 1.33/1.53 tff(898,plain,
% 1.33/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[897, 896])).
% 1.33/1.53 tff(899,plain,
% 1.33/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[898, 894])).
% 1.33/1.53 tff(900,plain,(
% 1.33/1.53 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.33/1.53 inference(skolemize,[status(sab)],[899])).
% 1.33/1.53 tff(901,plain,
% 1.33/1.53 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[900, 893])).
% 1.33/1.53 tff(902,plain,
% 1.33/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c0_1(a16)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(903,plain,
% 1.33/1.53 (((~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_1(a3)) | (~c0_1(a3))) <=> (c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(904,plain,
% 1.33/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_1(a3)) | (~c0_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c0_1(a16))))),
% 1.33/1.53 inference(monotonicity,[status(thm)],[903])).
% 1.33/1.53 tff(905,plain,
% 1.33/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_1(a3)) | (~c0_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.33/1.53 inference(transitivity,[status(thm)],[904, 902])).
% 1.33/1.53 tff(906,plain,
% 1.33/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_1(a3)) | (~c0_1(a3)))),
% 1.33/1.53 inference(quant_inst,[status(thm)],[])).
% 1.33/1.53 tff(907,plain,
% 1.33/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)) | (~c1_1(a16)) | (~c0_1(a16))),
% 1.33/1.53 inference(modus_ponens,[status(thm)],[906, 905])).
% 1.33/1.53 tff(908,plain,
% 1.33/1.53 (~c0_1(a3)),
% 1.33/1.53 inference(unit_resolution,[status(thm)],[907, 101, 856, 848, 877, 876, 840, 803, 901])).
% 1.33/1.53 tff(909,plain,
% 1.33/1.53 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.33/1.53 inference(bind,[status(th)],[])).
% 1.33/1.53 tff(910,plain,
% 1.33/1.53 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.33/1.53 inference(quant_intro,[status(thm)],[909])).
% 1.33/1.53 tff(911,plain,
% 1.33/1.53 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.33/1.53 inference(rewrite,[status(thm)],[])).
% 1.33/1.53 tff(912,plain,
% 1.33/1.53 (^[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)) | c2_1(V) | 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)) | c2_1(V) | 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)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.37/1.53 inference(bind,[status(th)],[])).
% 1.37/1.53 tff(913,plain,
% 1.37/1.53 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.37/1.53 inference(quant_intro,[status(thm)],[912])).
% 1.37/1.53 tff(914,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)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 1.37/1.53 tff(915,plain,
% 1.37/1.53 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[914, 913])).
% 1.37/1.53 tff(916,plain,
% 1.37/1.53 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[915, 911])).
% 1.37/1.53 tff(917,plain,(
% 1.37/1.53 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.37/1.53 inference(skolemize,[status(sab)],[916])).
% 1.37/1.53 tff(918,plain,
% 1.37/1.53 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[917, 910])).
% 1.37/1.53 tff(919,plain,
% 1.37/1.53 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(920,plain,
% 1.37/1.53 ((hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (hskp12 | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(921,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | (~c0_1(a16))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[920])).
% 1.37/1.54 tff(922,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[921, 919])).
% 1.37/1.54 tff(923,plain,
% 1.37/1.54 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(924,plain,
% 1.37/1.54 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a16) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | (~c0_1(a16))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[923, 922])).
% 1.37/1.54 tff(925,plain,
% 1.37/1.54 (hskp12),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[924, 101, 856, 848, 876, 840, 803, 918, 908])).
% 1.37/1.54 tff(926,plain,
% 1.37/1.54 (((~hskp12) | (~c3_1(a20))) <=> ((~hskp12) | (~c3_1(a20)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(927,plain,
% 1.37/1.54 (((~c3_1(a20)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a20)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(928,axiom,((~c3_1(a20)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.37/1.54 tff(929,plain,
% 1.37/1.54 ((~hskp12) | (~c3_1(a20))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[928, 927])).
% 1.37/1.54 tff(930,plain,
% 1.37/1.54 ((~hskp12) | (~c3_1(a20))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[929, 926])).
% 1.37/1.54 tff(931,plain,
% 1.37/1.54 (~c3_1(a20)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[930, 925])).
% 1.37/1.54 tff(932,plain,
% 1.37/1.54 (((~hskp12) | (~c1_1(a20))) <=> ((~hskp12) | (~c1_1(a20)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(933,plain,
% 1.37/1.54 (((~c1_1(a20)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a20)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(934,axiom,((~c1_1(a20)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.37/1.54 tff(935,plain,
% 1.37/1.54 ((~hskp12) | (~c1_1(a20))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[934, 933])).
% 1.37/1.54 tff(936,plain,
% 1.37/1.54 ((~hskp12) | (~c1_1(a20))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[935, 932])).
% 1.37/1.54 tff(937,plain,
% 1.37/1.54 (~c1_1(a20)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[936, 925])).
% 1.37/1.54 tff(938,plain,
% 1.37/1.54 (((~hskp12) | c2_1(a20)) <=> ((~hskp12) | c2_1(a20))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(939,axiom,((~hskp12) | c2_1(a20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.37/1.54 tff(940,plain,
% 1.37/1.54 ((~hskp12) | c2_1(a20)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[939, 938])).
% 1.37/1.54 tff(941,plain,
% 1.37/1.54 ((~hskp12) | c2_1(a20)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[940, 938])).
% 1.37/1.54 tff(942,plain,
% 1.37/1.54 ((~hskp12) | c2_1(a20)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[941, 938])).
% 1.37/1.54 tff(943,plain,
% 1.37/1.54 ((~hskp12) | c2_1(a20)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[942, 938])).
% 1.37/1.54 tff(944,plain,
% 1.37/1.54 ((~hskp12) | c2_1(a20)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[943, 938])).
% 1.37/1.54 tff(945,plain,
% 1.37/1.54 (c2_1(a20)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[944, 925])).
% 1.37/1.54 tff(946,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(947,plain,
% 1.37/1.54 ((hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a13) | c2_1(a13) | c0_1(a13)) <=> (hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(948,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a13) | c2_1(a13) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[947])).
% 1.37/1.54 tff(949,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a13) | c2_1(a13) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[948, 946])).
% 1.37/1.54 tff(950,plain,
% 1.37/1.54 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a13) | c2_1(a13) | c0_1(a13))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(951,plain,
% 1.37/1.54 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[950, 949])).
% 1.37/1.54 tff(952,plain,
% 1.37/1.54 (hskp5),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[951, 101, 945, 937, 931, 801, 799, 275, 891])).
% 1.37/1.54 tff(953,plain,
% 1.37/1.54 (~c2_1(a11)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[291, 952])).
% 1.37/1.54 tff(954,plain,
% 1.37/1.54 (~c1_1(a11)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[297, 952])).
% 1.37/1.54 tff(955,plain,
% 1.37/1.54 (c0_1(a11)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[305, 952])).
% 1.37/1.54 tff(956,plain,
% 1.37/1.54 (((~hskp10) | c3_1(a18)) <=> ((~hskp10) | c3_1(a18))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(957,axiom,((~hskp10) | c3_1(a18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.37/1.54 tff(958,plain,
% 1.37/1.54 ((~hskp10) | c3_1(a18)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[957, 956])).
% 1.37/1.54 tff(959,plain,
% 1.37/1.54 ((~hskp10) | c3_1(a18)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[958, 956])).
% 1.37/1.54 tff(960,plain,
% 1.37/1.54 ((~hskp10) | c3_1(a18)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[959, 956])).
% 1.37/1.54 tff(961,plain,
% 1.37/1.54 ((~hskp10) | c3_1(a18)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[960, 956])).
% 1.37/1.54 tff(962,plain,
% 1.37/1.54 ((~hskp10) | c3_1(a18)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[961, 956])).
% 1.37/1.54 tff(963,plain,
% 1.37/1.54 (c3_1(a18)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[962, 863])).
% 1.37/1.54 tff(964,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(965,plain,
% 1.37/1.54 (((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18))) <=> (c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(966,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[965])).
% 1.37/1.54 tff(967,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[966, 964])).
% 1.37/1.54 tff(968,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(969,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[968, 967])).
% 1.37/1.54 tff(970,plain,
% 1.37/1.54 ($false),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[969, 101, 963, 955, 875, 869, 954, 953, 697, 884])).
% 1.37/1.54 tff(971,plain,(hskp21 | hskp1 | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | hskp24 | hskp3 | c2_1(a15) | c3_1(a15) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.54 tff(972,plain,
% 1.37/1.54 (hskp21),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[971, 526, 144, 143, 142, 191, 48, 698, 444, 451])).
% 1.37/1.54 tff(973,plain,
% 1.37/1.54 (c1_1(a38)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[603, 972])).
% 1.37/1.54 tff(974,plain,
% 1.37/1.54 (c0_1(a38)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[595, 972])).
% 1.37/1.54 tff(975,plain,
% 1.37/1.54 (^[U: $i] : refl((hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(976,plain,
% 1.37/1.54 (![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[975])).
% 1.37/1.54 tff(977,plain,
% 1.37/1.54 (![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(978,plain,
% 1.37/1.54 (^[U: $i] : 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(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)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp24))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) <=> (hskp24 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) | hskp6) <=> ((hskp24 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp6))), rewrite(((hskp24 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) | hskp6) <=> (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(979,plain,
% 1.37/1.54 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) | hskp6) <=> ![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[978])).
% 1.37/1.54 tff(980,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp24) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 1.37/1.54 tff(981,plain,
% 1.37/1.54 (![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[980, 979])).
% 1.37/1.54 tff(982,plain,
% 1.37/1.54 (![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[981, 977])).
% 1.37/1.54 tff(983,plain,(
% 1.37/1.54 ![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(skolemize,[status(sab)],[982])).
% 1.37/1.54 tff(984,plain,
% 1.37/1.54 (![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[983, 976])).
% 1.37/1.54 tff(985,plain,
% 1.37/1.54 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | c2_1(a38) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a38) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(986,plain,
% 1.37/1.54 ((hskp24 | hskp6 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38))) <=> (hskp24 | hskp6 | c2_1(a38) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(987,plain,
% 1.37/1.54 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | c2_1(a38) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[986])).
% 1.37/1.54 tff(988,plain,
% 1.37/1.54 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a38) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[987, 985])).
% 1.37/1.54 tff(989,plain,
% 1.37/1.54 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(990,plain,
% 1.37/1.54 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a38) | (~ndr1_0) | (~c0_1(a38)) | (~c1_1(a38))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[989, 988])).
% 1.37/1.54 tff(991,plain,
% 1.37/1.54 (hskp24 | hskp6 | (~c0_1(a38)) | (~c1_1(a38))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[990, 101, 450, 984])).
% 1.37/1.54 tff(992,plain,
% 1.37/1.54 (hskp6),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[991, 974, 526, 973])).
% 1.37/1.54 tff(993,plain,
% 1.37/1.54 (~c3_1(a13)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[177, 992])).
% 1.37/1.54 tff(994,plain,
% 1.37/1.54 (~c1_1(a13)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[183, 992])).
% 1.37/1.54 tff(995,plain,
% 1.37/1.54 (~c0_1(a13)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[189, 992])).
% 1.37/1.54 tff(996,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(997,plain,
% 1.37/1.54 (((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(998,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[997])).
% 1.37/1.54 tff(999,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[998, 996])).
% 1.37/1.54 tff(1000,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(1001,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[1000, 999])).
% 1.37/1.54 tff(1002,plain,
% 1.37/1.54 (~c3_1(a38)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[1001, 101, 974, 973, 450, 995, 994, 993, 36])).
% 1.37/1.54 tff(1003,plain,
% 1.37/1.54 (hskp2),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[232, 101, 191, 995, 994, 993, 47])).
% 1.37/1.54 tff(1004,plain,
% 1.37/1.54 (~c2_1(a3)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[197, 1003])).
% 1.37/1.54 tff(1005,plain,
% 1.37/1.54 (c3_1(a3)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[205, 1003])).
% 1.37/1.54 tff(1006,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a38) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a38) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(1007,plain,
% 1.37/1.54 (((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38))) <=> (c2_1(a38) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(1008,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a38) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[1007])).
% 1.37/1.54 tff(1009,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a38) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[1008, 1006])).
% 1.37/1.54 tff(1010,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(1011,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a38) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 1.37/1.54 tff(1012,plain,
% 1.37/1.54 (~c0_1(a3)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[1011, 101, 974, 973, 1005, 450, 1004, 901, 1002])).
% 1.37/1.54 tff(1013,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a38) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | c3_1(a38) | (~c1_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a38) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | c3_1(a38) | (~c1_1(a38)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(1014,plain,
% 1.37/1.54 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a38) | c2_1(a38) | (~c1_1(a38)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c2_1(a38) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | c3_1(a38) | (~c1_1(a38)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(1015,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a38) | c2_1(a38) | (~c1_1(a38)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a38) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | c3_1(a38) | (~c1_1(a38))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[1014])).
% 1.37/1.54 tff(1016,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a38) | c2_1(a38) | (~c1_1(a38)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a38) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | c3_1(a38) | (~c1_1(a38)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[1015, 1013])).
% 1.37/1.54 tff(1017,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a38) | c2_1(a38) | (~c1_1(a38)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(1018,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a38) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | c3_1(a38) | (~c1_1(a38))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 1.37/1.54 tff(1019,plain,
% 1.37/1.54 ($false),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[1018, 101, 973, 1005, 144, 143, 450, 1004, 142, 680, 1002, 1012])).
% 1.37/1.54 tff(1020,plain,(hskp24 | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a38) | c3_1(a1) | hskp1 | hskp3 | c2_1(a15) | c3_1(a15) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.54 tff(1021,plain,
% 1.37/1.54 (hskp24),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[1020, 191, 756, 450, 755, 754, 48, 698, 444, 451])).
% 1.37/1.54 tff(1022,plain,
% 1.37/1.54 (c2_1(a58)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[442, 1021])).
% 1.37/1.54 tff(1023,plain,
% 1.37/1.54 (~hskp2),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[222, 191, 1022, 37, 26])).
% 1.37/1.54 tff(1024,plain,
% 1.37/1.54 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(1025,plain,
% 1.37/1.54 ((hskp2 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15)) <=> (hskp2 | hskp1 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(1026,plain,
% 1.37/1.54 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15)))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[1025])).
% 1.37/1.54 tff(1027,plain,
% 1.37/1.54 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15))),
% 1.37/1.54 inference(transitivity,[status(thm)],[1026, 1024])).
% 1.37/1.54 tff(1028,plain,
% 1.37/1.54 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | c0_1(a15))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(1029,plain,
% 1.37/1.54 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c1_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 1.37/1.54 tff(1030,plain,
% 1.37/1.54 (hskp2 | hskp1 | c3_1(a15) | c0_1(a15)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[1029, 101, 451, 47])).
% 1.37/1.54 tff(1031,plain,
% 1.37/1.54 (c0_1(a15)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[1030, 1023, 444, 191])).
% 1.37/1.54 tff(1032,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a15) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | (~c0_1(a15)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(1033,plain,
% 1.37/1.54 (((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a15) | c1_1(a15) | c3_1(a15)) <=> (c1_1(a15) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | (~c0_1(a15)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(1034,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a15) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | (~c0_1(a15))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[1033])).
% 1.37/1.55 tff(1035,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | (~c0_1(a15)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[1034, 1032])).
% 1.37/1.55 tff(1036,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a15) | c1_1(a15) | c3_1(a15))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(1037,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | (~c0_1(a15))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 1.37/1.55 tff(1038,plain,
% 1.37/1.55 (c0_1(a1) | (~c0_1(a15))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1037, 101, 756, 451, 698, 444, 755, 323])).
% 1.37/1.55 tff(1039,plain,
% 1.37/1.55 (c0_1(a1)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1038, 1031])).
% 1.37/1.55 tff(1040,plain,
% 1.37/1.55 (hskp6 | (~c0_1(a1))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[150, 101, 754, 756, 755, 141])).
% 1.37/1.55 tff(1041,plain,
% 1.37/1.55 (hskp6),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1040, 1039])).
% 1.37/1.55 tff(1042,plain,
% 1.37/1.55 (~c0_1(a13)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[189, 1041])).
% 1.37/1.55 tff(1043,plain,
% 1.37/1.55 (~c3_1(a13)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[177, 1041])).
% 1.37/1.55 tff(1044,assumption,(~hskp2), introduced(assumption)).
% 1.37/1.55 tff(1045,plain,
% 1.37/1.55 (c0_1(a15)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1030, 1044, 444, 191])).
% 1.37/1.55 tff(1046,plain,
% 1.37/1.55 (c0_1(a1) | (~c0_1(a15))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1037, 101, 143, 451, 698, 444, 142, 323])).
% 1.37/1.55 tff(1047,plain,
% 1.37/1.55 (c0_1(a1)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1046, 1045])).
% 1.37/1.55 tff(1048,plain,
% 1.37/1.55 (hskp2 | c0_1(a13) | c1_1(a13)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[232, 101, 191, 224, 47])).
% 1.37/1.55 tff(1049,plain,
% 1.37/1.55 (c1_1(a13)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1048, 1044, 226])).
% 1.37/1.55 tff(1050,plain,
% 1.37/1.55 (~hskp6),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[183, 1049])).
% 1.37/1.55 tff(1051,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[151, 1050, 1047])).
% 1.37/1.55 tff(1052,plain,(hskp2 | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | hskp1 | c3_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(1053,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1052, 1043, 1042, 756, 755, 451, 698, 444, 754, 191, 1023])).
% 1.37/1.55 tff(1054,plain,(hskp1 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a58) | c1_1(a58) | c2_1(a38) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(1055,plain,
% 1.37/1.55 (hskp1),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1054, 444, 698, 451, 37, 26, 450, 48])).
% 1.37/1.55 tff(1056,plain,
% 1.37/1.55 (~c2_1(a2)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[247, 1055])).
% 1.37/1.55 tff(1057,plain,
% 1.37/1.55 (~c0_1(a2)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[253, 1055])).
% 1.37/1.55 tff(1058,plain,
% 1.37/1.55 (~c3_1(a2)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[241, 1055])).
% 1.37/1.55 tff(1059,plain,
% 1.37/1.55 (~c0_1(a37)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[631, 814])).
% 1.37/1.55 tff(1060,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c0_1(a18) | c1_1(a18) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c0_1(a18) | c1_1(a18) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1061,plain,
% 1.37/1.55 (((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18))) <=> (c0_1(a37) | c0_1(a18) | c1_1(a18) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1062,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c0_1(a18) | c1_1(a18) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[1061])).
% 1.37/1.55 tff(1063,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c0_1(a18) | c1_1(a18) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[1062, 1060])).
% 1.37/1.55 tff(1064,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c0_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(1065,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c0_1(a18) | c1_1(a18) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 1.37/1.55 tff(1066,plain,
% 1.37/1.55 (~c0_1(a15)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1065, 101, 815, 963, 1059, 875, 869, 451, 698, 697, 817])).
% 1.37/1.55 tff(1067,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a18) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a18)) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a18) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a18)) | (~c3_1(a18)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1068,plain,
% 1.37/1.55 (((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a15) | c0_1(a15) | c3_1(a15)) <=> (c1_1(a18) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a18)) | (~c3_1(a18)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1069,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a15) | c0_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a18) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a18)) | (~c3_1(a18))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[1068])).
% 1.37/1.55 tff(1070,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a15) | c0_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a18) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a18)) | (~c3_1(a18)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[1069, 1067])).
% 1.37/1.55 tff(1071,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a15) | c0_1(a15) | c3_1(a15))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(1072,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a18) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a18)) | (~c3_1(a18))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 1.37/1.55 tff(1073,plain,
% 1.37/1.55 (~c2_1(a18)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1072, 101, 963, 869, 451, 698, 444, 344, 1066])).
% 1.37/1.55 tff(1074,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a37) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a37) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | (~c3_1(a37)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1075,plain,
% 1.37/1.55 ((hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37))) <=> (hskp12 | c0_1(a37) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | (~c3_1(a37)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1076,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a37) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | (~c3_1(a37))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[1075])).
% 1.37/1.55 tff(1077,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a37) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | (~c3_1(a37)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[1076, 1074])).
% 1.37/1.55 tff(1078,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(1079,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a37) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a37) | (~c3_1(a37))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 1.37/1.55 tff(1080,plain,
% 1.37/1.55 (hskp12),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1079, 101, 815, 856, 848, 1059, 840, 918, 817])).
% 1.37/1.55 tff(1081,plain,
% 1.37/1.55 (~c3_1(a20)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[930, 1080])).
% 1.37/1.55 tff(1082,plain,
% 1.37/1.55 (~c1_1(a20)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[936, 1080])).
% 1.37/1.55 tff(1083,plain,
% 1.37/1.55 (c2_1(a20)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[944, 1080])).
% 1.37/1.55 tff(1084,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a20)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1085,plain,
% 1.37/1.55 ((hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a20)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1086,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a20))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[1085])).
% 1.37/1.55 tff(1087,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a20)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[1086, 1084])).
% 1.37/1.55 tff(1088,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(1089,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a20) | c3_1(a20) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a20))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 1.37/1.55 tff(1090,plain,
% 1.37/1.55 (hskp5),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1089, 101, 1083, 1082, 1081, 14, 13, 12, 275])).
% 1.37/1.55 tff(1091,plain,
% 1.37/1.55 (~c2_1(a11)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[291, 1090])).
% 1.37/1.55 tff(1092,plain,
% 1.37/1.55 (~c1_1(a11)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[297, 1090])).
% 1.37/1.55 tff(1093,plain,
% 1.37/1.55 (c0_1(a11)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[305, 1090])).
% 1.37/1.55 tff(1094,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[969, 101, 963, 1093, 875, 869, 1092, 1091, 697, 1073])).
% 1.37/1.55 tff(1095,plain,(hskp21 | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(1096,plain,
% 1.37/1.55 (hskp21),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1095, 526, 698, 444, 14, 13, 12, 144, 143, 142, 451, 48])).
% 1.37/1.55 tff(1097,plain,
% 1.37/1.55 (hskp27),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[624, 1096, 450, 13, 14, 12])).
% 1.37/1.55 tff(1098,plain,
% 1.37/1.55 (c3_1(a12)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[560, 1097])).
% 1.37/1.55 tff(1099,plain,
% 1.37/1.55 (c1_1(a12)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[568, 1097])).
% 1.37/1.55 tff(1100,plain,
% 1.37/1.55 (~c2_1(a12)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[575, 101, 526, 48, 1099, 1098, 10])).
% 1.37/1.55 tff(1101,plain,
% 1.37/1.55 (c1_1(a38)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[603, 1096])).
% 1.37/1.55 tff(1102,plain,
% 1.37/1.55 (c0_1(a38)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[595, 1096])).
% 1.37/1.55 tff(1103,plain,
% 1.37/1.55 (hskp6),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[991, 1102, 526, 1101])).
% 1.37/1.55 tff(1104,plain,
% 1.37/1.55 (~c3_1(a13)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[177, 1103])).
% 1.37/1.55 tff(1105,plain,
% 1.37/1.55 (~c1_1(a13)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[183, 1103])).
% 1.37/1.55 tff(1106,plain,
% 1.37/1.55 (~c0_1(a13)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[189, 1103])).
% 1.37/1.55 tff(1107,plain,
% 1.37/1.55 (~c3_1(a38)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1001, 101, 1102, 1101, 450, 1106, 1105, 1104, 36])).
% 1.37/1.55 tff(1108,plain,
% 1.37/1.55 (((~hskp27) | c0_1(a12)) <=> ((~hskp27) | c0_1(a12))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1109,axiom,((~hskp27) | c0_1(a12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.37/1.55 tff(1110,plain,
% 1.37/1.55 ((~hskp27) | c0_1(a12)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 1.37/1.55 tff(1111,plain,
% 1.37/1.55 ((~hskp27) | c0_1(a12)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1110, 1108])).
% 1.37/1.55 tff(1112,plain,
% 1.37/1.55 ((~hskp27) | c0_1(a12)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1111, 1108])).
% 1.37/1.55 tff(1113,plain,
% 1.37/1.55 ((~hskp27) | c0_1(a12)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1112, 1108])).
% 1.37/1.55 tff(1114,plain,
% 1.37/1.55 ((~hskp27) | c0_1(a12)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1113, 1108])).
% 1.37/1.55 tff(1115,plain,
% 1.37/1.55 (c0_1(a12)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1114, 1097])).
% 1.37/1.55 tff(1116,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a12))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a12))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1117,plain,
% 1.37/1.55 (((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a12) | (~c3_1(a12)) | (~c0_1(a12)) | c2_1(a12) | (~c1_1(a12)) | (~c0_1(a12))) <=> ((~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a12))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1118,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a12) | (~c3_1(a12)) | (~c0_1(a12)) | c2_1(a12) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a12)))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[1117])).
% 1.37/1.55 tff(1119,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a12) | (~c3_1(a12)) | (~c0_1(a12)) | c2_1(a12) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a12))),
% 1.37/1.55 inference(transitivity,[status(thm)],[1118, 1116])).
% 1.37/1.55 tff(1120,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a12) | (~c3_1(a12)) | (~c0_1(a12)) | c2_1(a12) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(1121,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a12)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 1.37/1.55 tff(1122,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1121, 101, 1115, 1099, 1098, 1102, 1101, 901, 1107, 1100])).
% 1.37/1.55 tff(1123,plain,(hskp24 | c2_1(a38) | hskp3 | c2_1(a2) | c0_1(a2) | c3_1(a2) | c2_1(a15) | c3_1(a15) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(1124,plain,
% 1.37/1.55 (hskp24),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1123, 12, 48, 13, 14, 450, 698, 444, 754, 756, 755, 451])).
% 1.37/1.55 tff(1125,plain,
% 1.37/1.55 (c2_1(a58)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[442, 1124])).
% 1.37/1.55 tff(1126,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1127,plain,
% 1.37/1.55 (((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1128,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[1127])).
% 1.37/1.55 tff(1129,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[1128, 1126])).
% 1.37/1.55 tff(1130,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(1131,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 1.37/1.55 tff(1132,plain,
% 1.37/1.55 (c0_1(a2) | c3_1(a2) | (~c2_1(a58)) | (~c3_1(a58))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1131, 101, 26, 451, 698, 444, 13, 344])).
% 1.37/1.55 tff(1133,plain,
% 1.37/1.55 (~c3_1(a58)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1132, 1125, 14, 12])).
% 1.37/1.55 tff(1134,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a58)) | c3_1(a58))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1135,plain,
% 1.37/1.55 (((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c3_1(a15)) <=> (c0_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a58)) | c3_1(a58))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1136,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a58)) | c3_1(a58)))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[1135])).
% 1.37/1.55 tff(1137,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a58)) | c3_1(a58))),
% 1.37/1.55 inference(transitivity,[status(thm)],[1136, 1134])).
% 1.37/1.55 tff(1138,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c3_1(a15))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(1139,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a58)) | c3_1(a58)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 1.37/1.55 tff(1140,plain,
% 1.37/1.55 (~c0_1(a15)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1139, 101, 1125, 37, 451, 698, 444, 323, 1133])).
% 1.37/1.55 tff(1141,plain,
% 1.37/1.55 (hskp18),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[379, 1133, 1125])).
% 1.37/1.55 tff(1142,plain,
% 1.37/1.55 (~c3_1(a31)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[385, 1141])).
% 1.37/1.55 tff(1143,plain,
% 1.37/1.55 (c1_1(a31)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[393, 1141])).
% 1.37/1.55 tff(1144,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a58) | c3_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | c3_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1145,plain,
% 1.37/1.55 (((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c0_1(a15)) <=> (c1_1(a58) | c3_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(1146,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a58) | c3_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58)))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[1145])).
% 1.37/1.55 tff(1147,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | c3_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58))),
% 1.37/1.56 inference(transitivity,[status(thm)],[1146, 1144])).
% 1.37/1.56 tff(1148,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a15) | c1_1(a15) | c0_1(a15))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(1149,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | c3_1(a31) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a58)) | c3_1(a58)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 1.37/1.56 tff(1150,plain,
% 1.37/1.56 (c2_1(a31)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1149, 101, 1125, 1143, 26, 1142, 451, 698, 362, 1133, 1140])).
% 1.37/1.56 tff(1151,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a58) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a58)) | c3_1(a58))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1152,plain,
% 1.37/1.56 ((hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a15) | c2_1(a15) | c0_1(a15)) <=> (hskp5 | c1_1(a58) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a58)) | c3_1(a58))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1153,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a15) | c2_1(a15) | c0_1(a15))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a58) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a58)) | c3_1(a58)))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[1152])).
% 1.37/1.56 tff(1154,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a15) | c2_1(a15) | c0_1(a15))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a58)) | c3_1(a58))),
% 1.37/1.56 inference(transitivity,[status(thm)],[1153, 1151])).
% 1.37/1.56 tff(1155,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a15) | c2_1(a15) | c0_1(a15))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(1156,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a58)) | c3_1(a58)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 1.37/1.56 tff(1157,plain,
% 1.37/1.56 (hskp5),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1156, 101, 1125, 26, 698, 444, 275, 1133, 1140])).
% 1.37/1.56 tff(1158,plain,
% 1.37/1.56 (~c2_1(a11)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[291, 1157])).
% 1.37/1.56 tff(1159,plain,
% 1.37/1.56 (~c1_1(a11)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[297, 1157])).
% 1.37/1.56 tff(1160,plain,
% 1.37/1.56 (c0_1(a11)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[305, 1157])).
% 1.37/1.56 tff(1161,plain,
% 1.37/1.56 (~c3_1(a11)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[417, 101, 1143, 1160, 1142, 1159, 1158, 264, 1150])).
% 1.37/1.56 tff(1162,plain,
% 1.37/1.56 (~c0_1(a31)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[423, 1141])).
% 1.37/1.56 tff(1163,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1164,plain,
% 1.37/1.56 (((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15)) <=> (c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1165,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[1164])).
% 1.37/1.56 tff(1166,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[1165, 1163])).
% 1.37/1.56 tff(1167,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(1168,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 1.37/1.56 tff(1169,plain,
% 1.37/1.56 ($false),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1168, 101, 1160, 1162, 1142, 451, 698, 444, 1159, 323, 1150, 1161])).
% 1.37/1.56 tff(1170,plain,(c3_1(a2) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c1_1(a58) | c0_1(a58) | hskp3 | c0_1(a2) | c2_1(a2) | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.56 tff(1171,plain,
% 1.37/1.56 ($false),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1170, 1058, 1057, 698, 444, 26, 37, 48, 451, 1056, 450])).
% 1.37/1.56 tff(1172,plain,(c3_1(a15) | c2_1(a15) | c1_1(a58) | c0_1(a58) | hskp3 | c1_1(a15) | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.56 tff(1173,plain,
% 1.37/1.56 (c3_1(a15)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1172, 698, 26, 37, 48, 451, 450])).
% 1.37/1.56 tff(1174,assumption,(c3_1(a15)), introduced(assumption)).
% 1.37/1.56 tff(1175,plain,
% 1.37/1.56 (hskp0),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[545, 191, 48, 526, 37, 26])).
% 1.37/1.56 tff(1176,plain,
% 1.37/1.56 (~c3_1(a1)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[114, 1175])).
% 1.37/1.56 tff(1177,plain,
% 1.37/1.56 (c2_1(a1)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[122, 1175])).
% 1.37/1.56 tff(1178,plain,
% 1.37/1.56 (c1_1(a1)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[130, 1175])).
% 1.37/1.56 tff(1179,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1180,plain,
% 1.37/1.56 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15))) <=> (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1181,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[1180])).
% 1.37/1.56 tff(1182,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[1181, 1179])).
% 1.37/1.56 tff(1183,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(1184,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 1.37/1.56 tff(1185,plain,
% 1.37/1.56 (~c0_1(a15)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1184, 101, 1178, 1177, 451, 698, 1174, 1176, 264])).
% 1.37/1.56 tff(1186,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | c0_1(a15))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1187,plain,
% 1.37/1.56 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | c0_1(a15))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1188,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | c0_1(a15)))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[1187])).
% 1.37/1.56 tff(1189,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | c0_1(a15))),
% 1.37/1.56 inference(transitivity,[status(thm)],[1188, 1186])).
% 1.37/1.56 tff(1190,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(1191,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | c0_1(a15)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 1.37/1.56 tff(1192,plain,
% 1.37/1.56 (~c1_1(a2)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1191, 101, 1178, 1177, 698, 1174, 13, 12, 1176, 680, 1185])).
% 1.37/1.56 tff(1193,plain,
% 1.37/1.56 (~hskp20),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[643, 11, 13, 12, 14, 497])).
% 1.37/1.56 tff(1194,plain,
% 1.37/1.56 ($false),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[508, 1193, 497, 191])).
% 1.37/1.56 tff(1195,plain,(hskp0 | hskp1 | c2_1(a2) | c3_1(a2) | c0_1(a2) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.56 tff(1196,plain,
% 1.37/1.56 (hskp0),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1195, 14, 13, 12, 191, 48, 37, 26])).
% 1.37/1.56 tff(1197,plain,
% 1.37/1.56 (~c3_1(a1)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[114, 1196])).
% 1.37/1.56 tff(1198,plain,
% 1.37/1.56 (c2_1(a1)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[122, 1196])).
% 1.37/1.56 tff(1199,plain,
% 1.37/1.56 (c1_1(a1)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[130, 1196])).
% 1.37/1.56 tff(1200,plain,
% 1.37/1.56 (~c0_1(a15)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1184, 101, 1199, 1198, 451, 698, 1174, 1197, 264])).
% 1.37/1.56 tff(1201,plain,
% 1.37/1.56 (~c1_1(a2)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1191, 101, 1199, 1198, 698, 1174, 13, 12, 1197, 680, 1200])).
% 1.37/1.56 tff(1202,plain,
% 1.37/1.56 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1203,plain,
% 1.37/1.56 ((hskp2 | hskp1 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c0_1(a2)) <=> (hskp2 | hskp1 | c0_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1204,plain,
% 1.37/1.56 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c0_1(a2))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2)))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[1203])).
% 1.37/1.56 tff(1205,plain,
% 1.37/1.56 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c0_1(a2))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 1.37/1.56 inference(transitivity,[status(thm)],[1204, 1202])).
% 1.37/1.56 tff(1206,plain,
% 1.37/1.56 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c3_1(a2) | c1_1(a2) | c0_1(a2))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(1207,plain,
% 1.37/1.56 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 1.37/1.56 tff(1208,plain,
% 1.37/1.56 (hskp2 | hskp1 | c0_1(a2) | c1_1(a2)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1207, 101, 12, 47])).
% 1.37/1.56 tff(1209,plain,
% 1.37/1.56 (hskp2),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1208, 1201, 191, 14])).
% 1.37/1.56 tff(1210,plain,
% 1.37/1.56 (~c2_1(a3)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[197, 1209])).
% 1.37/1.56 tff(1211,plain,
% 1.37/1.56 (c3_1(a3)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[205, 1209])).
% 1.37/1.56 tff(1212,plain,
% 1.37/1.56 (c1_1(a3)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[213, 1209])).
% 1.37/1.56 tff(1213,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1214,plain,
% 1.37/1.56 ((hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp9 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1215,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | (~c1_1(a3))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[1214])).
% 1.37/1.56 tff(1216,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.37/1.56 inference(transitivity,[status(thm)],[1215, 1213])).
% 1.37/1.56 tff(1217,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(1218,plain,
% 1.37/1.56 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | (~c1_1(a3))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 1.37/1.56 tff(1219,plain,
% 1.37/1.56 (hskp9),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1218, 101, 1212, 1211, 1199, 1198, 1210, 1197, 827])).
% 1.37/1.56 tff(1220,plain,
% 1.37/1.56 (~c3_1(a16)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[839, 1219])).
% 1.37/1.56 tff(1221,plain,
% 1.37/1.56 (c1_1(a16)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[847, 1219])).
% 1.37/1.56 tff(1222,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a16)) | c2_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a16)) | c2_1(a16))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1223,plain,
% 1.37/1.56 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a16)) | c2_1(a16))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1224,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a16)) | c2_1(a16)))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[1223])).
% 1.37/1.56 tff(1225,plain,
% 1.37/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a16)) | c2_1(a16))),
% 1.37/1.56 inference(transitivity,[status(thm)],[1224, 1222])).
% 1.37/1.56 tff(1226,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 1.37/1.56 inference(quant_inst,[status(thm)],[])).
% 1.37/1.56 tff(1227,plain,
% 1.37/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a16)) | c2_1(a16)),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 1.37/1.56 tff(1228,plain,
% 1.37/1.56 (c2_1(a16)),
% 1.37/1.56 inference(unit_resolution,[status(thm)],[1227, 101, 1221, 1199, 1198, 1220, 698, 1174, 1197, 680, 1200])).
% 1.37/1.56 tff(1229,plain,
% 1.37/1.56 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 1.37/1.56 inference(bind,[status(th)],[])).
% 1.37/1.56 tff(1230,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.56 inference(quant_intro,[status(thm)],[1229])).
% 1.37/1.56 tff(1231,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1232,plain,
% 1.37/1.56 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | 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)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_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) | c2_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 1.37/1.56 inference(bind,[status(th)],[])).
% 1.37/1.56 tff(1233,plain,
% 1.37/1.56 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.56 inference(quant_intro,[status(thm)],[1232])).
% 1.37/1.56 tff(1234,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.37/1.56 tff(1235,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 1.37/1.56 tff(1236,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[1235, 1231])).
% 1.37/1.56 tff(1237,plain,(
% 1.37/1.56 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.56 inference(skolemize,[status(sab)],[1236])).
% 1.37/1.56 tff(1238,plain,
% 1.37/1.56 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 1.37/1.56 inference(modus_ponens,[status(thm)],[1237, 1230])).
% 1.37/1.56 tff(1239,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a3) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a3) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1240,plain,
% 1.37/1.56 ((hskp6 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp6 | c2_1(a3) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.37/1.56 inference(rewrite,[status(thm)],[])).
% 1.37/1.56 tff(1241,plain,
% 1.37/1.56 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a3) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3))))),
% 1.37/1.56 inference(monotonicity,[status(thm)],[1240])).
% 1.37/1.57 tff(1242,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a3) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[1241, 1239])).
% 1.37/1.57 tff(1243,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(1244,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a3) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1243, 1242])).
% 1.37/1.57 tff(1245,plain,
% 1.37/1.57 (hskp6),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1244, 101, 1212, 1211, 1210, 14, 13, 12, 1238])).
% 1.37/1.57 tff(1246,plain,
% 1.37/1.57 (~c1_1(a13)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[183, 1245])).
% 1.37/1.57 tff(1247,plain,
% 1.37/1.57 (~c0_1(a13)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[189, 1245])).
% 1.37/1.57 tff(1248,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a13) | c1_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a13) | c1_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a13)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1249,plain,
% 1.37/1.57 ((hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13))) <=> (hskp1 | c0_1(a13) | c1_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a13)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1250,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a13) | c1_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a13))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[1249])).
% 1.37/1.57 tff(1251,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a13) | c1_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a13)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[1250, 1248])).
% 1.37/1.57 tff(1252,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(1253,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a13) | c1_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c2_1(a13))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 1.37/1.57 tff(1254,plain,
% 1.37/1.57 (~c2_1(a13)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1253, 101, 191, 1212, 1211, 1247, 1246, 1210, 58])).
% 1.37/1.57 tff(1255,plain,
% 1.37/1.57 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.37/1.57 inference(bind,[status(th)],[])).
% 1.37/1.57 tff(1256,plain,
% 1.37/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.37/1.57 inference(quant_intro,[status(thm)],[1255])).
% 1.37/1.57 tff(1257,plain,
% 1.37/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1258,plain,
% 1.37/1.57 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.37/1.57 inference(bind,[status(th)],[])).
% 1.37/1.57 tff(1259,plain,
% 1.37/1.57 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.37/1.57 inference(quant_intro,[status(thm)],[1258])).
% 1.37/1.57 tff(1260,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 1.37/1.57 tff(1261,plain,
% 1.37/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 1.37/1.57 tff(1262,plain,
% 1.37/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1261, 1257])).
% 1.37/1.57 tff(1263,plain,(
% 1.37/1.57 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.37/1.57 inference(skolemize,[status(sab)],[1262])).
% 1.37/1.57 tff(1264,plain,
% 1.37/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1263, 1256])).
% 1.37/1.57 tff(1265,plain,
% 1.37/1.57 (~c3_1(a13)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[177, 1245])).
% 1.37/1.57 tff(1266,plain,
% 1.37/1.57 (c0_1(a16)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[855, 1219])).
% 1.37/1.57 tff(1267,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c1_1(a16)) | (~c0_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1268,plain,
% 1.37/1.57 ((hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (hskp12 | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1269,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c1_1(a16)) | (~c0_1(a16))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[1268])).
% 1.37/1.57 tff(1270,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c1_1(a16)) | (~c0_1(a16)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[1269, 1267])).
% 1.37/1.57 tff(1271,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(1272,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c3_1(a16) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a15) | (~c1_1(a16)) | (~c0_1(a16))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 1.37/1.57 tff(1273,plain,
% 1.37/1.57 (hskp12),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1272, 101, 1266, 1221, 1220, 698, 1174, 918, 1200])).
% 1.37/1.57 tff(1274,plain,
% 1.37/1.57 (~c1_1(a20)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[936, 1273])).
% 1.37/1.57 tff(1275,plain,
% 1.37/1.57 (c2_1(a20)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[944, 1273])).
% 1.37/1.57 tff(1276,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a20) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a20) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1277,plain,
% 1.37/1.57 (((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c1_1(a20) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1278,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a20) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[1277])).
% 1.37/1.57 tff(1279,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a20) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[1278, 1276])).
% 1.37/1.57 tff(1280,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(1281,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a20) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 1.37/1.57 tff(1282,plain,
% 1.37/1.57 (~c0_1(a20)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1281, 101, 1275, 1221, 1274, 1220, 1247, 1265, 1264, 1254, 1228])).
% 1.37/1.57 tff(1283,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a20) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a20) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | (~c2_1(a20)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1284,plain,
% 1.37/1.57 ((hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20))) <=> (hskp1 | c1_1(a20) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | (~c2_1(a20)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1285,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c1_1(a20) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | (~c2_1(a20))))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[1284])).
% 1.37/1.57 tff(1286,plain,
% 1.37/1.57 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a20) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | (~c2_1(a20)))),
% 1.37/1.57 inference(transitivity,[status(thm)],[1285, 1283])).
% 1.37/1.57 tff(1287,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(1288,plain,
% 1.37/1.57 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c1_1(a20) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | c0_1(a20) | (~c2_1(a20))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 1.37/1.57 tff(1289,plain,
% 1.37/1.57 ($false),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1288, 101, 191, 1275, 1212, 1211, 1274, 1210, 58, 1282])).
% 1.37/1.57 tff(1290,plain,(c0_1(a2) | hskp1 | c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | c1_1(a15) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.57 tff(1291,plain,
% 1.37/1.57 (c0_1(a2)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1290, 191, 698, 1174, 13, 12, 451, 48, 37, 26])).
% 1.37/1.57 tff(1292,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1293,plain,
% 1.37/1.57 (((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1294,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15)))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[1293])).
% 1.37/1.57 tff(1295,plain,
% 1.37/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))),
% 1.37/1.57 inference(transitivity,[status(thm)],[1294, 1292])).
% 1.37/1.57 tff(1296,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(1297,plain,
% 1.37/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15)),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 1.37/1.57 tff(1298,plain,
% 1.37/1.57 ($false),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1297, 101, 451, 698, 1174, 1291, 13, 697, 1185, 1192])).
% 1.37/1.57 tff(1299,plain,(hskp1 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a2) | c3_1(a2) | hskp3 | hskp24 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.57 tff(1300,plain,
% 1.37/1.57 (hskp1),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1299, 13, 698, 1174, 451, 12, 48, 526, 37, 26])).
% 1.37/1.57 tff(1301,plain,
% 1.37/1.57 (~c0_1(a2)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[253, 1300])).
% 1.37/1.57 tff(1302,plain,
% 1.37/1.57 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 1.37/1.57 inference(bind,[status(th)],[])).
% 1.37/1.57 tff(1303,plain,
% 1.37/1.57 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.57 inference(quant_intro,[status(thm)],[1302])).
% 1.37/1.57 tff(1304,plain,
% 1.37/1.57 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1305,plain,
% 1.37/1.57 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_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) | c3_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp8))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 1.37/1.57 inference(bind,[status(th)],[])).
% 1.37/1.57 tff(1306,plain,
% 1.37/1.57 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.57 inference(quant_intro,[status(thm)],[1305])).
% 1.37/1.57 tff(1307,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.37/1.57 tff(1308,plain,
% 1.37/1.57 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1307, 1306])).
% 1.37/1.57 tff(1309,plain,
% 1.37/1.57 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1308, 1304])).
% 1.37/1.57 tff(1310,plain,(
% 1.37/1.57 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.57 inference(skolemize,[status(sab)],[1309])).
% 1.37/1.57 tff(1311,plain,
% 1.37/1.57 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1310, 1303])).
% 1.37/1.57 tff(1312,plain,
% 1.37/1.57 (((~hskp8) | (~c3_1(a15))) <=> ((~hskp8) | (~c3_1(a15)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1313,plain,
% 1.37/1.57 (((~c3_1(a15)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a15)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1314,axiom,((~c3_1(a15)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.37/1.57 tff(1315,plain,
% 1.37/1.57 ((~hskp8) | (~c3_1(a15))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 1.37/1.57 tff(1316,plain,
% 1.37/1.57 ((~hskp8) | (~c3_1(a15))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1315, 1312])).
% 1.37/1.57 tff(1317,plain,
% 1.37/1.57 (~hskp8),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1316, 1174])).
% 1.37/1.57 tff(1318,plain,
% 1.37/1.57 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp7 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp7 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1319,plain,
% 1.37/1.57 ((hskp8 | hskp7 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | c2_1(a2)) <=> (hskp8 | hskp7 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1320,plain,
% 1.37/1.57 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | c2_1(a2))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp7 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0)))),
% 1.37/1.57 inference(monotonicity,[status(thm)],[1319])).
% 1.37/1.57 tff(1321,plain,
% 1.37/1.57 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | c2_1(a2))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp7 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 1.37/1.57 inference(transitivity,[status(thm)],[1320, 1318])).
% 1.37/1.57 tff(1322,plain,
% 1.37/1.57 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp8 | hskp7 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | c2_1(a2))),
% 1.37/1.57 inference(quant_inst,[status(thm)],[])).
% 1.37/1.57 tff(1323,plain,
% 1.37/1.57 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp8 | hskp7 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0)),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1322, 1321])).
% 1.37/1.57 tff(1324,plain,
% 1.37/1.57 (hskp7 | c0_1(a2) | c2_1(a2)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1323, 101, 1317, 12, 1311])).
% 1.37/1.57 tff(1325,plain,
% 1.37/1.57 (hskp7),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1324, 1301, 13])).
% 1.37/1.57 tff(1326,plain,
% 1.37/1.57 (((~hskp7) | (~c2_1(a14))) <=> ((~hskp7) | (~c2_1(a14)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1327,plain,
% 1.37/1.57 (((~c2_1(a14)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a14)))),
% 1.37/1.57 inference(rewrite,[status(thm)],[])).
% 1.37/1.57 tff(1328,axiom,((~c2_1(a14)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.37/1.57 tff(1329,plain,
% 1.37/1.57 ((~hskp7) | (~c2_1(a14))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1328, 1327])).
% 1.37/1.57 tff(1330,plain,
% 1.37/1.57 ((~hskp7) | (~c2_1(a14))),
% 1.37/1.57 inference(modus_ponens,[status(thm)],[1329, 1326])).
% 1.37/1.57 tff(1331,plain,
% 1.37/1.57 (~c2_1(a14)),
% 1.37/1.57 inference(unit_resolution,[status(thm)],[1330, 1325])).
% 1.37/1.58 tff(1332,plain,
% 1.37/1.58 (((~hskp7) | c1_1(a14)) <=> ((~hskp7) | c1_1(a14))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1333,axiom,((~hskp7) | c1_1(a14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.37/1.58 tff(1334,plain,
% 1.37/1.58 ((~hskp7) | c1_1(a14)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 1.37/1.58 tff(1335,plain,
% 1.37/1.58 ((~hskp7) | c1_1(a14)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1334, 1332])).
% 1.37/1.58 tff(1336,plain,
% 1.37/1.58 ((~hskp7) | c1_1(a14)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1335, 1332])).
% 1.37/1.58 tff(1337,plain,
% 1.37/1.58 ((~hskp7) | c1_1(a14)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1336, 1332])).
% 1.37/1.58 tff(1338,plain,
% 1.37/1.58 ((~hskp7) | c1_1(a14)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1337, 1332])).
% 1.37/1.58 tff(1339,plain,
% 1.37/1.58 (c1_1(a14)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1338, 1325])).
% 1.37/1.58 tff(1340,plain,
% 1.37/1.58 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c1_1(a14)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1341,plain,
% 1.37/1.58 ((hskp28 | hskp0 | (~ndr1_0) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14))) <=> (hskp28 | hskp0 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c1_1(a14)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1342,plain,
% 1.37/1.58 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c1_1(a14))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[1341])).
% 1.37/1.58 tff(1343,plain,
% 1.37/1.58 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c1_1(a14)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[1342, 1340])).
% 1.37/1.58 tff(1344,plain,
% 1.37/1.58 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(1345,plain,
% 1.37/1.58 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c1_1(a14))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 1.37/1.58 tff(1346,plain,
% 1.37/1.58 (hskp28 | hskp0 | (~c3_1(a14))),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1345, 101, 1339, 1331, 540])).
% 1.37/1.58 tff(1347,plain,
% 1.37/1.58 (~c3_1(a14)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1346, 497, 11])).
% 1.37/1.58 tff(1348,plain,
% 1.37/1.58 (((~hskp7) | (~c0_1(a14))) <=> ((~hskp7) | (~c0_1(a14)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1349,plain,
% 1.37/1.58 (((~c0_1(a14)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a14)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1350,axiom,((~c0_1(a14)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.37/1.58 tff(1351,plain,
% 1.37/1.58 ((~hskp7) | (~c0_1(a14))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 1.37/1.58 tff(1352,plain,
% 1.37/1.58 ((~hskp7) | (~c0_1(a14))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1351, 1348])).
% 1.37/1.58 tff(1353,plain,
% 1.37/1.58 (~c0_1(a14)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1352, 1325])).
% 1.37/1.58 tff(1354,plain,
% 1.37/1.58 (~hskp27),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[585, 11, 497, 526, 48])).
% 1.37/1.58 tff(1355,plain,
% 1.37/1.58 ((hskp27 | hskp13 | hskp8) <=> (hskp27 | hskp13 | hskp8)),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1356,plain,
% 1.37/1.58 (((hskp27 | hskp13) | hskp8) <=> (hskp27 | hskp13 | hskp8)),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1357,plain,
% 1.37/1.58 ((hskp27 | hskp13) <=> (hskp27 | hskp13)),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1358,plain,
% 1.37/1.58 (((hskp27 | hskp13) | hskp8) <=> ((hskp27 | hskp13) | hskp8)),
% 1.37/1.58 inference(monotonicity,[status(thm)],[1357])).
% 1.37/1.58 tff(1359,plain,
% 1.37/1.58 (((hskp27 | hskp13) | hskp8) <=> (hskp27 | hskp13 | hskp8)),
% 1.37/1.58 inference(transitivity,[status(thm)],[1358, 1356])).
% 1.37/1.58 tff(1360,axiom,((hskp27 | hskp13) | hskp8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 1.37/1.58 tff(1361,plain,
% 1.37/1.58 (hskp27 | hskp13 | hskp8),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 1.37/1.58 tff(1362,plain,
% 1.37/1.58 (hskp27 | hskp13 | hskp8),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1361, 1355])).
% 1.37/1.58 tff(1363,plain,
% 1.37/1.58 (hskp27 | hskp13 | hskp8),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1362, 1355])).
% 1.37/1.58 tff(1364,plain,
% 1.37/1.58 (hskp27 | hskp13 | hskp8),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1363, 1355])).
% 1.37/1.58 tff(1365,plain,
% 1.37/1.58 (hskp27 | hskp13 | hskp8),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1364, 1355])).
% 1.37/1.58 tff(1366,plain,
% 1.37/1.58 (hskp13),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1365, 1354, 1317])).
% 1.37/1.58 tff(1367,plain,
% 1.37/1.58 (~c3_1(a21)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[774, 1366])).
% 1.37/1.58 tff(1368,plain,
% 1.37/1.58 (~hskp20),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[643, 11, 13, 12, 1301, 497])).
% 1.37/1.58 tff(1369,plain,
% 1.37/1.58 (^[U: $i] : refl((hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(1370,plain,
% 1.37/1.58 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[1369])).
% 1.37/1.58 tff(1371,plain,
% 1.37/1.58 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1372,plain,
% 1.37/1.58 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp22))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp20) <=> ((hskp22 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp20))), rewrite(((hskp22 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U))) | hskp20) <=> (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp20) <=> (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(1373,plain,
% 1.37/1.58 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp20) <=> ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[1372])).
% 1.37/1.58 tff(1374,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp22) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 1.37/1.58 tff(1375,plain,
% 1.37/1.58 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 1.37/1.58 tff(1376,plain,
% 1.37/1.58 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1375, 1371])).
% 1.37/1.58 tff(1377,plain,(
% 1.37/1.58 ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.37/1.58 inference(skolemize,[status(sab)],[1376])).
% 1.37/1.58 tff(1378,plain,
% 1.37/1.58 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1377, 1370])).
% 1.37/1.58 tff(1379,plain,
% 1.37/1.58 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp20 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1380,plain,
% 1.37/1.58 ((hskp22 | hskp20 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15))) <=> (hskp22 | hskp20 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1381,plain,
% 1.37/1.58 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0)))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[1380])).
% 1.37/1.58 tff(1382,plain,
% 1.37/1.58 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp20 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))),
% 1.37/1.58 inference(transitivity,[status(thm)],[1381, 1379])).
% 1.37/1.58 tff(1383,plain,
% 1.37/1.58 ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(1384,plain,
% 1.37/1.58 ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp20 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 1.37/1.58 tff(1385,plain,
% 1.37/1.58 (hskp22 | hskp20 | c2_1(a15) | (~c3_1(a15))),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1384, 101, 451, 1378])).
% 1.37/1.58 tff(1386,plain,
% 1.37/1.58 (hskp22),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1385, 1368, 698, 1174])).
% 1.37/1.58 tff(1387,plain,
% 1.37/1.58 (((~hskp22) | (~c1_1(a42))) <=> ((~hskp22) | (~c1_1(a42)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1388,plain,
% 1.37/1.58 (((~c1_1(a42)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a42)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1389,axiom,((~c1_1(a42)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.37/1.58 tff(1390,plain,
% 1.37/1.58 ((~hskp22) | (~c1_1(a42))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 1.37/1.58 tff(1391,plain,
% 1.37/1.58 ((~hskp22) | (~c1_1(a42))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1390, 1387])).
% 1.37/1.58 tff(1392,plain,
% 1.37/1.58 (~c1_1(a42)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1391, 1386])).
% 1.37/1.58 tff(1393,plain,
% 1.37/1.58 (c2_1(a21)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[782, 1366])).
% 1.37/1.58 tff(1394,plain,
% 1.37/1.58 (((~hskp22) | c2_1(a42)) <=> ((~hskp22) | c2_1(a42))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1395,axiom,((~hskp22) | c2_1(a42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.37/1.58 tff(1396,plain,
% 1.37/1.58 ((~hskp22) | c2_1(a42)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.37/1.58 tff(1397,plain,
% 1.37/1.58 ((~hskp22) | c2_1(a42)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1396, 1394])).
% 1.37/1.58 tff(1398,plain,
% 1.37/1.58 ((~hskp22) | c2_1(a42)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1397, 1394])).
% 1.37/1.58 tff(1399,plain,
% 1.37/1.58 ((~hskp22) | c2_1(a42)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1398, 1394])).
% 1.37/1.58 tff(1400,plain,
% 1.37/1.58 ((~hskp22) | c2_1(a42)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1399, 1394])).
% 1.37/1.58 tff(1401,plain,
% 1.37/1.58 (c2_1(a42)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1400, 1386])).
% 1.37/1.58 tff(1402,plain,
% 1.37/1.58 (((~hskp22) | c0_1(a42)) <=> ((~hskp22) | c0_1(a42))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1403,axiom,((~hskp22) | c0_1(a42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.37/1.58 tff(1404,plain,
% 1.37/1.58 ((~hskp22) | c0_1(a42)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 1.37/1.58 tff(1405,plain,
% 1.37/1.58 ((~hskp22) | c0_1(a42)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1404, 1402])).
% 1.37/1.58 tff(1406,plain,
% 1.37/1.58 ((~hskp22) | c0_1(a42)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1405, 1402])).
% 1.37/1.58 tff(1407,plain,
% 1.37/1.58 ((~hskp22) | c0_1(a42)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1406, 1402])).
% 1.37/1.58 tff(1408,plain,
% 1.37/1.58 ((~hskp22) | c0_1(a42)),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1407, 1402])).
% 1.37/1.58 tff(1409,plain,
% 1.37/1.58 (c0_1(a42)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1408, 1386])).
% 1.37/1.58 tff(1410,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c3_1(a21) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a21) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1411,plain,
% 1.37/1.58 (((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a14) | c0_1(a14) | c3_1(a14)) <=> (c1_1(a42) | c3_1(a21) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1412,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a14) | c0_1(a14) | c3_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c3_1(a21) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[1411])).
% 1.37/1.58 tff(1413,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a14) | c0_1(a14) | c3_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a21) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[1412, 1410])).
% 1.37/1.58 tff(1414,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a14) | c0_1(a14) | c3_1(a14))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(1415,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a21) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 1.37/1.58 tff(1416,plain,
% 1.37/1.58 (~c1_1(a21)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1415, 101, 1409, 1401, 1393, 1392, 1367, 1353, 1331, 1264, 1347])).
% 1.37/1.58 tff(1417,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | c1_1(a21) | (~c2_1(a21)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1418,plain,
% 1.37/1.58 (((~ndr1_0) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | c1_1(a21) | (~c2_1(a21)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1419,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | c1_1(a21) | (~c2_1(a21))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[1418])).
% 1.37/1.58 tff(1420,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | c1_1(a21) | (~c2_1(a21)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[1419, 1417])).
% 1.37/1.58 tff(1421,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(1422,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | c1_1(a21) | (~c2_1(a21))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 1.37/1.58 tff(1423,plain,
% 1.37/1.58 ($false),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1422, 101, 452, 1393, 1339, 37, 26, 1367, 1331, 362, 1347, 1416])).
% 1.37/1.58 tff(1424,plain,(hskp0 | c0_1(a58) | c1_1(a58) | c2_1(a15) | (~c3_1(a15)) | c1_1(a15) | c2_1(a2) | c3_1(a2) | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.37/1.58 tff(1425,plain,
% 1.37/1.58 (hskp0),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1424, 13, 26, 698, 1174, 451, 37, 12, 526, 48])).
% 1.37/1.58 tff(1426,plain,
% 1.37/1.58 (~c3_1(a1)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[114, 1425])).
% 1.37/1.58 tff(1427,plain,
% 1.37/1.58 (c2_1(a1)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[122, 1425])).
% 1.37/1.58 tff(1428,plain,
% 1.37/1.58 (c1_1(a1)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[130, 1425])).
% 1.37/1.58 tff(1429,plain,
% 1.37/1.58 (~c0_1(a15)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1184, 101, 1428, 1427, 451, 698, 1174, 1426, 264])).
% 1.37/1.58 tff(1430,plain,
% 1.37/1.58 (~c0_1(a15)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1184, 101, 144, 143, 451, 698, 1174, 142, 264])).
% 1.37/1.58 tff(1431,assumption,(hskp9), introduced(assumption)).
% 1.37/1.58 tff(1432,plain,
% 1.37/1.58 (~c3_1(a16)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[839, 1431])).
% 1.37/1.58 tff(1433,plain,
% 1.37/1.58 (c1_1(a16)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[847, 1431])).
% 1.37/1.58 tff(1434,plain,
% 1.37/1.58 (c2_1(a16)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1227, 101, 1433, 144, 143, 1432, 698, 1174, 142, 680, 1430])).
% 1.37/1.58 tff(1435,plain,
% 1.37/1.58 (c0_1(a16)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[855, 1431])).
% 1.37/1.58 tff(1436,plain,
% 1.37/1.58 (hskp12),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1272, 101, 1435, 1433, 1432, 698, 1174, 918, 1430])).
% 1.37/1.58 tff(1437,plain,
% 1.37/1.58 (~c1_1(a20)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[936, 1436])).
% 1.37/1.58 tff(1438,plain,
% 1.37/1.58 (c2_1(a20)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[944, 1436])).
% 1.37/1.58 tff(1439,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a20) | c3_1(a16) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a20) | c3_1(a16) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1440,plain,
% 1.37/1.58 (((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a20) | c3_1(a16) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1441,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a20) | c3_1(a16) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[1440])).
% 1.37/1.58 tff(1442,plain,
% 1.37/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a20) | c3_1(a16) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[1441, 1439])).
% 1.37/1.58 tff(1443,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(1444,plain,
% 1.37/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a20) | c3_1(a16) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a16)) | (~c2_1(a16)) | (~c0_1(a20)) | (~c2_1(a20))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 1.37/1.58 tff(1445,plain,
% 1.37/1.58 (~c0_1(a20)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1444, 101, 1438, 1433, 1437, 1432, 14, 13, 12, 1264, 1434])).
% 1.37/1.58 tff(1446,plain,
% 1.37/1.58 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(1447,plain,
% 1.37/1.58 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[1446])).
% 1.37/1.58 tff(1448,plain,
% 1.37/1.58 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1449,plain,
% 1.37/1.58 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(1450,plain,
% 1.37/1.58 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[1449])).
% 1.37/1.58 tff(1451,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.37/1.58 tff(1452,plain,
% 1.37/1.58 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 1.37/1.58 tff(1453,plain,
% 1.37/1.58 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1452, 1448])).
% 1.37/1.58 tff(1454,plain,(
% 1.37/1.58 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.58 inference(skolemize,[status(sab)],[1453])).
% 1.37/1.58 tff(1455,plain,
% 1.37/1.58 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1454, 1447])).
% 1.37/1.58 tff(1456,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c1_1(a20) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a20) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1457,plain,
% 1.37/1.58 ((hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20))) <=> (hskp2 | c1_1(a20) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1458,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c1_1(a20) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[1457])).
% 1.37/1.58 tff(1459,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a20) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))),
% 1.37/1.58 inference(transitivity,[status(thm)],[1458, 1456])).
% 1.37/1.58 tff(1460,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a20) | c1_1(a20) | (~c2_1(a20)))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(1461,plain,
% 1.37/1.58 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a20) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[1460, 1459])).
% 1.37/1.58 tff(1462,plain,
% 1.37/1.58 ($false),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1461, 101, 1044, 1438, 1437, 451, 698, 1174, 1455, 1445])).
% 1.37/1.58 tff(1463,plain,((~hskp9) | hskp2 | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.58 tff(1464,plain,
% 1.37/1.58 (~hskp9),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1463, 1044, 451, 698, 1174, 14, 13, 12, 144, 143, 142])).
% 1.37/1.58 tff(1465,plain,
% 1.37/1.58 (hskp7),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1324, 14, 13])).
% 1.37/1.58 tff(1466,plain,
% 1.37/1.58 (~c2_1(a14)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1330, 1465])).
% 1.37/1.58 tff(1467,plain,
% 1.37/1.58 (c1_1(a14)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[1338, 1465])).
% 1.37/1.58 tff(1468,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)) | (~c1_1(a14)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1469,plain,
% 1.37/1.58 ((hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14))) <=> (hskp9 | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)) | (~c1_1(a14)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(1470,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)) | (~c1_1(a14))))),
% 1.37/1.58 inference(monotonicity,[status(thm)],[1469])).
% 1.37/1.58 tff(1471,plain,
% 1.37/1.58 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)) | (~c1_1(a14)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[1470, 1468])).
% 1.37/1.59 tff(1472,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a14) | (~c3_1(a14)) | (~c1_1(a14)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(1473,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)) | (~c1_1(a14))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 1.37/1.59 tff(1474,plain,
% 1.37/1.59 (hskp9 | (~c3_1(a14))),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1473, 101, 1467, 144, 143, 1466, 142, 827])).
% 1.37/1.59 tff(1475,plain,
% 1.37/1.59 (~c3_1(a14)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1474, 1464])).
% 1.37/1.59 tff(1476,plain,
% 1.37/1.59 ((hskp17 | hskp9 | hskp2) <=> (hskp17 | hskp9 | hskp2)),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1477,plain,
% 1.37/1.59 (((hskp9 | hskp2) | hskp17) <=> (hskp17 | hskp9 | hskp2)),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1478,plain,
% 1.37/1.59 ((hskp9 | hskp2) <=> (hskp9 | hskp2)),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1479,plain,
% 1.37/1.59 (((hskp9 | hskp2) | hskp17) <=> ((hskp9 | hskp2) | hskp17)),
% 1.37/1.59 inference(monotonicity,[status(thm)],[1478])).
% 1.37/1.59 tff(1480,plain,
% 1.37/1.59 (((hskp9 | hskp2) | hskp17) <=> (hskp17 | hskp9 | hskp2)),
% 1.37/1.59 inference(transitivity,[status(thm)],[1479, 1477])).
% 1.37/1.59 tff(1481,axiom,((hskp9 | hskp2) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 1.37/1.59 tff(1482,plain,
% 1.37/1.59 (hskp17 | hskp9 | hskp2),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 1.37/1.59 tff(1483,plain,
% 1.37/1.59 (hskp17 | hskp9 | hskp2),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1482, 1476])).
% 1.37/1.59 tff(1484,plain,
% 1.37/1.59 (hskp17 | hskp9 | hskp2),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1483, 1476])).
% 1.37/1.59 tff(1485,plain,
% 1.37/1.59 (hskp17 | hskp9 | hskp2),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1484, 1476])).
% 1.37/1.59 tff(1486,plain,
% 1.37/1.59 (hskp17 | hskp9 | hskp2),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1485, 1476])).
% 1.37/1.59 tff(1487,plain,
% 1.37/1.59 (hskp17),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1486, 1464, 1044])).
% 1.37/1.59 tff(1488,plain,
% 1.37/1.59 (((~hskp17) | (~c2_1(a28))) <=> ((~hskp17) | (~c2_1(a28)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1489,plain,
% 1.37/1.59 (((~c2_1(a28)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a28)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1490,axiom,((~c2_1(a28)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.37/1.59 tff(1491,plain,
% 1.37/1.59 ((~hskp17) | (~c2_1(a28))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1490, 1489])).
% 1.37/1.59 tff(1492,plain,
% 1.37/1.59 ((~hskp17) | (~c2_1(a28))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1491, 1488])).
% 1.37/1.59 tff(1493,plain,
% 1.37/1.59 (~c2_1(a28)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1492, 1487])).
% 1.37/1.59 tff(1494,plain,
% 1.37/1.59 (((~hskp17) | (~c0_1(a28))) <=> ((~hskp17) | (~c0_1(a28)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1495,plain,
% 1.37/1.59 (((~c0_1(a28)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a28)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1496,axiom,((~c0_1(a28)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.37/1.59 tff(1497,plain,
% 1.37/1.59 ((~hskp17) | (~c0_1(a28))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 1.37/1.59 tff(1498,plain,
% 1.37/1.59 ((~hskp17) | (~c0_1(a28))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1497, 1494])).
% 1.37/1.59 tff(1499,plain,
% 1.37/1.59 (~c0_1(a28)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1498, 1487])).
% 1.37/1.59 tff(1500,plain,
% 1.37/1.59 (((~hskp17) | c3_1(a28)) <=> ((~hskp17) | c3_1(a28))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1501,axiom,((~hskp17) | c3_1(a28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.37/1.59 tff(1502,plain,
% 1.37/1.59 ((~hskp17) | c3_1(a28)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 1.37/1.59 tff(1503,plain,
% 1.37/1.59 ((~hskp17) | c3_1(a28)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1502, 1500])).
% 1.37/1.59 tff(1504,plain,
% 1.37/1.59 ((~hskp17) | c3_1(a28)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1503, 1500])).
% 1.37/1.59 tff(1505,plain,
% 1.37/1.59 ((~hskp17) | c3_1(a28)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1504, 1500])).
% 1.37/1.59 tff(1506,plain,
% 1.37/1.59 ((~hskp17) | c3_1(a28)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1505, 1500])).
% 1.37/1.59 tff(1507,plain,
% 1.37/1.59 (c3_1(a28)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1506, 1487])).
% 1.37/1.59 tff(1508,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a28) | c2_1(a28) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | (~c1_1(a14)) | (~c3_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a28) | c2_1(a28) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | (~c1_1(a14)) | (~c3_1(a28)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1509,plain,
% 1.37/1.59 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a28) | c0_1(a28) | (~c3_1(a28))) <=> (c0_1(a28) | c2_1(a28) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | (~c1_1(a14)) | (~c3_1(a28)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1510,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a28) | c0_1(a28) | (~c3_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a28) | c2_1(a28) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | (~c1_1(a14)) | (~c3_1(a28))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[1509])).
% 1.37/1.59 tff(1511,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a28) | c0_1(a28) | (~c3_1(a28)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a28) | c2_1(a28) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | (~c1_1(a14)) | (~c3_1(a28)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[1510, 1508])).
% 1.37/1.59 tff(1512,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a28) | c0_1(a28) | (~c3_1(a28)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(1513,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a28) | c2_1(a28) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a14) | (~c1_1(a14)) | (~c3_1(a28))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 1.37/1.59 tff(1514,plain,
% 1.37/1.59 ($false),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1513, 101, 1507, 1467, 144, 143, 1499, 1493, 1466, 142, 680, 1475])).
% 1.37/1.59 tff(1515,plain,(hskp2 | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.59 tff(1516,plain,
% 1.37/1.59 (hskp2),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1515, 1428, 1427, 1426, 451, 698, 1174, 1301, 13, 12])).
% 1.37/1.59 tff(1517,plain,
% 1.37/1.59 (~c2_1(a3)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[197, 1516])).
% 1.37/1.59 tff(1518,plain,
% 1.37/1.59 (c3_1(a3)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[205, 1516])).
% 1.37/1.59 tff(1519,plain,
% 1.37/1.59 (c1_1(a3)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[213, 1516])).
% 1.37/1.59 tff(1520,plain,
% 1.37/1.59 (hskp9),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1218, 101, 1519, 1518, 1428, 1427, 1517, 1426, 827])).
% 1.37/1.59 tff(1521,plain,
% 1.37/1.59 (~c3_1(a16)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[839, 1520])).
% 1.37/1.59 tff(1522,plain,
% 1.37/1.59 (c1_1(a16)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[847, 1520])).
% 1.37/1.59 tff(1523,plain,
% 1.37/1.59 (c0_1(a16)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[855, 1520])).
% 1.37/1.59 tff(1524,plain,
% 1.37/1.59 (hskp12),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1272, 101, 1523, 1522, 1521, 698, 1174, 918, 1429])).
% 1.37/1.59 tff(1525,plain,
% 1.37/1.59 (~c3_1(a20)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[930, 1524])).
% 1.37/1.59 tff(1526,plain,
% 1.37/1.59 (~c1_1(a20)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[936, 1524])).
% 1.37/1.59 tff(1527,plain,
% 1.37/1.59 (c2_1(a20)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[944, 1524])).
% 1.37/1.59 tff(1528,plain,
% 1.37/1.59 (hskp5),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1089, 101, 1527, 1526, 1525, 1301, 13, 12, 275])).
% 1.37/1.59 tff(1529,plain,
% 1.37/1.59 (~c2_1(a11)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[291, 1528])).
% 1.37/1.59 tff(1530,plain,
% 1.37/1.59 (~c1_1(a11)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[297, 1528])).
% 1.37/1.59 tff(1531,plain,
% 1.37/1.59 (c0_1(a11)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[305, 1528])).
% 1.37/1.59 tff(1532,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c0_1(a15))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1533,plain,
% 1.37/1.59 (((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c0_1(a15))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1534,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c0_1(a15)))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[1533])).
% 1.37/1.59 tff(1535,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c0_1(a15))),
% 1.37/1.59 inference(transitivity,[status(thm)],[1534, 1532])).
% 1.37/1.59 tff(1536,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)) | c1_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(1537,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c0_1(a15)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1536, 1535])).
% 1.37/1.59 tff(1538,plain,
% 1.37/1.59 ($false),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1537, 101, 1531, 451, 698, 1174, 1530, 1529, 697, 1429])).
% 1.37/1.59 tff(1539,plain,(c2_1(a2) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c3_1(a2) | c1_1(a58) | c0_1(a58) | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.37/1.59 tff(1540,plain,
% 1.37/1.59 (c2_1(a2)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1539, 12, 698, 1174, 451, 26, 37, 526, 48])).
% 1.37/1.59 tff(1541,plain,
% 1.37/1.59 (~hskp1),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[247, 1540])).
% 1.37/1.59 tff(1542,plain,
% 1.37/1.59 (hskp0),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[545, 1541, 48, 526, 37, 26])).
% 1.37/1.59 tff(1543,plain,
% 1.37/1.59 (~c3_1(a1)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[114, 1542])).
% 1.37/1.59 tff(1544,plain,
% 1.37/1.59 (c2_1(a1)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[122, 1542])).
% 1.37/1.59 tff(1545,plain,
% 1.37/1.59 (c1_1(a1)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[130, 1542])).
% 1.37/1.59 tff(1546,plain,
% 1.37/1.59 (~c0_1(a15)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1184, 101, 1545, 1544, 451, 698, 1174, 1543, 264])).
% 1.37/1.59 tff(1547,assumption,(~c0_1(a15)), introduced(assumption)).
% 1.37/1.59 tff(1548,assumption,(c2_1(a2)), introduced(assumption)).
% 1.37/1.59 tff(1549,plain,
% 1.37/1.59 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | (~ndr1_0))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | (~ndr1_0))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1550,plain,
% 1.37/1.59 ((hskp18 | hskp3 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | (~c2_1(a2))) <=> (hskp18 | hskp3 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | (~ndr1_0))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1551,plain,
% 1.37/1.59 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | (~c2_1(a2)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | (~ndr1_0)))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[1550])).
% 1.37/1.59 tff(1552,plain,
% 1.37/1.59 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | (~c2_1(a2)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | (~ndr1_0))),
% 1.37/1.59 inference(transitivity,[status(thm)],[1551, 1549])).
% 1.37/1.59 tff(1553,plain,
% 1.37/1.59 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a2) | c0_1(a2) | (~c2_1(a2)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(1554,plain,
% 1.37/1.59 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | (~ndr1_0)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1553, 1552])).
% 1.37/1.59 tff(1555,plain,
% 1.37/1.59 (hskp18 | c0_1(a2) | (~c2_1(a2))),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1554, 101, 48, 12, 372])).
% 1.37/1.59 tff(1556,plain,
% 1.37/1.59 (hskp18),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1555, 14, 1548])).
% 1.37/1.59 tff(1557,plain,
% 1.37/1.59 (~c3_1(a31)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[385, 1556])).
% 1.37/1.59 tff(1558,plain,
% 1.37/1.59 (c1_1(a31)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[393, 1556])).
% 1.37/1.59 tff(1559,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a31) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a31) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1560,plain,
% 1.37/1.59 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15))) <=> (c3_1(a31) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1561,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a31) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31)))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[1560])).
% 1.37/1.59 tff(1562,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a31) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31))),
% 1.37/1.59 inference(transitivity,[status(thm)],[1561, 1559])).
% 1.37/1.59 tff(1563,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c2_1(a15) | c0_1(a15) | (~c3_1(a15)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(1564,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a31) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a15) | (~c1_1(a31)) | c2_1(a31)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 1.37/1.59 tff(1565,plain,
% 1.37/1.59 (c2_1(a31)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1564, 101, 1558, 144, 143, 1557, 698, 1174, 142, 680, 1547])).
% 1.37/1.59 tff(1566,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1567,plain,
% 1.37/1.59 ((hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c0_1(a2) | (~c2_1(a2))) <=> (hskp6 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1568,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c0_1(a2) | (~c2_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[1567])).
% 1.37/1.59 tff(1569,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c0_1(a2) | (~c2_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[1568, 1566])).
% 1.37/1.59 tff(1570,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c0_1(a2) | (~c2_1(a2)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(1571,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a2) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 1.37/1.59 tff(1572,plain,
% 1.37/1.59 (hskp6 | c0_1(a2)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1571, 101, 144, 143, 1548, 12, 142, 162])).
% 1.37/1.59 tff(1573,plain,
% 1.37/1.59 (hskp6),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1572, 14])).
% 1.37/1.59 tff(1574,plain,
% 1.37/1.59 (~c3_1(a13)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[177, 1573])).
% 1.37/1.59 tff(1575,plain,
% 1.37/1.59 (~c1_1(a13)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[183, 1573])).
% 1.37/1.59 tff(1576,plain,
% 1.37/1.59 (~c0_1(a13)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[189, 1573])).
% 1.37/1.59 tff(1577,plain,
% 1.37/1.59 (~hskp1),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[247, 1548])).
% 1.37/1.59 tff(1578,plain,
% 1.37/1.59 (hskp2),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[232, 101, 1577, 1576, 1575, 1574, 47])).
% 1.37/1.59 tff(1579,plain,
% 1.37/1.59 (~c2_1(a3)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[197, 1578])).
% 1.37/1.59 tff(1580,plain,
% 1.37/1.59 (c3_1(a3)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[205, 1578])).
% 1.37/1.59 tff(1581,plain,
% 1.37/1.59 (c1_1(a3)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[213, 1578])).
% 1.37/1.59 tff(1582,plain,
% 1.37/1.59 (~c2_1(a13)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1253, 101, 1577, 1581, 1580, 1576, 1575, 1579, 58])).
% 1.37/1.59 tff(1583,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c3_1(a31) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c1_1(a31)) | (~c2_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c3_1(a31) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1584,plain,
% 1.37/1.59 ((hskp9 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp9 | c3_1(a31) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1585,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | c3_1(a31) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c1_1(a31)) | (~c2_1(a31))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[1584])).
% 1.37/1.59 tff(1586,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c3_1(a31) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[1585, 1583])).
% 1.37/1.59 tff(1587,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(1588,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | c3_1(a31) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c1_1(a31)) | (~c2_1(a31))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1587, 1586])).
% 1.37/1.59 tff(1589,plain,
% 1.37/1.59 (hskp9),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1588, 101, 1558, 1581, 1580, 1557, 1579, 827, 1565])).
% 1.37/1.59 tff(1590,plain,
% 1.37/1.59 (~c3_1(a16)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[839, 1589])).
% 1.37/1.59 tff(1591,plain,
% 1.37/1.59 (c1_1(a16)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[847, 1589])).
% 1.37/1.59 tff(1592,plain,
% 1.37/1.59 (c0_1(a16)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[855, 1589])).
% 1.37/1.59 tff(1593,plain,
% 1.37/1.59 (hskp12),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1272, 101, 1592, 1591, 1590, 698, 1174, 918, 1547])).
% 1.37/1.59 tff(1594,plain,
% 1.37/1.59 (~c1_1(a20)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[936, 1593])).
% 1.37/1.59 tff(1595,plain,
% 1.37/1.59 (c2_1(a20)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[944, 1593])).
% 1.37/1.59 tff(1596,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a31) | c1_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c0_1(a20)) | (~c2_1(a20)) | (~c1_1(a31)) | (~c2_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a31) | c1_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c0_1(a20)) | (~c2_1(a20)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1597,plain,
% 1.37/1.59 (((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c3_1(a31) | c1_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c0_1(a20)) | (~c2_1(a20)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1598,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a31) | c1_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c0_1(a20)) | (~c2_1(a20)) | (~c1_1(a31)) | (~c2_1(a31))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[1597])).
% 1.37/1.59 tff(1599,plain,
% 1.37/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a31) | c1_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c0_1(a20)) | (~c2_1(a20)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[1598, 1596])).
% 1.37/1.59 tff(1600,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a20) | (~c2_1(a20)) | (~c0_1(a20)) | c2_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(1601,plain,
% 1.37/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a31) | c1_1(a20) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c0_1(a20)) | (~c2_1(a20)) | (~c1_1(a31)) | (~c2_1(a31))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 1.37/1.59 tff(1602,plain,
% 1.37/1.59 (~c0_1(a20)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1601, 101, 1558, 1595, 1557, 1594, 1576, 1574, 1264, 1582, 1565])).
% 1.37/1.59 tff(1603,plain,
% 1.37/1.59 ($false),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1288, 101, 1577, 1595, 1581, 1580, 1594, 1579, 58, 1602])).
% 1.37/1.59 tff(1604,plain,(c0_1(a2) | c2_1(a15) | (~c3_1(a15)) | c0_1(a15) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | (~c2_1(a2)) | c3_1(a2) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.37/1.59 tff(1605,plain,
% 1.37/1.59 (c0_1(a2)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1604, 1546, 1174, 698, 1545, 1544, 1543, 1540, 12, 48])).
% 1.37/1.59 tff(1606,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~c0_1(a2)) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | (~c0_1(a2)) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1607,plain,
% 1.37/1.59 ((hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | (~c2_1(a2)) | (~c0_1(a2))) <=> (hskp6 | (~c0_1(a2)) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(1608,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | (~c2_1(a2)) | (~c0_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~c0_1(a2)) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[1607])).
% 1.37/1.59 tff(1609,plain,
% 1.37/1.59 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | (~c2_1(a2)) | (~c0_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | (~c0_1(a2)) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[1608, 1606])).
% 1.37/1.59 tff(1610,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | (~c2_1(a2)) | (~c0_1(a2)))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(1611,plain,
% 1.37/1.59 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | (~c0_1(a2)) | (~c2_1(a2)) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[1610, 1609])).
% 1.37/1.59 tff(1612,plain,
% 1.37/1.59 (hskp6 | (~c0_1(a2))),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1611, 101, 1545, 1544, 1540, 12, 1543, 141])).
% 1.37/1.59 tff(1613,plain,
% 1.37/1.59 (hskp6),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1612, 1605])).
% 1.37/1.59 tff(1614,plain,
% 1.37/1.59 (~c3_1(a13)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[177, 1613])).
% 1.37/1.59 tff(1615,plain,
% 1.37/1.59 (~c1_1(a13)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[183, 1613])).
% 1.37/1.59 tff(1616,plain,
% 1.37/1.59 (~c0_1(a13)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[189, 1613])).
% 1.37/1.59 tff(1617,plain,
% 1.37/1.59 (hskp2),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[232, 101, 1541, 1616, 1615, 1614, 47])).
% 1.37/1.59 tff(1618,plain,
% 1.37/1.59 (~c2_1(a3)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[197, 1617])).
% 1.37/1.59 tff(1619,plain,
% 1.37/1.59 (c3_1(a3)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[205, 1617])).
% 1.37/1.59 tff(1620,plain,
% 1.37/1.59 (c1_1(a3)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[213, 1617])).
% 1.37/1.59 tff(1621,plain,
% 1.37/1.59 (hskp9),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1218, 101, 1620, 1619, 1545, 1544, 1618, 1543, 827])).
% 1.37/1.59 tff(1622,plain,
% 1.37/1.59 (~c3_1(a16)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[839, 1621])).
% 1.37/1.59 tff(1623,plain,
% 1.37/1.59 (c1_1(a16)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[847, 1621])).
% 1.37/1.59 tff(1624,plain,
% 1.37/1.59 (c2_1(a16)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1227, 101, 1623, 1545, 1544, 1622, 698, 1174, 1543, 680, 1546])).
% 1.37/1.59 tff(1625,plain,
% 1.37/1.59 (~c2_1(a13)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1253, 101, 1541, 1620, 1619, 1616, 1615, 1618, 58])).
% 1.37/1.59 tff(1626,plain,
% 1.37/1.59 (c0_1(a16)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[855, 1621])).
% 1.37/1.59 tff(1627,plain,
% 1.37/1.59 (hskp12),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[1272, 101, 1626, 1623, 1622, 698, 1174, 918, 1546])).
% 1.37/1.59 tff(1628,plain,
% 1.37/1.59 (~c1_1(a20)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[936, 1627])).
% 1.37/1.60 tff(1629,plain,
% 1.37/1.60 (c2_1(a20)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[944, 1627])).
% 1.37/1.60 tff(1630,plain,
% 1.37/1.60 (~c0_1(a20)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1281, 101, 1629, 1623, 1628, 1622, 1616, 1614, 1264, 1625, 1624])).
% 1.37/1.60 tff(1631,plain,
% 1.37/1.60 ($false),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1288, 101, 1541, 1629, 1620, 1619, 1628, 1618, 58, 1630])).
% 1.37/1.60 tff(1632,plain,(c3_1(a2) | c2_1(a15) | (~c3_1(a15)) | hskp3 | c1_1(a15) | hskp24 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.60 tff(1633,plain,
% 1.37/1.60 (c3_1(a2)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1632, 526, 1174, 48, 451, 698, 37, 26])).
% 1.37/1.60 tff(1634,plain,
% 1.37/1.60 (~hskp1),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[241, 1633])).
% 1.37/1.60 tff(1635,plain,
% 1.37/1.60 (hskp0),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[545, 1634, 48, 526, 37, 26])).
% 1.37/1.60 tff(1636,plain,
% 1.37/1.60 (~c3_1(a1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[114, 1635])).
% 1.37/1.60 tff(1637,plain,
% 1.37/1.60 (c2_1(a1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[122, 1635])).
% 1.37/1.60 tff(1638,plain,
% 1.37/1.60 (c1_1(a1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[130, 1635])).
% 1.37/1.60 tff(1639,plain,
% 1.37/1.60 (~c0_1(a15)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1184, 101, 1638, 1637, 451, 698, 1174, 1636, 264])).
% 1.37/1.60 tff(1640,plain,
% 1.37/1.60 (hskp6),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[171, 1638, 1637, 1636])).
% 1.37/1.60 tff(1641,plain,
% 1.37/1.60 (~c3_1(a13)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[177, 1640])).
% 1.37/1.60 tff(1642,plain,
% 1.37/1.60 (~c1_1(a13)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[183, 1640])).
% 1.37/1.60 tff(1643,plain,
% 1.37/1.60 (~c0_1(a13)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[189, 1640])).
% 1.37/1.60 tff(1644,plain,
% 1.37/1.60 (hskp2),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[232, 101, 1634, 1643, 1642, 1641, 47])).
% 1.37/1.60 tff(1645,plain,
% 1.37/1.60 (~c2_1(a3)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[197, 1644])).
% 1.37/1.60 tff(1646,plain,
% 1.37/1.60 (c3_1(a3)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[205, 1644])).
% 1.37/1.60 tff(1647,plain,
% 1.37/1.60 (c1_1(a3)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[213, 1644])).
% 1.37/1.60 tff(1648,plain,
% 1.37/1.60 (hskp9),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1218, 101, 1647, 1646, 1638, 1637, 1645, 1636, 827])).
% 1.37/1.60 tff(1649,plain,
% 1.37/1.60 (~c3_1(a16)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[839, 1648])).
% 1.37/1.60 tff(1650,plain,
% 1.37/1.60 (c1_1(a16)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[847, 1648])).
% 1.37/1.60 tff(1651,plain,
% 1.37/1.60 (c2_1(a16)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1227, 101, 1650, 1638, 1637, 1649, 698, 1174, 1636, 680, 1639])).
% 1.37/1.60 tff(1652,plain,
% 1.37/1.60 (~c2_1(a13)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1253, 101, 1634, 1647, 1646, 1643, 1642, 1645, 58])).
% 1.37/1.60 tff(1653,plain,
% 1.37/1.60 (c0_1(a16)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[855, 1648])).
% 1.37/1.60 tff(1654,plain,
% 1.37/1.60 (hskp12),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1272, 101, 1653, 1650, 1649, 698, 1174, 918, 1639])).
% 1.37/1.60 tff(1655,plain,
% 1.37/1.60 (~c1_1(a20)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[936, 1654])).
% 1.37/1.60 tff(1656,plain,
% 1.37/1.60 (c2_1(a20)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[944, 1654])).
% 1.37/1.60 tff(1657,plain,
% 1.37/1.60 (~c0_1(a20)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1281, 101, 1656, 1650, 1655, 1649, 1643, 1641, 1264, 1652, 1651])).
% 1.37/1.60 tff(1658,plain,
% 1.37/1.60 ($false),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1288, 101, 1634, 1656, 1647, 1646, 1655, 1645, 58, 1657])).
% 1.37/1.60 tff(1659,plain,(hskp24 | c2_1(a15) | (~c3_1(a15)) | c1_1(a15) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.60 tff(1660,plain,
% 1.37/1.60 (hskp24),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1659, 698, 1173, 451, 48, 37, 26])).
% 1.37/1.60 tff(1661,plain,
% 1.37/1.60 (c2_1(a58)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[442, 1660])).
% 1.37/1.60 tff(1662,plain,
% 1.37/1.60 (hskp0),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[108, 1661, 26])).
% 1.37/1.60 tff(1663,plain,
% 1.37/1.60 (~c3_1(a1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[114, 1662])).
% 1.37/1.60 tff(1664,plain,
% 1.37/1.60 (c2_1(a1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[122, 1662])).
% 1.37/1.60 tff(1665,plain,
% 1.37/1.60 (c1_1(a1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[130, 1662])).
% 1.37/1.60 tff(1666,plain,
% 1.37/1.60 (~c0_1(a15)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1184, 101, 1665, 1664, 451, 698, 1173, 1663, 264])).
% 1.37/1.60 tff(1667,plain,
% 1.37/1.60 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(1668,plain,
% 1.37/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[1667])).
% 1.37/1.60 tff(1669,plain,
% 1.37/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1670,plain,
% 1.37/1.60 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 1.37/1.60 inference(bind,[status(th)],[])).
% 1.37/1.60 tff(1671,plain,
% 1.37/1.60 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(quant_intro,[status(thm)],[1670])).
% 1.37/1.60 tff(1672,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause202')).
% 1.37/1.60 tff(1673,plain,
% 1.37/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 1.37/1.60 tff(1674,plain,
% 1.37/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[1673, 1669])).
% 1.37/1.60 tff(1675,plain,(
% 1.37/1.60 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(skolemize,[status(sab)],[1674])).
% 1.37/1.60 tff(1676,plain,
% 1.37/1.60 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[1675, 1668])).
% 1.37/1.60 tff(1677,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c2_1(a58)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1678,plain,
% 1.37/1.60 ((hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58))) <=> (hskp2 | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c2_1(a58)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1679,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c2_1(a58))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[1678])).
% 1.37/1.60 tff(1680,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c2_1(a58)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[1679, 1677])).
% 1.37/1.60 tff(1681,plain,
% 1.37/1.60 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(1682,plain,
% 1.37/1.60 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a58) | c1_1(a58) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c2_1(a58))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[1681, 1680])).
% 1.37/1.60 tff(1683,plain,
% 1.37/1.60 (hskp2 | c2_1(a15) | (~c3_1(a15)) | (~c2_1(a58))),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1682, 101, 37, 26, 451, 1455])).
% 1.37/1.60 tff(1684,plain,
% 1.37/1.60 (hskp2),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1683, 1661, 698, 1173])).
% 1.37/1.60 tff(1685,plain,
% 1.37/1.60 (~c2_1(a3)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[197, 1684])).
% 1.37/1.60 tff(1686,plain,
% 1.37/1.60 (c3_1(a3)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[205, 1684])).
% 1.37/1.60 tff(1687,plain,
% 1.37/1.60 (c1_1(a3)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[213, 1684])).
% 1.37/1.60 tff(1688,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1689,plain,
% 1.37/1.60 (((~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15))) <=> (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1690,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[1689])).
% 1.37/1.60 tff(1691,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[1690, 1688])).
% 1.37/1.60 tff(1692,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a15) | c1_1(a15) | (~c3_1(a15)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(1693,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a15) | c2_1(a15) | (~c3_1(a15)) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[1692, 1691])).
% 1.37/1.60 tff(1694,plain,
% 1.37/1.60 (~c0_1(a3)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1693, 101, 1687, 1686, 451, 698, 1173, 1685, 1676])).
% 1.37/1.60 tff(1695,plain,
% 1.37/1.60 (hskp1),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[222, 1684, 1661, 37, 26])).
% 1.37/1.60 tff(1696,plain,
% 1.37/1.60 (~c3_1(a2)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[241, 1695])).
% 1.37/1.60 tff(1697,plain,
% 1.37/1.60 (~c2_1(a2)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[247, 1695])).
% 1.37/1.60 tff(1698,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a3) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | (~c3_1(a3)) | c0_1(a3))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a3) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | (~c3_1(a3)) | c0_1(a3))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1699,plain,
% 1.37/1.60 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c2_1(a3) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | (~c3_1(a3)) | c0_1(a3))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1700,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a3) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | (~c3_1(a3)) | c0_1(a3)))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[1699])).
% 1.37/1.60 tff(1701,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a3) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | (~c3_1(a3)) | c0_1(a3))),
% 1.37/1.60 inference(transitivity,[status(thm)],[1700, 1698])).
% 1.37/1.60 tff(1702,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(1703,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a3) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a2)) | (~c3_1(a3)) | c0_1(a3)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 1.37/1.60 tff(1704,plain,
% 1.37/1.60 (~c1_1(a2)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1703, 101, 1686, 1665, 1664, 1685, 1697, 1696, 1663, 680, 1694])).
% 1.37/1.60 tff(1705,plain,
% 1.37/1.60 (~c0_1(a2)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[253, 1695])).
% 1.37/1.60 tff(1706,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1707,plain,
% 1.37/1.60 (((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1708,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a58)) | (~c3_1(a58))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[1707])).
% 1.37/1.60 tff(1709,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[1708, 1706])).
% 1.37/1.60 tff(1710,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(1711,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | (~c2_1(a58)) | (~c3_1(a58))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[1710, 1709])).
% 1.37/1.60 tff(1712,plain,
% 1.37/1.60 (~c3_1(a58)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1711, 101, 1661, 26, 1705, 1697, 1696, 344, 1704])).
% 1.37/1.60 tff(1713,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1714,plain,
% 1.37/1.60 ((hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp5 | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1715,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[1714])).
% 1.37/1.60 tff(1716,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 1.37/1.60 inference(transitivity,[status(thm)],[1715, 1713])).
% 1.37/1.60 tff(1717,plain,
% 1.37/1.60 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(1718,plain,
% 1.37/1.60 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 1.37/1.60 tff(1719,plain,
% 1.37/1.60 (hskp5),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1718, 101, 1661, 26, 1705, 1697, 1696, 275, 1712])).
% 1.37/1.60 tff(1720,plain,
% 1.37/1.60 (~c2_1(a11)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[291, 1719])).
% 1.37/1.60 tff(1721,plain,
% 1.37/1.60 (~c1_1(a11)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[297, 1719])).
% 1.37/1.60 tff(1722,plain,
% 1.37/1.60 (c0_1(a11)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[305, 1719])).
% 1.37/1.60 tff(1723,plain,
% 1.37/1.60 ($false),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1537, 101, 1722, 451, 698, 1173, 1721, 1720, 697, 1666])).
% 1.37/1.60 tff(1724,plain,(c2_1(a15) | c1_1(a15) | c1_1(a58) | c0_1(a58) | hskp3 | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.60 tff(1725,plain,
% 1.37/1.60 (c2_1(a15)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1724, 451, 26, 37, 48, 450])).
% 1.37/1.60 tff(1726,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1727,plain,
% 1.37/1.60 ((hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1728,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0)))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[1727])).
% 1.37/1.60 tff(1729,plain,
% 1.37/1.60 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 1.37/1.60 inference(transitivity,[status(thm)],[1728, 1726])).
% 1.37/1.60 tff(1730,plain,
% 1.37/1.60 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(1731,plain,
% 1.37/1.60 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0)),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 1.37/1.60 tff(1732,plain,
% 1.37/1.60 (hskp5 | c0_1(a2) | c2_1(a2)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1731, 101, 451, 1725, 444, 12, 275])).
% 1.37/1.60 tff(1733,plain,
% 1.37/1.60 (hskp5),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1732, 682, 683])).
% 1.37/1.60 tff(1734,plain,
% 1.37/1.60 (~c2_1(a11)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[291, 1733])).
% 1.37/1.60 tff(1735,plain,
% 1.37/1.60 (~c1_1(a11)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[297, 1733])).
% 1.37/1.60 tff(1736,plain,
% 1.37/1.60 (c0_1(a11)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[305, 1733])).
% 1.37/1.60 tff(1737,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a58)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1738,plain,
% 1.37/1.60 (((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a58)))),
% 1.37/1.60 inference(rewrite,[status(thm)],[])).
% 1.37/1.60 tff(1739,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a58))))),
% 1.37/1.60 inference(monotonicity,[status(thm)],[1738])).
% 1.37/1.60 tff(1740,plain,
% 1.37/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a58)))),
% 1.37/1.60 inference(transitivity,[status(thm)],[1739, 1737])).
% 1.37/1.60 tff(1741,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 1.37/1.60 inference(quant_inst,[status(thm)],[])).
% 1.37/1.60 tff(1742,plain,
% 1.37/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | (~c3_1(a58))),
% 1.37/1.60 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 1.37/1.60 tff(1743,plain,
% 1.37/1.60 ($false),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1742, 101, 452, 1736, 37, 26, 1735, 1734, 697, 687])).
% 1.37/1.60 tff(1744,plain,(hskp0 | c0_1(a58) | c1_1(a58) | c2_1(a38) | c3_1(a2) | c1_1(a15) | c3_1(a15) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.37/1.60 tff(1745,plain,
% 1.37/1.60 (hskp0),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1744, 12, 26, 450, 37, 451, 444, 48])).
% 1.37/1.60 tff(1746,plain,
% 1.37/1.60 (~c3_1(a1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[114, 1745])).
% 1.37/1.60 tff(1747,plain,
% 1.37/1.60 (c2_1(a1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[122, 1745])).
% 1.37/1.60 tff(1748,plain,
% 1.37/1.60 (c1_1(a1)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[130, 1745])).
% 1.37/1.60 tff(1749,assumption,(c2_1(a15)), introduced(assumption)).
% 1.37/1.60 tff(1750,plain,
% 1.37/1.60 (hskp5 | c0_1(a2) | c2_1(a2)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1731, 101, 451, 1749, 444, 12, 275])).
% 1.37/1.60 tff(1751,plain,
% 1.37/1.60 (hskp5),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[1750, 14, 13])).
% 1.37/1.60 tff(1752,plain,
% 1.37/1.60 (~c2_1(a11)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[291, 1751])).
% 1.37/1.60 tff(1753,plain,
% 1.37/1.60 (~c1_1(a11)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[297, 1751])).
% 1.37/1.60 tff(1754,plain,
% 1.37/1.60 (c0_1(a11)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[305, 1751])).
% 1.37/1.60 tff(1755,plain,
% 1.37/1.60 (~c3_1(a11)),
% 1.37/1.60 inference(unit_resolution,[status(thm)],[312, 101, 1754, 144, 143, 1753, 1752, 142, 264])).
% 1.37/1.61 tff(1756,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1757,plain,
% 1.37/1.61 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a15) | (~c2_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1758,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15))))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[1757])).
% 1.37/1.61 tff(1759,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)))),
% 1.37/1.61 inference(transitivity,[status(thm)],[1758, 1756])).
% 1.37/1.61 tff(1760,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(1761,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 1.37/1.61 tff(1762,plain,
% 1.37/1.61 (c0_1(a2) | (~c0_1(a15))),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1761, 101, 144, 143, 451, 1749, 13, 12, 142, 1264])).
% 1.37/1.61 tff(1763,plain,
% 1.37/1.61 (~c0_1(a15)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1762, 14])).
% 1.37/1.61 tff(1764,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~c2_1(a15)) | c3_1(a15) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c2_1(a15)) | c3_1(a15) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | c0_1(a15))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1765,plain,
% 1.37/1.61 (((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a11) | c1_1(a11) | c3_1(a11)) <=> ((~c2_1(a15)) | c3_1(a15) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | c0_1(a15))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1766,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a11) | c1_1(a11) | c3_1(a11))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~c2_1(a15)) | c3_1(a15) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | c0_1(a15)))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[1765])).
% 1.37/1.61 tff(1767,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a11) | c1_1(a11) | c3_1(a11))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c2_1(a15)) | c3_1(a15) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | c0_1(a15))),
% 1.37/1.61 inference(transitivity,[status(thm)],[1766, 1764])).
% 1.37/1.61 tff(1768,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a11) | c1_1(a11) | c3_1(a11))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(1769,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c2_1(a15)) | c3_1(a15) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | c0_1(a15)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[1768, 1767])).
% 1.37/1.61 tff(1770,plain,
% 1.37/1.61 ($false),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1769, 101, 1754, 1749, 444, 1753, 1752, 323, 1763, 1755])).
% 1.37/1.61 tff(1771,plain,(c0_1(a2) | (~c2_1(a15)) | c3_1(a15) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | c1_1(a15) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.61 tff(1772,plain,
% 1.37/1.61 (c0_1(a2)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1771, 13, 444, 144, 143, 142, 451, 1749, 12])).
% 1.37/1.61 tff(1773,plain,
% 1.37/1.61 (~hskp1),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[253, 1772])).
% 1.37/1.61 tff(1774,plain,
% 1.37/1.61 (hskp2 | hskp1),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[232, 101, 324, 278, 277, 47])).
% 1.37/1.61 tff(1775,plain,
% 1.37/1.61 (hskp2),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1774, 1773])).
% 1.37/1.61 tff(1776,plain,
% 1.37/1.61 (~c2_1(a3)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[197, 1775])).
% 1.37/1.61 tff(1777,plain,
% 1.37/1.61 (^[U: $i] : refl((hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 1.37/1.61 inference(bind,[status(th)],[])).
% 1.37/1.61 tff(1778,plain,
% 1.37/1.61 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.37/1.61 inference(quant_intro,[status(thm)],[1777])).
% 1.37/1.61 tff(1779,plain,
% 1.37/1.61 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1780,plain,
% 1.37/1.61 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp10) | hskp1) <=> ((hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp1))), rewrite(((hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp1) <=> (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp10) | hskp1) <=> (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 1.37/1.61 inference(bind,[status(th)],[])).
% 1.37/1.61 tff(1781,plain,
% 1.37/1.61 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp10) | hskp1) <=> ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.37/1.61 inference(quant_intro,[status(thm)],[1780])).
% 1.37/1.61 tff(1782,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp10) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.37/1.61 tff(1783,plain,
% 1.37/1.61 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 1.37/1.61 tff(1784,plain,
% 1.37/1.61 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[1783, 1779])).
% 1.37/1.61 tff(1785,plain,(
% 1.37/1.61 ![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.37/1.61 inference(skolemize,[status(sab)],[1784])).
% 1.37/1.61 tff(1786,plain,
% 1.37/1.61 (![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[1785, 1778])).
% 1.37/1.61 tff(1787,plain,
% 1.37/1.61 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1788,plain,
% 1.37/1.61 ((hskp10 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15))) <=> (hskp10 | hskp1 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1789,plain,
% 1.37/1.61 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0)))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[1788])).
% 1.37/1.61 tff(1790,plain,
% 1.37/1.61 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0))),
% 1.37/1.61 inference(transitivity,[status(thm)],[1789, 1787])).
% 1.37/1.61 tff(1791,plain,
% 1.37/1.61 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(1792,plain,
% 1.37/1.61 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 1.37/1.61 tff(1793,plain,
% 1.37/1.61 (hskp10 | hskp1 | (~c2_1(a15)) | c3_1(a15)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1792, 101, 451, 1786])).
% 1.37/1.61 tff(1794,plain,
% 1.37/1.61 (hskp10),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1793, 1773, 1749, 444])).
% 1.37/1.61 tff(1795,plain,
% 1.37/1.61 (~c1_1(a18)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[868, 1794])).
% 1.37/1.61 tff(1796,plain,
% 1.37/1.61 (~c0_1(a18)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[874, 1794])).
% 1.37/1.61 tff(1797,plain,
% 1.37/1.61 (c3_1(a3)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[205, 1775])).
% 1.37/1.61 tff(1798,plain,
% 1.37/1.61 (c1_1(a3)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[213, 1775])).
% 1.37/1.61 tff(1799,plain,
% 1.37/1.61 (~c2_1(a18)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[883, 101, 1773, 1798, 1797, 1796, 1795, 1776, 58])).
% 1.37/1.61 tff(1800,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1801,plain,
% 1.37/1.61 (((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a2) | (~c0_1(a2)) | (~c1_1(a2)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1802,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a2) | (~c0_1(a2)) | (~c1_1(a2)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a3)) | (~c1_1(a3))))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[1801])).
% 1.37/1.61 tff(1803,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a2) | (~c0_1(a2)) | (~c1_1(a2)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.37/1.61 inference(transitivity,[status(thm)],[1802, 1800])).
% 1.37/1.61 tff(1804,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a2) | (~c0_1(a2)) | (~c1_1(a2)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(1805,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a3)) | (~c1_1(a3))),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[1804, 1803])).
% 1.37/1.61 tff(1806,plain,
% 1.37/1.61 (~c1_1(a2)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1805, 101, 1798, 1797, 324, 278, 277, 1776, 1772, 13, 36])).
% 1.37/1.61 tff(1807,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~c2_1(a15)) | c3_1(a15) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c2_1(a15)) | c3_1(a15) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1808,plain,
% 1.37/1.61 (((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a2) | c1_1(a2) | c3_1(a2)) <=> ((~c2_1(a15)) | c3_1(a15) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1809,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a2) | c1_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~c2_1(a15)) | c3_1(a15) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15)))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[1808])).
% 1.37/1.61 tff(1810,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a2) | c1_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c2_1(a15)) | c3_1(a15) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15))),
% 1.37/1.61 inference(transitivity,[status(thm)],[1809, 1807])).
% 1.37/1.61 tff(1811,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a2) | c1_1(a2) | c3_1(a2))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(1812,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c2_1(a15)) | c3_1(a15) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a15)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 1.37/1.61 tff(1813,plain,
% 1.37/1.61 ((~c0_1(a2)) | c1_1(a2) | c0_1(a15)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1812, 101, 1749, 444, 13, 12, 323])).
% 1.37/1.61 tff(1814,plain,
% 1.37/1.61 (c0_1(a15)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1813, 1806, 1772])).
% 1.37/1.61 tff(1815,plain,
% 1.37/1.61 (~c2_1(a58)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[222, 1775, 1773, 37, 26])).
% 1.37/1.61 tff(1816,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)) | c3_1(a58))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1817,plain,
% 1.37/1.61 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | c3_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)) | c3_1(a58))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1818,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)) | c3_1(a58)))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[1817])).
% 1.37/1.61 tff(1819,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)) | c3_1(a58))),
% 1.37/1.61 inference(transitivity,[status(thm)],[1818, 1816])).
% 1.37/1.61 tff(1820,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a15) | (~c2_1(a15)) | (~c0_1(a15)) | c2_1(a58) | c0_1(a58) | c3_1(a58))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(1821,plain,
% 1.37/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a15)) | c3_1(a58)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[1820, 1819])).
% 1.37/1.61 tff(1822,plain,
% 1.37/1.61 ((~c0_1(a15)) | c3_1(a58)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1821, 101, 1815, 144, 143, 37, 451, 1749, 142, 1264])).
% 1.37/1.61 tff(1823,plain,
% 1.37/1.61 (c3_1(a58)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1822, 1814])).
% 1.37/1.61 tff(1824,plain,
% 1.37/1.61 (~c2_1(a13)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1253, 101, 1773, 1798, 1797, 324, 278, 1776, 58])).
% 1.37/1.61 tff(1825,plain,
% 1.37/1.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1826,plain,
% 1.37/1.61 ((hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a13) | c2_1(a13) | c0_1(a13)) <=> (hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 1.37/1.61 inference(rewrite,[status(thm)],[])).
% 1.37/1.61 tff(1827,plain,
% 1.37/1.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a13) | c2_1(a13) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13)))),
% 1.37/1.61 inference(monotonicity,[status(thm)],[1826])).
% 1.37/1.61 tff(1828,plain,
% 1.37/1.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a13) | c2_1(a13) | c0_1(a13))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 1.37/1.61 inference(transitivity,[status(thm)],[1827, 1825])).
% 1.37/1.61 tff(1829,plain,
% 1.37/1.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c3_1(a13) | c2_1(a13) | c0_1(a13))),
% 1.37/1.61 inference(quant_inst,[status(thm)],[])).
% 1.37/1.61 tff(1830,plain,
% 1.37/1.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13)),
% 1.37/1.61 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 1.37/1.61 tff(1831,plain,
% 1.37/1.61 (hskp5 | c2_1(a13)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1830, 101, 451, 1749, 444, 324, 277, 275])).
% 1.37/1.61 tff(1832,plain,
% 1.37/1.61 (hskp5),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[1831, 1824])).
% 1.37/1.61 tff(1833,plain,
% 1.37/1.61 (~c2_1(a11)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[291, 1832])).
% 1.37/1.61 tff(1834,plain,
% 1.37/1.61 (~c1_1(a11)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[297, 1832])).
% 1.37/1.61 tff(1835,plain,
% 1.37/1.61 (c0_1(a11)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[305, 1832])).
% 1.37/1.61 tff(1836,plain,
% 1.37/1.61 (c3_1(a18)),
% 1.37/1.61 inference(unit_resolution,[status(thm)],[962, 1794])).
% 1.37/1.61 tff(1837,plain,
% 1.37/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)) | (~c3_1(a58)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1838,plain,
% 1.37/1.62 (((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (c0_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)) | (~c3_1(a58)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1839,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)) | (~c3_1(a58))))),
% 1.37/1.62 inference(monotonicity,[status(thm)],[1838])).
% 1.37/1.62 tff(1840,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)) | (~c3_1(a58)))),
% 1.37/1.62 inference(transitivity,[status(thm)],[1839, 1837])).
% 1.37/1.62 tff(1841,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a18) | c0_1(a18) | (~c3_1(a18)) | c1_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 1.37/1.62 inference(quant_inst,[status(thm)],[])).
% 1.37/1.62 tff(1842,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a11) | c2_1(a11) | (~ndr1_0) | (~c0_1(a11)) | c2_1(a18) | (~c3_1(a18)) | (~c3_1(a58))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 1.37/1.62 tff(1843,plain,
% 1.37/1.62 ($false),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1842, 101, 1836, 1835, 37, 26, 1796, 1834, 1833, 697, 1823, 1799])).
% 1.37/1.62 tff(1844,plain,(c2_1(a2) | c0_1(a58) | c1_1(a58) | (~c1_1(a1)) | (~c2_1(a1)) | c1_1(a15) | (~c2_1(a15)) | c3_1(a1) | c3_1(a15) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.62 tff(1845,plain,
% 1.37/1.62 (c2_1(a2)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1844, 1748, 26, 37, 1747, 451, 1725, 1746, 444, 12])).
% 1.37/1.62 tff(1846,plain,
% 1.37/1.62 (~hskp1),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[247, 1845])).
% 1.37/1.62 tff(1847,plain,
% 1.37/1.62 (hskp6),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[171, 1748, 1747, 1746])).
% 1.37/1.62 tff(1848,plain,
% 1.37/1.62 (~c3_1(a13)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[177, 1847])).
% 1.37/1.62 tff(1849,plain,
% 1.37/1.62 (~c1_1(a13)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[183, 1847])).
% 1.37/1.62 tff(1850,plain,
% 1.37/1.62 (~c0_1(a13)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[189, 1847])).
% 1.37/1.62 tff(1851,plain,
% 1.37/1.62 (hskp2 | hskp1),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[232, 101, 1850, 1849, 1848, 47])).
% 1.37/1.62 tff(1852,plain,
% 1.37/1.62 (hskp2),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1851, 1846])).
% 1.37/1.62 tff(1853,plain,
% 1.37/1.62 (~c2_1(a3)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[197, 1852])).
% 1.37/1.62 tff(1854,plain,
% 1.37/1.62 (hskp10),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1793, 1846, 1725, 444])).
% 1.37/1.62 tff(1855,plain,
% 1.37/1.62 (~c1_1(a18)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[868, 1854])).
% 1.37/1.62 tff(1856,plain,
% 1.37/1.62 (~c0_1(a18)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[874, 1854])).
% 1.37/1.62 tff(1857,plain,
% 1.37/1.62 (c3_1(a3)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[205, 1852])).
% 1.37/1.62 tff(1858,plain,
% 1.37/1.62 (c1_1(a3)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[213, 1852])).
% 1.37/1.62 tff(1859,plain,
% 1.37/1.62 (~c2_1(a18)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[883, 101, 1846, 1858, 1857, 1856, 1855, 1853, 58])).
% 1.37/1.62 tff(1860,plain,
% 1.37/1.62 (~c2_1(a13)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1253, 101, 1846, 1858, 1857, 1850, 1849, 1853, 58])).
% 1.37/1.62 tff(1861,plain,
% 1.37/1.62 (hskp5 | c2_1(a13)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1830, 101, 451, 1725, 444, 1850, 1848, 275])).
% 1.37/1.62 tff(1862,plain,
% 1.37/1.62 (hskp5),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1861, 1860])).
% 1.37/1.62 tff(1863,plain,
% 1.37/1.62 (~c2_1(a11)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[291, 1862])).
% 1.37/1.62 tff(1864,plain,
% 1.37/1.62 (~c1_1(a11)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[297, 1862])).
% 1.37/1.62 tff(1865,plain,
% 1.37/1.62 (c0_1(a11)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[305, 1862])).
% 1.37/1.62 tff(1866,plain,
% 1.37/1.62 (c3_1(a18)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[962, 1854])).
% 1.37/1.62 tff(1867,plain,
% 1.37/1.62 ($false),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[969, 101, 1866, 1865, 1856, 1855, 1864, 1863, 697, 1859])).
% 1.37/1.62 tff(1868,plain,(c3_1(a2) | c1_1(a15) | c3_1(a15) | c1_1(a58) | c0_1(a58) | c2_1(a38) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.37/1.62 tff(1869,plain,
% 1.37/1.62 (c3_1(a2)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1868, 444, 451, 26, 37, 450, 48])).
% 1.37/1.62 tff(1870,plain,
% 1.37/1.62 (~hskp1),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[241, 1869])).
% 1.37/1.62 tff(1871,plain,
% 1.37/1.62 (hskp0),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[548, 1870, 48, 37, 26])).
% 1.37/1.62 tff(1872,plain,
% 1.37/1.62 (~c3_1(a1)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[114, 1871])).
% 1.37/1.62 tff(1873,plain,
% 1.37/1.62 (c2_1(a1)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[122, 1871])).
% 1.37/1.62 tff(1874,plain,
% 1.37/1.62 (c1_1(a1)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[130, 1871])).
% 1.37/1.62 tff(1875,plain,
% 1.37/1.62 (hskp6),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[171, 1874, 1873, 1872])).
% 1.37/1.62 tff(1876,plain,
% 1.37/1.62 (~c3_1(a13)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[177, 1875])).
% 1.37/1.62 tff(1877,plain,
% 1.37/1.62 (~c1_1(a13)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[183, 1875])).
% 1.37/1.62 tff(1878,plain,
% 1.37/1.62 (~c0_1(a13)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[189, 1875])).
% 1.37/1.62 tff(1879,plain,
% 1.37/1.62 (hskp2),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[232, 101, 1870, 1878, 1877, 1876, 47])).
% 1.37/1.62 tff(1880,plain,
% 1.37/1.62 (~c2_1(a3)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[197, 1879])).
% 1.37/1.62 tff(1881,plain,
% 1.37/1.62 (hskp10),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1793, 1870, 1725, 444])).
% 1.37/1.62 tff(1882,plain,
% 1.37/1.62 (~c1_1(a18)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[868, 1881])).
% 1.37/1.62 tff(1883,plain,
% 1.37/1.62 (~c0_1(a18)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[874, 1881])).
% 1.37/1.62 tff(1884,plain,
% 1.37/1.62 (c3_1(a3)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[205, 1879])).
% 1.37/1.62 tff(1885,plain,
% 1.37/1.62 (c1_1(a3)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[213, 1879])).
% 1.37/1.62 tff(1886,plain,
% 1.37/1.62 (~c2_1(a18)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[883, 101, 1870, 1885, 1884, 1883, 1882, 1880, 58])).
% 1.37/1.62 tff(1887,plain,
% 1.37/1.62 (~c2_1(a13)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1253, 101, 1870, 1885, 1884, 1878, 1877, 1880, 58])).
% 1.37/1.62 tff(1888,plain,
% 1.37/1.62 (hskp5 | c2_1(a13)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1830, 101, 451, 1725, 444, 1878, 1876, 275])).
% 1.37/1.62 tff(1889,plain,
% 1.37/1.62 (hskp5),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1888, 1887])).
% 1.37/1.62 tff(1890,plain,
% 1.37/1.62 (~c2_1(a11)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[291, 1889])).
% 1.37/1.62 tff(1891,plain,
% 1.37/1.62 (~c1_1(a11)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[297, 1889])).
% 1.37/1.62 tff(1892,plain,
% 1.37/1.62 (c0_1(a11)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[305, 1889])).
% 1.37/1.62 tff(1893,plain,
% 1.37/1.62 (c3_1(a18)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[962, 1881])).
% 1.37/1.62 tff(1894,plain,
% 1.37/1.62 ($false),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[969, 101, 1893, 1892, 1883, 1882, 1891, 1890, 697, 1886])).
% 1.37/1.62 tff(1895,plain,(c3_1(a15) | c1_1(a15) | hskp3 | c0_1(a58) | c1_1(a58) | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.62 tff(1896,plain,
% 1.37/1.62 (c3_1(a15)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1895, 451, 48, 37, 26, 450])).
% 1.37/1.62 tff(1897,plain,
% 1.37/1.62 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c0_1(a15))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c0_1(a15))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1898,plain,
% 1.37/1.62 ((hskp3 | hskp0 | (~ndr1_0) | c1_1(a15) | c0_1(a15) | (~c2_1(a15))) <=> (hskp3 | hskp0 | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c0_1(a15))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1899,plain,
% 1.37/1.62 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a15) | c0_1(a15) | (~c2_1(a15)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c0_1(a15)))),
% 1.37/1.62 inference(monotonicity,[status(thm)],[1898])).
% 1.37/1.62 tff(1900,plain,
% 1.37/1.62 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a15) | c0_1(a15) | (~c2_1(a15)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c0_1(a15))),
% 1.37/1.62 inference(transitivity,[status(thm)],[1899, 1897])).
% 1.37/1.62 tff(1901,plain,
% 1.37/1.62 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a15) | c0_1(a15) | (~c2_1(a15)))),
% 1.37/1.62 inference(quant_inst,[status(thm)],[])).
% 1.37/1.62 tff(1902,plain,
% 1.37/1.62 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c1_1(a15) | (~c2_1(a15)) | (~ndr1_0) | c0_1(a15)),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 1.37/1.62 tff(1903,plain,
% 1.37/1.62 (hskp0 | (~c2_1(a15)) | c0_1(a15)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1902, 101, 48, 451, 69])).
% 1.37/1.62 tff(1904,plain,
% 1.37/1.62 (c0_1(a15)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1903, 11, 1725])).
% 1.37/1.62 tff(1905,plain,
% 1.37/1.62 (^[U: $i] : refl((hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.37/1.62 inference(bind,[status(th)],[])).
% 1.37/1.62 tff(1906,plain,
% 1.37/1.62 (![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.37/1.62 inference(quant_intro,[status(thm)],[1905])).
% 1.37/1.62 tff(1907,plain,
% 1.37/1.62 (![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1908,plain,
% 1.37/1.62 (^[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)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp24) <=> ((hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp24) <=> (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.37/1.62 inference(bind,[status(th)],[])).
% 1.37/1.62 tff(1909,plain,
% 1.37/1.62 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp24) <=> ![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.37/1.62 inference(quant_intro,[status(thm)],[1908])).
% 1.37/1.62 tff(1910,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.37/1.62 tff(1911,plain,
% 1.37/1.62 (![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 1.37/1.62 tff(1912,plain,
% 1.37/1.62 (![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[1911, 1907])).
% 1.37/1.62 tff(1913,plain,(
% 1.37/1.62 ![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.37/1.62 inference(skolemize,[status(sab)],[1912])).
% 1.37/1.62 tff(1914,plain,
% 1.37/1.62 (![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[1913, 1906])).
% 1.37/1.62 tff(1915,plain,
% 1.37/1.62 (((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp13 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1916,plain,
% 1.37/1.62 ((hskp24 | hskp13 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15))) <=> (hskp24 | hskp13 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1917,plain,
% 1.37/1.62 (((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15))))),
% 1.37/1.62 inference(monotonicity,[status(thm)],[1916])).
% 1.37/1.62 tff(1918,plain,
% 1.37/1.62 (((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp13 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15)))),
% 1.37/1.62 inference(transitivity,[status(thm)],[1917, 1915])).
% 1.37/1.62 tff(1919,plain,
% 1.37/1.62 ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | c1_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 1.37/1.62 inference(quant_inst,[status(thm)],[])).
% 1.37/1.62 tff(1920,plain,
% 1.37/1.62 ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp13 | c1_1(a15) | (~c3_1(a15)) | (~ndr1_0) | (~c0_1(a15))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[1919, 1918])).
% 1.37/1.62 tff(1921,plain,
% 1.37/1.62 (hskp24 | hskp13 | (~c3_1(a15)) | (~c0_1(a15))),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1920, 101, 451, 1914])).
% 1.37/1.62 tff(1922,plain,
% 1.37/1.62 (hskp13),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1921, 1904, 1896, 552])).
% 1.37/1.62 tff(1923,plain,
% 1.37/1.62 (~c3_1(a21)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[774, 1922])).
% 1.37/1.62 tff(1924,plain,
% 1.37/1.62 (c2_1(a21)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[782, 1922])).
% 1.37/1.62 tff(1925,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c1_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c1_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1926,plain,
% 1.37/1.62 (((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | c0_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c1_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1927,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c1_1(a21)) | (~c2_1(a21)) | (~c3_1(a58))))),
% 1.37/1.62 inference(monotonicity,[status(thm)],[1926])).
% 1.37/1.62 tff(1928,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c1_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))),
% 1.37/1.62 inference(transitivity,[status(thm)],[1927, 1925])).
% 1.37/1.62 tff(1929,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 1.37/1.62 inference(quant_inst,[status(thm)],[])).
% 1.37/1.62 tff(1930,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c1_1(a21)) | (~c2_1(a21)) | (~c3_1(a58))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[1929, 1928])).
% 1.37/1.62 tff(1931,plain,
% 1.37/1.62 (~c1_1(a21)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1930, 101, 452, 1924, 37, 1923, 551, 12, 680, 670, 662])).
% 1.37/1.62 tff(1932,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | c1_1(a21) | (~c2_1(a21)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1933,plain,
% 1.37/1.62 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | c1_1(a21) | (~c2_1(a21)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1934,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | c1_1(a21) | (~c2_1(a21))))),
% 1.37/1.62 inference(monotonicity,[status(thm)],[1933])).
% 1.37/1.62 tff(1935,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | c1_1(a21) | (~c2_1(a21)))),
% 1.37/1.62 inference(transitivity,[status(thm)],[1934, 1932])).
% 1.37/1.62 tff(1936,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 1.37/1.62 inference(quant_inst,[status(thm)],[])).
% 1.37/1.62 tff(1937,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | c1_1(a21) | (~c2_1(a21))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 1.37/1.62 tff(1938,plain,
% 1.37/1.62 ($false),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1937, 101, 452, 1924, 37, 26, 1923, 551, 12, 362, 662, 1931])).
% 1.37/1.62 tff(1939,plain,(hskp0 | c0_1(a58) | c1_1(a58) | c3_1(a2) | c2_1(a38) | hskp3 | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.62 tff(1940,plain,
% 1.37/1.62 (hskp0),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1939, 12, 26, 37, 450, 48, 451])).
% 1.37/1.62 tff(1941,plain,
% 1.37/1.62 (~c3_1(a1)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[114, 1940])).
% 1.37/1.62 tff(1942,plain,
% 1.37/1.62 (c2_1(a1)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[122, 1940])).
% 1.37/1.62 tff(1943,plain,
% 1.37/1.62 (c1_1(a1)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[130, 1940])).
% 1.37/1.62 tff(1944,plain,
% 1.37/1.62 (hskp2),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[233, 191])).
% 1.37/1.62 tff(1945,plain,
% 1.37/1.62 (~c2_1(a3)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[197, 1944])).
% 1.37/1.62 tff(1946,plain,
% 1.37/1.62 (c3_1(a3)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[205, 1944])).
% 1.37/1.62 tff(1947,plain,
% 1.37/1.62 (c1_1(a3)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[213, 1944])).
% 1.37/1.62 tff(1948,plain,
% 1.37/1.62 (~c2_1(a13)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1253, 101, 191, 1947, 1946, 226, 225, 1945, 58])).
% 1.37/1.62 tff(1949,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1950,plain,
% 1.37/1.62 (((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1951,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))))),
% 1.37/1.62 inference(monotonicity,[status(thm)],[1950])).
% 1.37/1.62 tff(1952,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 1.37/1.62 inference(transitivity,[status(thm)],[1951, 1949])).
% 1.37/1.62 tff(1953,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.37/1.62 inference(quant_inst,[status(thm)],[])).
% 1.37/1.62 tff(1954,plain,
% 1.37/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[1953, 1952])).
% 1.37/1.62 tff(1955,plain,
% 1.37/1.62 (~c0_1(a3)),
% 1.37/1.62 inference(unit_resolution,[status(thm)],[1954, 101, 1947, 1946, 226, 225, 224, 1945, 36])).
% 1.37/1.62 tff(1956,plain,
% 1.37/1.62 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.37/1.62 inference(bind,[status(th)],[])).
% 1.37/1.62 tff(1957,plain,
% 1.37/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_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) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.62 inference(quant_intro,[status(thm)],[1956])).
% 1.37/1.62 tff(1958,plain,
% 1.37/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_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) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.62 inference(rewrite,[status(thm)],[])).
% 1.37/1.62 tff(1959,plain,
% 1.37/1.62 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.37/1.62 inference(bind,[status(th)],[])).
% 1.37/1.62 tff(1960,plain,
% 1.37/1.62 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.62 inference(quant_intro,[status(thm)],[1959])).
% 1.37/1.62 tff(1961,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 1.37/1.62 tff(1962,plain,
% 1.37/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[1961, 1960])).
% 1.37/1.62 tff(1963,plain,
% 1.37/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[1962, 1958])).
% 1.37/1.62 tff(1964,plain,(
% 1.37/1.62 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.62 inference(skolemize,[status(sab)],[1963])).
% 1.37/1.62 tff(1965,plain,
% 1.37/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.37/1.62 inference(modus_ponens,[status(thm)],[1964, 1957])).
% 1.37/1.62 tff(1966,plain,
% 1.37/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(1967,plain,
% 1.37/1.63 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3))) <=> (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(1968,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3))))),
% 1.37/1.63 inference(monotonicity,[status(thm)],[1967])).
% 1.37/1.63 tff(1969,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)))),
% 1.37/1.63 inference(transitivity,[status(thm)],[1968, 1966])).
% 1.37/1.63 tff(1970,plain,
% 1.37/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3)))),
% 1.37/1.63 inference(quant_inst,[status(thm)],[])).
% 1.37/1.63 tff(1971,plain,
% 1.37/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3))),
% 1.37/1.63 inference(modus_ponens,[status(thm)],[1970, 1969])).
% 1.37/1.63 tff(1972,plain,
% 1.37/1.63 ((~c0_1(a2)) | c0_1(a3)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1971, 101, 1947, 451, 1749, 1174, 1945, 13, 12, 1965])).
% 1.37/1.63 tff(1973,plain,
% 1.37/1.63 (~c0_1(a2)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1972, 1955])).
% 1.37/1.63 tff(1974,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(1975,plain,
% 1.37/1.63 (((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(1976,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13)))),
% 1.37/1.63 inference(monotonicity,[status(thm)],[1975])).
% 1.37/1.63 tff(1977,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13))),
% 1.37/1.63 inference(transitivity,[status(thm)],[1976, 1974])).
% 1.37/1.63 tff(1978,plain,
% 1.37/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 1.37/1.63 inference(quant_inst,[status(thm)],[])).
% 1.37/1.63 tff(1979,plain,
% 1.37/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13)),
% 1.37/1.63 inference(modus_ponens,[status(thm)],[1978, 1977])).
% 1.37/1.63 tff(1980,plain,
% 1.37/1.63 (c0_1(a2) | c2_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1979, 101, 451, 1749, 1174, 225, 224, 13, 12, 344])).
% 1.37/1.63 tff(1981,plain,
% 1.37/1.63 ($false),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1980, 1973, 1948])).
% 1.37/1.63 tff(1982,plain,(hskp1 | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.63 tff(1983,plain,
% 1.37/1.63 (hskp1),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1982, 13, 1749, 1174, 278, 277, 451, 12, 324])).
% 1.37/1.63 tff(1984,plain,
% 1.37/1.63 (~c0_1(a2)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[253, 1983])).
% 1.37/1.63 tff(1985,plain,
% 1.37/1.63 (c0_1(a2) | c2_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1979, 101, 451, 1749, 1174, 278, 277, 13, 12, 344])).
% 1.37/1.63 tff(1986,plain,
% 1.37/1.63 (c2_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1985, 1984])).
% 1.37/1.63 tff(1987,plain,
% 1.37/1.63 (hskp5 | c0_1(a2) | c2_1(a2) | (~c2_1(a13))),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[284, 101, 278, 277, 12, 275])).
% 1.37/1.63 tff(1988,plain,
% 1.37/1.63 (hskp5),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1987, 1986, 13, 1984])).
% 1.37/1.63 tff(1989,plain,
% 1.37/1.63 (~c2_1(a11)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[291, 1988])).
% 1.37/1.63 tff(1990,plain,
% 1.37/1.63 (~c1_1(a11)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[297, 1988])).
% 1.37/1.63 tff(1991,plain,
% 1.37/1.63 (c0_1(a11)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[305, 1988])).
% 1.37/1.63 tff(1992,plain,
% 1.37/1.63 (~c3_1(a11)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[312, 101, 1991, 144, 143, 1990, 1989, 142, 264])).
% 1.37/1.63 tff(1993,plain,
% 1.37/1.63 (((~hskp8) | (~c2_1(a15))) <=> ((~hskp8) | (~c2_1(a15)))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(1994,plain,
% 1.37/1.63 (((~c2_1(a15)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a15)))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(1995,axiom,((~c2_1(a15)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.37/1.63 tff(1996,plain,
% 1.37/1.63 ((~hskp8) | (~c2_1(a15))),
% 1.37/1.63 inference(modus_ponens,[status(thm)],[1995, 1994])).
% 1.37/1.63 tff(1997,plain,
% 1.37/1.63 ((~hskp8) | (~c2_1(a15))),
% 1.37/1.63 inference(modus_ponens,[status(thm)],[1996, 1993])).
% 1.37/1.63 tff(1998,plain,
% 1.37/1.63 (~hskp8),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1997, 1749])).
% 1.37/1.63 tff(1999,plain,
% 1.37/1.63 (hskp7 | c0_1(a2) | c2_1(a2)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1323, 101, 1998, 12, 1311])).
% 1.37/1.63 tff(2000,plain,
% 1.37/1.63 (hskp7),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1999, 1984, 13])).
% 1.37/1.63 tff(2001,plain,
% 1.37/1.63 (~c2_1(a14)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1330, 2000])).
% 1.37/1.63 tff(2002,plain,
% 1.37/1.63 (~c0_1(a14)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1352, 2000])).
% 1.37/1.63 tff(2003,plain,
% 1.37/1.63 (c1_1(a14)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1338, 2000])).
% 1.37/1.63 tff(2004,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a14) | c2_1(a14) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c1_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a14) | c2_1(a14) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c1_1(a14)))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(2005,plain,
% 1.37/1.63 (((~ndr1_0) | c3_1(a11) | c2_1(a11) | (~c0_1(a11)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14))) <=> (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a14) | c2_1(a14) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c1_1(a14)))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(2006,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a11) | c2_1(a11) | (~c0_1(a11)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a14) | c2_1(a14) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c1_1(a14))))),
% 1.37/1.63 inference(monotonicity,[status(thm)],[2005])).
% 1.37/1.63 tff(2007,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a11) | c2_1(a11) | (~c0_1(a11)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a14) | c2_1(a14) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c1_1(a14)))),
% 1.37/1.63 inference(transitivity,[status(thm)],[2006, 2004])).
% 1.37/1.63 tff(2008,plain,
% 1.37/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a11) | c2_1(a11) | (~c0_1(a11)) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))),
% 1.37/1.63 inference(quant_inst,[status(thm)],[])).
% 1.37/1.63 tff(2009,plain,
% 1.37/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a14) | c2_1(a14) | c2_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c1_1(a14))),
% 1.37/1.63 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 1.37/1.63 tff(2010,plain,
% 1.37/1.63 ($false),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[2009, 101, 2003, 1991, 451, 1749, 1174, 2002, 2001, 1989, 1965, 1992])).
% 1.37/1.63 tff(2011,plain,(c2_1(a2) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.63 tff(2012,plain,
% 1.37/1.63 (c2_1(a2)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[2011, 1943, 1725, 1896, 451, 1942, 1941, 12])).
% 1.37/1.63 tff(2013,plain,
% 1.37/1.63 (~hskp1),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[247, 2012])).
% 1.37/1.63 tff(2014,plain,
% 1.37/1.63 (hskp6),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[171, 1943, 1942, 1941])).
% 1.37/1.63 tff(2015,plain,
% 1.37/1.63 (~c3_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[177, 2014])).
% 1.37/1.63 tff(2016,plain,
% 1.37/1.63 (~c1_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[183, 2014])).
% 1.37/1.63 tff(2017,plain,
% 1.37/1.63 (~c0_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[189, 2014])).
% 1.37/1.63 tff(2018,plain,
% 1.37/1.63 (hskp2 | hskp1),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[232, 101, 2017, 2016, 2015, 47])).
% 1.37/1.63 tff(2019,plain,
% 1.37/1.63 (hskp2),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[2018, 2013])).
% 1.37/1.63 tff(2020,plain,
% 1.37/1.63 (~c2_1(a3)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[197, 2019])).
% 1.37/1.63 tff(2021,plain,
% 1.37/1.63 (c3_1(a3)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[205, 2019])).
% 1.37/1.63 tff(2022,plain,
% 1.37/1.63 (c1_1(a3)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[213, 2019])).
% 1.37/1.63 tff(2023,plain,
% 1.37/1.63 (~c2_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1253, 101, 2013, 2022, 2021, 2017, 2016, 2020, 58])).
% 1.37/1.63 tff(2024,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(2025,plain,
% 1.37/1.63 (((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(2026,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13)))),
% 1.37/1.63 inference(monotonicity,[status(thm)],[2025])).
% 1.37/1.63 tff(2027,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 1.37/1.63 inference(transitivity,[status(thm)],[2026, 2024])).
% 1.37/1.63 tff(2028,plain,
% 1.37/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.37/1.63 inference(quant_inst,[status(thm)],[])).
% 1.37/1.63 tff(2029,plain,
% 1.37/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13)),
% 1.37/1.63 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 1.37/1.63 tff(2030,plain,
% 1.37/1.63 ($false),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[2029, 101, 451, 1725, 1896, 2017, 2016, 2015, 344, 2023])).
% 1.37/1.63 tff(2031,plain,(c3_1(a2) | c1_1(a15) | c1_1(a58) | c0_1(a58) | c2_1(a38) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.37/1.63 tff(2032,plain,
% 1.37/1.63 (c3_1(a2)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[2031, 451, 26, 37, 450, 48])).
% 1.37/1.63 tff(2033,plain,
% 1.37/1.63 (~hskp1),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[241, 2032])).
% 1.37/1.63 tff(2034,plain,
% 1.37/1.63 (hskp0),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[548, 2033, 48, 37, 26])).
% 1.37/1.63 tff(2035,plain,
% 1.37/1.63 (~c3_1(a1)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[114, 2034])).
% 1.37/1.63 tff(2036,plain,
% 1.37/1.63 (c2_1(a1)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[122, 2034])).
% 1.37/1.63 tff(2037,plain,
% 1.37/1.63 (c1_1(a1)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[130, 2034])).
% 1.37/1.63 tff(2038,plain,
% 1.37/1.63 (hskp6),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[171, 2037, 2036, 2035])).
% 1.37/1.63 tff(2039,plain,
% 1.37/1.63 (~c3_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[177, 2038])).
% 1.37/1.63 tff(2040,plain,
% 1.37/1.63 (~c1_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[183, 2038])).
% 1.37/1.63 tff(2041,plain,
% 1.37/1.63 (~c0_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[189, 2038])).
% 1.37/1.63 tff(2042,plain,
% 1.37/1.63 (hskp2),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[232, 101, 2033, 2041, 2040, 2039, 47])).
% 1.37/1.63 tff(2043,plain,
% 1.37/1.63 (~c2_1(a3)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[197, 2042])).
% 1.37/1.63 tff(2044,plain,
% 1.37/1.63 (c3_1(a3)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[205, 2042])).
% 1.37/1.63 tff(2045,plain,
% 1.37/1.63 (c1_1(a3)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[213, 2042])).
% 1.37/1.63 tff(2046,plain,
% 1.37/1.63 (~c2_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1253, 101, 2033, 2045, 2044, 2041, 2040, 2043, 58])).
% 1.37/1.63 tff(2047,plain,
% 1.37/1.63 ($false),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[2029, 101, 451, 1725, 1896, 2041, 2040, 2039, 344, 2046])).
% 1.37/1.63 tff(2048,plain,(c1_1(a15) | hskp3 | c0_1(a58) | c1_1(a58) | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.63 tff(2049,plain,
% 1.37/1.63 (c1_1(a15)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[2048, 450, 37, 26, 48])).
% 1.37/1.63 tff(2050,plain,
% 1.37/1.63 (hskp0),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[548, 191, 48, 37, 26])).
% 1.37/1.63 tff(2051,plain,
% 1.37/1.63 (~c3_1(a1)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[114, 2050])).
% 1.37/1.63 tff(2052,plain,
% 1.37/1.63 (c2_1(a1)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[122, 2050])).
% 1.37/1.63 tff(2053,plain,
% 1.37/1.63 (c1_1(a1)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[130, 2050])).
% 1.37/1.63 tff(2054,plain,
% 1.37/1.63 (hskp6),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[171, 2053, 2052, 2051])).
% 1.37/1.63 tff(2055,plain,
% 1.37/1.63 (~c3_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[177, 2054])).
% 1.37/1.63 tff(2056,plain,
% 1.37/1.63 (~c1_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[183, 2054])).
% 1.37/1.63 tff(2057,plain,
% 1.37/1.63 (~c0_1(a13)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[189, 2054])).
% 1.37/1.63 tff(2058,plain,
% 1.37/1.63 (hskp2),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[232, 101, 191, 2057, 2056, 2055, 47])).
% 1.37/1.63 tff(2059,plain,
% 1.37/1.63 (~c2_1(a3)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[197, 2058])).
% 1.37/1.63 tff(2060,assumption,(c1_1(a15)), introduced(assumption)).
% 1.37/1.63 tff(2061,plain,
% 1.37/1.63 (c3_1(a3)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[205, 2058])).
% 1.37/1.63 tff(2062,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(2063,plain,
% 1.37/1.63 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> ((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(2064,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3)))),
% 1.37/1.63 inference(monotonicity,[status(thm)],[2063])).
% 1.37/1.63 tff(2065,plain,
% 1.37/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 1.37/1.63 inference(transitivity,[status(thm)],[2064, 2062])).
% 1.37/1.63 tff(2066,plain,
% 1.37/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.37/1.63 inference(quant_inst,[status(thm)],[])).
% 1.37/1.63 tff(2067,plain,
% 1.37/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3)),
% 1.37/1.63 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 1.37/1.63 tff(2068,plain,
% 1.37/1.63 (c0_1(a3)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[2067, 101, 2061, 2053, 2052, 2060, 698, 444, 2059, 2051, 680])).
% 1.37/1.63 tff(2069,plain,
% 1.37/1.63 (c1_1(a3)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[213, 2058])).
% 1.37/1.63 tff(2070,plain,
% 1.37/1.63 ($false),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[1954, 101, 2069, 2061, 2057, 2056, 2055, 2059, 36, 2068])).
% 1.37/1.63 tff(2071,plain,(hskp1 | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.63 tff(2072,plain,
% 1.37/1.63 (hskp1),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[2071, 698, 2049, 444, 48, 37, 26])).
% 1.37/1.63 tff(2073,plain,
% 1.37/1.63 (~c3_1(a2)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[241, 2072])).
% 1.37/1.63 tff(2074,plain,
% 1.37/1.63 (~c2_1(a2)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[247, 2072])).
% 1.37/1.63 tff(2075,plain,
% 1.37/1.63 (~c0_1(a2)),
% 1.37/1.63 inference(unit_resolution,[status(thm)],[253, 2072])).
% 1.37/1.63 tff(2076,plain,
% 1.37/1.63 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~c1_1(a15)) | c2_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | (~c1_1(a15)) | c2_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a15)))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(2077,plain,
% 1.37/1.63 ((hskp27 | (~ndr1_0) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp27 | (~c1_1(a15)) | c2_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a15)))),
% 1.37/1.63 inference(rewrite,[status(thm)],[])).
% 1.37/1.63 tff(2078,plain,
% 1.37/1.63 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~c1_1(a15)) | c2_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a15))))),
% 1.37/1.63 inference(monotonicity,[status(thm)],[2077])).
% 1.37/1.63 tff(2079,plain,
% 1.37/1.63 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | (~c1_1(a15)) | c2_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a15)))),
% 1.37/1.63 inference(transitivity,[status(thm)],[2078, 2076])).
% 1.37/1.63 tff(2080,plain,
% 1.37/1.63 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.37/1.63 inference(quant_inst,[status(thm)],[])).
% 1.37/1.63 tff(2081,plain,
% 1.37/1.63 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | (~c1_1(a15)) | c2_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c0_1(a15))),
% 1.37/1.63 inference(modus_ponens,[status(thm)],[2080, 2079])).
% 1.46/1.63 tff(2082,plain,
% 1.46/1.63 (hskp27 | (~c0_1(a15))),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2081, 101, 2049, 698, 2075, 2074, 2073, 614])).
% 1.46/1.63 tff(2083,plain,
% 1.46/1.63 (~c0_1(a15)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2082, 586])).
% 1.46/1.63 tff(2084,plain,
% 1.46/1.63 (((~hskp8) | (~c1_1(a15))) <=> ((~hskp8) | (~c1_1(a15)))),
% 1.46/1.63 inference(rewrite,[status(thm)],[])).
% 1.46/1.63 tff(2085,plain,
% 1.46/1.63 (((~c1_1(a15)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a15)))),
% 1.46/1.63 inference(rewrite,[status(thm)],[])).
% 1.46/1.63 tff(2086,axiom,((~c1_1(a15)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.46/1.63 tff(2087,plain,
% 1.46/1.63 ((~hskp8) | (~c1_1(a15))),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[2086, 2085])).
% 1.46/1.63 tff(2088,plain,
% 1.46/1.63 ((~hskp8) | (~c1_1(a15))),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[2087, 2084])).
% 1.46/1.63 tff(2089,plain,
% 1.46/1.63 (~hskp8),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2088, 2049])).
% 1.46/1.63 tff(2090,plain,
% 1.46/1.63 (hskp13),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1365, 586, 2089])).
% 1.46/1.63 tff(2091,plain,
% 1.46/1.63 (~c3_1(a21)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[774, 2090])).
% 1.46/1.63 tff(2092,plain,
% 1.46/1.63 (~hskp20),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[643, 11, 2073, 2074, 2075, 497])).
% 1.46/1.63 tff(2093,plain,
% 1.46/1.63 (~hskp21),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[624, 586, 450, 2074, 2073, 2075])).
% 1.46/1.63 tff(2094,plain,
% 1.46/1.63 (c3_1(a58)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[669, 2093, 452, 2092])).
% 1.46/1.63 tff(2095,plain,
% 1.46/1.63 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | (~c3_1(a58)))),
% 1.46/1.63 inference(rewrite,[status(thm)],[])).
% 1.46/1.63 tff(2096,plain,
% 1.46/1.63 ((hskp22 | hskp20 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58))) <=> (hskp22 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | (~c3_1(a58)))),
% 1.46/1.63 inference(rewrite,[status(thm)],[])).
% 1.46/1.63 tff(2097,plain,
% 1.46/1.63 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | (~c3_1(a58))))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[2096])).
% 1.46/1.63 tff(2098,plain,
% 1.46/1.63 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | (~c3_1(a58)))),
% 1.46/1.63 inference(transitivity,[status(thm)],[2097, 2095])).
% 1.46/1.63 tff(2099,plain,
% 1.46/1.63 ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)))),
% 1.46/1.63 inference(quant_inst,[status(thm)],[])).
% 1.46/1.63 tff(2100,plain,
% 1.46/1.63 ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)))) | hskp22 | hskp20 | c2_1(a58) | c1_1(a58) | (~ndr1_0) | (~c3_1(a58))),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[2099, 2098])).
% 1.46/1.63 tff(2101,plain,
% 1.46/1.63 (hskp22 | hskp20 | c2_1(a58) | (~c3_1(a58))),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2100, 101, 26, 1378])).
% 1.46/1.63 tff(2102,plain,
% 1.46/1.63 (hskp22),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2101, 2094, 452, 2092])).
% 1.46/1.63 tff(2103,plain,
% 1.46/1.63 (~c1_1(a42)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1391, 2102])).
% 1.46/1.63 tff(2104,plain,
% 1.46/1.63 (c2_1(a21)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[782, 2090])).
% 1.46/1.63 tff(2105,plain,
% 1.46/1.63 (c2_1(a42)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1400, 2102])).
% 1.46/1.63 tff(2106,plain,
% 1.46/1.63 (c0_1(a42)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[1408, 2102])).
% 1.46/1.63 tff(2107,plain,
% 1.46/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c3_1(a21) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a21) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.46/1.63 inference(rewrite,[status(thm)],[])).
% 1.46/1.63 tff(2108,plain,
% 1.46/1.63 (((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a15) | c0_1(a15) | c3_1(a15)) <=> (c1_1(a42) | c3_1(a21) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.46/1.63 inference(rewrite,[status(thm)],[])).
% 1.46/1.63 tff(2109,plain,
% 1.46/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a15) | c0_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c3_1(a21) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42))))),
% 1.46/1.63 inference(monotonicity,[status(thm)],[2108])).
% 1.46/1.63 tff(2110,plain,
% 1.46/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a15) | c0_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a21) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.46/1.63 inference(transitivity,[status(thm)],[2109, 2107])).
% 1.46/1.63 tff(2111,plain,
% 1.46/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a15) | c0_1(a15) | c3_1(a15))),
% 1.46/1.63 inference(quant_inst,[status(thm)],[])).
% 1.46/1.63 tff(2112,plain,
% 1.46/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a21) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a42)) | (~c0_1(a42))),
% 1.46/1.63 inference(modus_ponens,[status(thm)],[2111, 2110])).
% 1.46/1.63 tff(2113,plain,
% 1.46/1.63 (~c1_1(a21)),
% 1.46/1.63 inference(unit_resolution,[status(thm)],[2112, 101, 2106, 2105, 2104, 2103, 2091, 698, 444, 1264, 2083])).
% 1.46/1.63 tff(2114,plain,
% 1.46/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 1.46/1.63 inference(rewrite,[status(thm)],[])).
% 1.46/1.63 tff(2115,plain,
% 1.46/1.63 (((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 1.46/1.63 inference(rewrite,[status(thm)],[])).
% 1.46/1.63 tff(2116,plain,
% 1.46/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21))))),
% 1.46/1.64 inference(monotonicity,[status(thm)],[2115])).
% 1.46/1.64 tff(2117,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 1.46/1.64 inference(transitivity,[status(thm)],[2116, 2114])).
% 1.46/1.64 tff(2118,plain,
% 1.46/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 1.46/1.64 inference(quant_inst,[status(thm)],[])).
% 1.46/1.64 tff(2119,plain,
% 1.46/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21))),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[2118, 2117])).
% 1.46/1.64 tff(2120,plain,
% 1.46/1.64 ($false),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2119, 101, 452, 2104, 37, 26, 2091, 2049, 698, 444, 362, 2113])).
% 1.46/1.64 tff(2121,plain,(hskp0 | c0_1(a58) | c1_1(a58) | c2_1(a15) | c3_1(a15) | c2_1(a38) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.46/1.64 tff(2122,plain,
% 1.46/1.64 (hskp0),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2121, 698, 26, 37, 444, 450, 48])).
% 1.46/1.64 tff(2123,plain,
% 1.46/1.64 (~c3_1(a1)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[114, 2122])).
% 1.46/1.64 tff(2124,plain,
% 1.46/1.64 (hskp7),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[1323, 101, 2089, 2075, 2074, 2073, 1311])).
% 1.46/1.64 tff(2125,plain,
% 1.46/1.64 (~c2_1(a14)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[1330, 2124])).
% 1.46/1.64 tff(2126,plain,
% 1.46/1.64 (~c0_1(a14)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[1352, 2124])).
% 1.46/1.64 tff(2127,plain,
% 1.46/1.64 (c2_1(a1)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[122, 2122])).
% 1.46/1.64 tff(2128,plain,
% 1.46/1.64 (c1_1(a1)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[130, 2122])).
% 1.46/1.64 tff(2129,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a14) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a14) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2130,plain,
% 1.46/1.64 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14))) <=> ((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a14) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2131,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a14) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14))))),
% 1.46/1.64 inference(monotonicity,[status(thm)],[2130])).
% 1.46/1.64 tff(2132,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a14) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14)))),
% 1.46/1.64 inference(transitivity,[status(thm)],[2131, 2129])).
% 1.46/1.64 tff(2133,plain,
% 1.46/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)))),
% 1.46/1.64 inference(quant_inst,[status(thm)],[])).
% 1.46/1.64 tff(2134,plain,
% 1.46/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a14) | c2_1(a14) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a14))),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 1.46/1.64 tff(2135,plain,
% 1.46/1.64 (~c3_1(a14)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2134, 101, 2128, 2127, 2049, 698, 444, 2126, 2125, 2123, 680])).
% 1.46/1.64 tff(2136,plain,
% 1.46/1.64 (hskp6),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[171, 2128, 2127, 2123])).
% 1.46/1.64 tff(2137,plain,
% 1.46/1.64 (~c3_1(a13)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[177, 2136])).
% 1.46/1.64 tff(2138,plain,
% 1.46/1.64 (~c1_1(a13)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[183, 2136])).
% 1.46/1.64 tff(2139,plain,
% 1.46/1.64 (~c0_1(a13)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[189, 2136])).
% 1.46/1.64 tff(2140,plain,
% 1.46/1.64 (~c2_1(a13)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[332, 2128, 2127, 2123, 2075, 2074, 2073])).
% 1.46/1.64 tff(2141,assumption,(~c3_1(a14)), introduced(assumption)).
% 1.46/1.64 tff(2142,assumption,(~c2_1(a14)), introduced(assumption)).
% 1.46/1.64 tff(2143,assumption,(~c0_1(a14)), introduced(assumption)).
% 1.46/1.64 tff(2144,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c0_1(a14) | c2_1(a14) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c3_1(a14) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c0_1(a14) | c2_1(a14) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c3_1(a14) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2145,plain,
% 1.46/1.64 (((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a14) | c0_1(a14) | c3_1(a14)) <=> (c1_1(a58) | c0_1(a14) | c2_1(a14) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c3_1(a14) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2146,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a14) | c0_1(a14) | c3_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a58) | c0_1(a14) | c2_1(a14) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c3_1(a14) | (~c2_1(a58)) | (~c3_1(a58))))),
% 1.46/1.64 inference(monotonicity,[status(thm)],[2145])).
% 1.46/1.64 tff(2147,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a14) | c0_1(a14) | c3_1(a14))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c0_1(a14) | c2_1(a14) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c3_1(a14) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.46/1.64 inference(transitivity,[status(thm)],[2146, 2144])).
% 1.46/1.64 tff(2148,plain,
% 1.46/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a14) | c0_1(a14) | c3_1(a14))),
% 1.46/1.64 inference(quant_inst,[status(thm)],[])).
% 1.46/1.64 tff(2149,plain,
% 1.46/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a58) | c0_1(a14) | c2_1(a14) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c3_1(a14) | (~c2_1(a58)) | (~c3_1(a58))),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[2148, 2147])).
% 1.46/1.64 tff(2150,plain,
% 1.46/1.64 (c2_1(a13) | (~c2_1(a58)) | (~c3_1(a58))),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2149, 101, 26, 2143, 2142, 225, 224, 344, 2141])).
% 1.46/1.64 tff(2151,plain,
% 1.46/1.64 (~c3_1(a58)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2150, 334, 59])).
% 1.46/1.64 tff(2152,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2153,plain,
% 1.46/1.64 (((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13)) <=> (c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2154,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58)))),
% 1.46/1.64 inference(monotonicity,[status(thm)],[2153])).
% 1.46/1.64 tff(2155,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58))),
% 1.46/1.64 inference(transitivity,[status(thm)],[2154, 2152])).
% 1.46/1.64 tff(2156,plain,
% 1.46/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)) | c2_1(a13) | c1_1(a13) | c0_1(a13))),
% 1.46/1.64 inference(quant_inst,[status(thm)],[])).
% 1.46/1.64 tff(2157,plain,
% 1.46/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a58)) | c3_1(a58)),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[2156, 2155])).
% 1.46/1.64 tff(2158,plain,
% 1.46/1.64 ($false),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2157, 101, 59, 26, 2060, 698, 444, 226, 225, 362, 334, 2151])).
% 1.46/1.64 tff(2159,plain,(c2_1(a13) | (~c2_1(a58)) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | c0_1(a14) | c2_1(a14) | c3_1(a13) | c3_1(a14)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.64 tff(2160,plain,
% 1.46/1.64 (~c2_1(a58)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2159, 2140, 26, 2049, 698, 444, 2139, 2138, 2126, 2125, 2137, 2135])).
% 1.46/1.64 tff(2161,plain,
% 1.46/1.64 (~hskp24),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[442, 2160])).
% 1.46/1.64 tff(2162,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2163,plain,
% 1.46/1.64 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2164,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58))))),
% 1.46/1.64 inference(monotonicity,[status(thm)],[2163])).
% 1.46/1.64 tff(2165,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))),
% 1.46/1.64 inference(transitivity,[status(thm)],[2164, 2162])).
% 1.46/1.64 tff(2166,plain,
% 1.46/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 1.46/1.64 inference(quant_inst,[status(thm)],[])).
% 1.46/1.64 tff(2167,plain,
% 1.46/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58))),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 1.46/1.64 tff(2168,plain,
% 1.46/1.64 (~c3_1(a58)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2167, 101, 726, 2128, 2127, 37, 2049, 698, 444, 2123, 680])).
% 1.46/1.64 tff(2169,assumption,(~c3_1(a58)), introduced(assumption)).
% 1.46/1.64 tff(2170,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a58) | c1_1(a58) | c2_1(a38) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a58) | c2_1(a38) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2171,plain,
% 1.46/1.64 (((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a58) | c0_1(a58) | c3_1(a58)) <=> (c0_1(a58) | c1_1(a58) | c2_1(a38) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2172,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a58) | c1_1(a58) | c2_1(a38) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58)))),
% 1.46/1.64 inference(monotonicity,[status(thm)],[2171])).
% 1.46/1.64 tff(2173,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a58) | c2_1(a38) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58))),
% 1.46/1.64 inference(transitivity,[status(thm)],[2172, 2170])).
% 1.46/1.64 tff(2174,plain,
% 1.46/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a38) | (~c3_1(a38)) | (~c1_1(a38)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a58) | c0_1(a58) | c3_1(a58))),
% 1.46/1.64 inference(quant_inst,[status(thm)],[])).
% 1.46/1.64 tff(2175,plain,
% 1.46/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a58) | c2_1(a38) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58)),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[2174, 2173])).
% 1.46/1.64 tff(2176,plain,
% 1.46/1.64 ((~c3_1(a38)) | (~c0_1(a38)) | (~c1_1(a38)) | c3_1(a58)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2175, 101, 37, 26, 450, 36])).
% 1.46/1.64 tff(2177,plain,
% 1.46/1.64 (~c3_1(a38)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2176, 596, 2169, 604])).
% 1.46/1.64 tff(2178,plain,
% 1.46/1.64 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))))),
% 1.46/1.64 inference(bind,[status(th)],[])).
% 1.46/1.64 tff(2179,plain,
% 1.46/1.64 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 1.46/1.64 inference(quant_intro,[status(thm)],[2178])).
% 1.46/1.64 tff(2180,plain,
% 1.46/1.64 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2181,plain,
% 1.46/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))))),
% 1.46/1.64 inference(bind,[status(th)],[])).
% 1.46/1.64 tff(2182,plain,
% 1.46/1.64 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 1.46/1.64 inference(quant_intro,[status(thm)],[2181])).
% 1.46/1.64 tff(2183,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.46/1.64 tff(2184,plain,
% 1.46/1.64 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[2183, 2182])).
% 1.46/1.64 tff(2185,plain,
% 1.46/1.64 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[2184, 2180])).
% 1.46/1.64 tff(2186,plain,(
% 1.46/1.64 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 1.46/1.64 inference(skolemize,[status(sab)],[2185])).
% 1.46/1.64 tff(2187,plain,
% 1.46/1.64 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[2186, 2179])).
% 1.46/1.64 tff(2188,plain,
% 1.46/1.64 (hskp27),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[624, 588, 450, 13, 12, 14])).
% 1.46/1.64 tff(2189,plain,
% 1.46/1.64 (c3_1(a12)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[560, 2188])).
% 1.46/1.64 tff(2190,plain,
% 1.46/1.64 (c1_1(a12)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[568, 2188])).
% 1.46/1.64 tff(2191,plain,
% 1.46/1.64 (c0_1(a12)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[1114, 2188])).
% 1.46/1.64 tff(2192,assumption,(~hskp8), introduced(assumption)).
% 1.46/1.64 tff(2193,plain,
% 1.46/1.64 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2194,plain,
% 1.46/1.64 ((hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38))) <=> (hskp8 | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2195,plain,
% 1.46/1.64 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))))),
% 1.46/1.64 inference(monotonicity,[status(thm)],[2194])).
% 1.46/1.64 tff(2196,plain,
% 1.46/1.64 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.46/1.64 inference(transitivity,[status(thm)],[2195, 2193])).
% 1.46/1.64 tff(2197,plain,
% 1.46/1.64 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.46/1.64 inference(quant_inst,[status(thm)],[])).
% 1.46/1.64 tff(2198,plain,
% 1.46/1.64 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))),
% 1.46/1.64 inference(modus_ponens,[status(thm)],[2197, 2196])).
% 1.46/1.64 tff(2199,plain,
% 1.46/1.64 ($false),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2198, 101, 2192, 2191, 2190, 2189, 596, 604, 2187, 2177])).
% 1.46/1.64 tff(2200,plain,((~hskp21) | hskp8 | c3_1(a58) | c0_1(a58) | c1_1(a58) | c2_1(a38) | c2_1(a2) | c3_1(a2) | c0_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.64 tff(2201,plain,
% 1.46/1.64 (~hskp21),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2200, 2168, 2089, 37, 26, 450, 2074, 2073, 2075])).
% 1.46/1.64 tff(2202,plain,
% 1.46/1.64 (hskp20),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[669, 2201, 726, 2168])).
% 1.46/1.64 tff(2203,plain,
% 1.46/1.64 (c3_1(a37)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[516, 2202])).
% 1.46/1.64 tff(2204,plain,
% 1.46/1.64 (c1_1(a37)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[524, 2202])).
% 1.46/1.64 tff(2205,plain,
% 1.46/1.64 (~c2_1(a37)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[529, 101, 526, 48, 2204, 2203, 10])).
% 1.46/1.64 tff(2206,plain,
% 1.46/1.64 (hskp13),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[768, 2201, 526])).
% 1.46/1.64 tff(2207,plain,
% 1.46/1.64 (~c3_1(a21)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[774, 2206])).
% 1.46/1.64 tff(2208,plain,
% 1.46/1.64 (c2_1(a21)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[782, 2206])).
% 1.46/1.64 tff(2209,plain,
% 1.46/1.64 (c1_1(a21)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[2119, 101, 726, 2208, 37, 26, 2207, 2049, 698, 444, 362])).
% 1.46/1.64 tff(2210,plain,
% 1.46/1.64 (~c0_1(a37)),
% 1.46/1.64 inference(unit_resolution,[status(thm)],[631, 2202])).
% 1.46/1.64 tff(2211,plain,
% 1.46/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | c2_1(a37) | (~c3_1(a37)))),
% 1.46/1.64 inference(rewrite,[status(thm)],[])).
% 1.46/1.64 tff(2212,plain,
% 1.46/1.64 (((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37))) <=> (c0_1(a37) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | c2_1(a37) | (~c3_1(a37)))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2213,plain,
% 1.46/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | c2_1(a37) | (~c3_1(a37))))),
% 1.46/1.65 inference(monotonicity,[status(thm)],[2212])).
% 1.46/1.65 tff(2214,plain,
% 1.46/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | c2_1(a37) | (~c3_1(a37)))),
% 1.46/1.65 inference(transitivity,[status(thm)],[2213, 2211])).
% 1.46/1.65 tff(2215,plain,
% 1.46/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))),
% 1.46/1.65 inference(quant_inst,[status(thm)],[])).
% 1.46/1.65 tff(2216,plain,
% 1.46/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | c2_1(a37) | (~c3_1(a37))),
% 1.46/1.65 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 1.46/1.65 tff(2217,plain,
% 1.46/1.65 ($false),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2216, 101, 2203, 2208, 2210, 2207, 2049, 698, 444, 680, 2209, 2205])).
% 1.46/1.65 tff(2218,plain,(c2_1(a58) | c2_1(a15) | c3_1(a15) | c0_1(a58) | c1_1(a58) | hskp24 | hskp3 | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.65 tff(2219,plain,
% 1.46/1.65 ($false),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2218, 2161, 2160, 444, 37, 26, 698, 48, 450])).
% 1.46/1.65 tff(2220,plain,(c2_1(a15) | c3_1(a15) | c0_1(a58) | c1_1(a58) | hskp3 | c2_1(a38)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.65 tff(2221,plain,
% 1.46/1.65 (c2_1(a15)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2220, 444, 37, 26, 48, 450])).
% 1.46/1.65 tff(2222,plain,
% 1.46/1.65 (~c0_1(a3)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[1954, 101, 2069, 2061, 2057, 2056, 2055, 2059, 36])).
% 1.46/1.65 tff(2223,plain,
% 1.46/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2224,plain,
% 1.46/1.65 ((hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2225,plain,
% 1.46/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3))))),
% 1.46/1.65 inference(monotonicity,[status(thm)],[2224])).
% 1.46/1.65 tff(2226,plain,
% 1.46/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.46/1.65 inference(transitivity,[status(thm)],[2225, 2223])).
% 1.46/1.65 tff(2227,plain,
% 1.46/1.65 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.46/1.65 inference(quant_inst,[status(thm)],[])).
% 1.46/1.65 tff(2228,plain,
% 1.46/1.65 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3))),
% 1.46/1.65 inference(modus_ponens,[status(thm)],[2227, 2226])).
% 1.46/1.65 tff(2229,plain,
% 1.46/1.65 (hskp9),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2228, 101, 2069, 2061, 2060, 1749, 444, 2059, 827])).
% 1.46/1.65 tff(2230,plain,
% 1.46/1.65 (~c3_1(a16)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[839, 2229])).
% 1.46/1.65 tff(2231,plain,
% 1.46/1.65 (c1_1(a16)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[847, 2229])).
% 1.46/1.65 tff(2232,plain,
% 1.46/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2233,plain,
% 1.46/1.65 (((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2234,plain,
% 1.46/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16)))),
% 1.46/1.65 inference(monotonicity,[status(thm)],[2233])).
% 1.46/1.65 tff(2235,plain,
% 1.46/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))),
% 1.46/1.65 inference(transitivity,[status(thm)],[2234, 2232])).
% 1.46/1.65 tff(2236,plain,
% 1.46/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.46/1.65 inference(quant_inst,[status(thm)],[])).
% 1.46/1.65 tff(2237,plain,
% 1.46/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16)),
% 1.46/1.65 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 1.46/1.65 tff(2238,plain,
% 1.46/1.65 (c2_1(a16)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2237, 101, 2231, 2061, 2230, 2060, 1749, 444, 2059, 680, 2222])).
% 1.46/1.65 tff(2239,plain,
% 1.46/1.65 (~c2_1(a13)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[1253, 101, 191, 2069, 2061, 2057, 2056, 2059, 58])).
% 1.46/1.65 tff(2240,plain,
% 1.46/1.65 (c0_1(a16)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[855, 2229])).
% 1.46/1.65 tff(2241,plain,
% 1.46/1.65 (hskp12),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[924, 101, 2240, 2231, 2061, 2230, 2059, 918, 2222])).
% 1.46/1.65 tff(2242,plain,
% 1.46/1.65 (~c1_1(a20)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[936, 2241])).
% 1.46/1.65 tff(2243,plain,
% 1.46/1.65 (c2_1(a20)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[944, 2241])).
% 1.46/1.65 tff(2244,plain,
% 1.46/1.65 (~c0_1(a20)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[1281, 101, 2243, 2231, 2242, 2230, 2057, 2055, 1264, 2239, 2238])).
% 1.46/1.65 tff(2245,plain,
% 1.46/1.65 ($false),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[1288, 101, 191, 2243, 2069, 2061, 2242, 2059, 58, 2244])).
% 1.46/1.65 tff(2246,plain,(hskp1 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.65 tff(2247,plain,
% 1.46/1.65 (hskp1),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2246, 2221, 2049, 444, 48, 37, 26])).
% 1.46/1.65 tff(2248,plain,
% 1.46/1.65 (~c3_1(a2)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[241, 2247])).
% 1.46/1.65 tff(2249,plain,
% 1.46/1.65 (~c0_1(a2)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[253, 2247])).
% 1.46/1.65 tff(2250,plain,
% 1.46/1.65 (~c2_1(a2)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[247, 2247])).
% 1.46/1.65 tff(2251,plain,
% 1.46/1.65 (~hskp20),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[643, 550, 12, 13, 11, 497])).
% 1.46/1.65 tff(2252,plain,
% 1.46/1.65 (~hskp27),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[585, 552, 11, 497, 48])).
% 1.46/1.65 tff(2253,plain,
% 1.46/1.65 (~hskp21),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[624, 2252, 450, 13, 12, 550])).
% 1.46/1.65 tff(2254,plain,
% 1.46/1.65 (c1_1(a2)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[661, 2253, 13, 2251])).
% 1.46/1.65 tff(2255,plain,
% 1.46/1.65 (c3_1(a58)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[669, 2253, 452, 2251])).
% 1.46/1.65 tff(2256,plain,
% 1.46/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a58)))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2257,plain,
% 1.46/1.65 (((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a58)))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2258,plain,
% 1.46/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a58))))),
% 1.46/1.65 inference(monotonicity,[status(thm)],[2257])).
% 1.46/1.65 tff(2259,plain,
% 1.46/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a58)))),
% 1.46/1.65 inference(transitivity,[status(thm)],[2258, 2256])).
% 1.46/1.65 tff(2260,plain,
% 1.46/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 1.46/1.65 inference(quant_inst,[status(thm)],[])).
% 1.46/1.65 tff(2261,plain,
% 1.46/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a58))),
% 1.46/1.65 inference(modus_ponens,[status(thm)],[2260, 2259])).
% 1.46/1.65 tff(2262,plain,
% 1.46/1.65 ($false),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2261, 101, 452, 37, 2049, 2221, 444, 13, 12, 680, 2255, 2254])).
% 1.46/1.65 tff(2263,plain,(hskp0 | c0_1(a58) | c3_1(a15) | c2_1(a2) | c3_1(a2) | c1_1(a58) | c2_1(a38) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.46/1.65 tff(2264,plain,
% 1.46/1.65 (hskp0),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2263, 13, 444, 37, 12, 26, 450, 48])).
% 1.46/1.65 tff(2265,plain,
% 1.46/1.65 (~c3_1(a1)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[114, 2264])).
% 1.46/1.65 tff(2266,plain,
% 1.46/1.65 (c2_1(a1)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[122, 2264])).
% 1.46/1.65 tff(2267,plain,
% 1.46/1.65 (c1_1(a1)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[130, 2264])).
% 1.46/1.65 tff(2268,plain,
% 1.46/1.65 (hskp6),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[171, 2267, 2266, 2265])).
% 1.46/1.65 tff(2269,plain,
% 1.46/1.65 (~c1_1(a13)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[183, 2268])).
% 1.46/1.65 tff(2270,plain,
% 1.46/1.65 (~c3_1(a13)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[177, 2268])).
% 1.46/1.65 tff(2271,plain,
% 1.46/1.65 (~c0_1(a13)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[189, 2268])).
% 1.46/1.65 tff(2272,plain,
% 1.46/1.65 (~c2_1(a13)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[332, 14, 2266, 2265, 2267, 13, 12])).
% 1.46/1.65 tff(2273,plain,
% 1.46/1.65 (~c2_1(a58)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[432, 2272, 2271, 2270, 26, 2269, 48, 37, 14, 13, 12])).
% 1.46/1.65 tff(2274,plain,
% 1.46/1.65 (~hskp24),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[442, 2273])).
% 1.46/1.65 tff(2275,plain,
% 1.46/1.65 (~hskp21),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2200, 2169, 2089, 37, 26, 450, 13, 12, 14])).
% 1.46/1.65 tff(2276,plain,
% 1.46/1.65 (hskp20),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[669, 2275, 726, 2169])).
% 1.46/1.65 tff(2277,plain,
% 1.46/1.65 (c3_1(a37)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[516, 2276])).
% 1.46/1.65 tff(2278,plain,
% 1.46/1.65 (c1_1(a37)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[524, 2276])).
% 1.46/1.65 tff(2279,plain,
% 1.46/1.65 (~c2_1(a37)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[529, 101, 526, 48, 2278, 2277, 10])).
% 1.46/1.65 tff(2280,plain,
% 1.46/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2281,plain,
% 1.46/1.65 ((hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))) <=> (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2282,plain,
% 1.46/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))))),
% 1.46/1.65 inference(monotonicity,[status(thm)],[2281])).
% 1.46/1.65 tff(2283,plain,
% 1.46/1.65 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.46/1.65 inference(transitivity,[status(thm)],[2282, 2280])).
% 1.46/1.65 tff(2284,plain,
% 1.46/1.65 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.46/1.65 inference(quant_inst,[status(thm)],[])).
% 1.46/1.65 tff(2285,plain,
% 1.46/1.65 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 1.46/1.65 inference(modus_ponens,[status(thm)],[2284, 2283])).
% 1.46/1.65 tff(2286,plain,
% 1.46/1.65 (hskp9),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2285, 101, 2278, 2277, 2049, 2221, 444, 827, 2279])).
% 1.46/1.65 tff(2287,plain,
% 1.46/1.65 (~c3_1(a16)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[839, 2286])).
% 1.46/1.65 tff(2288,plain,
% 1.46/1.65 (c1_1(a16)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[847, 2286])).
% 1.46/1.65 tff(2289,plain,
% 1.46/1.65 (c0_1(a16)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[855, 2286])).
% 1.46/1.65 tff(2290,plain,
% 1.46/1.65 (hskp10),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[862, 101, 2275, 2289, 2288, 2287, 813])).
% 1.46/1.65 tff(2291,plain,
% 1.46/1.65 (~c1_1(a18)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[868, 2290])).
% 1.46/1.65 tff(2292,plain,
% 1.46/1.65 (c3_1(a18)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[962, 2290])).
% 1.46/1.65 tff(2293,plain,
% 1.46/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a18) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a18) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a58))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2294,plain,
% 1.46/1.65 (((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a58) | c0_1(a58) | c3_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a18) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a58))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2295,plain,
% 1.46/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a18) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a58)))),
% 1.46/1.65 inference(monotonicity,[status(thm)],[2294])).
% 1.46/1.65 tff(2296,plain,
% 1.46/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a18) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a58))),
% 1.46/1.65 inference(transitivity,[status(thm)],[2295, 2293])).
% 1.46/1.65 tff(2297,plain,
% 1.46/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a58) | c0_1(a58) | c3_1(a58))),
% 1.46/1.65 inference(quant_inst,[status(thm)],[])).
% 1.46/1.65 tff(2298,plain,
% 1.46/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a18) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a58)),
% 1.46/1.65 inference(modus_ponens,[status(thm)],[2297, 2296])).
% 1.46/1.65 tff(2299,plain,
% 1.46/1.65 (~c2_1(a18)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2298, 101, 726, 2292, 37, 2291, 2269, 2270, 344, 2272, 2169])).
% 1.46/1.65 tff(2300,plain,
% 1.46/1.65 (~c0_1(a37)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[631, 2276])).
% 1.46/1.65 tff(2301,plain,
% 1.46/1.65 (hskp12),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[1079, 101, 2277, 2289, 2288, 2300, 2287, 918, 2279])).
% 1.46/1.65 tff(2302,plain,
% 1.46/1.65 (~c3_1(a20)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[930, 2301])).
% 1.46/1.65 tff(2303,plain,
% 1.46/1.65 (~c1_1(a20)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[936, 2301])).
% 1.46/1.65 tff(2304,plain,
% 1.46/1.65 (c2_1(a20)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[944, 2301])).
% 1.46/1.65 tff(2305,plain,
% 1.46/1.65 (hskp5),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[951, 101, 2304, 2303, 2302, 2271, 2270, 275, 2272])).
% 1.46/1.65 tff(2306,plain,
% 1.46/1.65 (~c2_1(a11)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[291, 2305])).
% 1.46/1.65 tff(2307,plain,
% 1.46/1.65 (~c1_1(a11)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[297, 2305])).
% 1.46/1.65 tff(2308,plain,
% 1.46/1.65 (~c0_1(a18)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[874, 2290])).
% 1.46/1.65 tff(2309,plain,
% 1.46/1.65 (c0_1(a11)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[305, 2305])).
% 1.46/1.65 tff(2310,plain,
% 1.46/1.65 ($false),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[969, 101, 2292, 2309, 2308, 2291, 2307, 2306, 697, 2299])).
% 1.46/1.65 tff(2311,plain,(c3_1(a58) | c2_1(a58) | c0_1(a58) | c3_1(a15) | hskp24 | hskp3 | c1_1(a58) | c2_1(a38) | c2_1(a2) | c3_1(a2) | c0_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.65 tff(2312,plain,
% 1.46/1.65 (c3_1(a58)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2311, 2273, 37, 444, 2274, 48, 26, 450, 13, 12, 14])).
% 1.46/1.65 tff(2313,plain,
% 1.46/1.65 (c3_1(a58)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2311, 726, 37, 444, 526, 48, 26, 450, 13, 12, 14])).
% 1.46/1.65 tff(2314,assumption,(c3_1(a58)), introduced(assumption)).
% 1.46/1.65 tff(2315,plain,
% 1.46/1.65 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2316,plain,
% 1.46/1.65 ((hskp21 | hskp20 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c2_1(a13)) <=> (hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2317,plain,
% 1.46/1.65 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13)))),
% 1.46/1.65 inference(monotonicity,[status(thm)],[2316])).
% 1.46/1.65 tff(2318,plain,
% 1.46/1.65 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c2_1(a13))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13))),
% 1.46/1.65 inference(transitivity,[status(thm)],[2317, 2315])).
% 1.46/1.65 tff(2319,plain,
% 1.46/1.65 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c2_1(a13))),
% 1.46/1.65 inference(quant_inst,[status(thm)],[])).
% 1.46/1.65 tff(2320,plain,
% 1.46/1.65 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13)),
% 1.46/1.65 inference(modus_ponens,[status(thm)],[2319, 2318])).
% 1.46/1.65 tff(2321,plain,
% 1.46/1.65 (hskp21 | hskp20 | c2_1(a13)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2320, 101, 225, 224, 654])).
% 1.46/1.65 tff(2322,plain,
% 1.46/1.65 (hskp20),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2321, 757, 334])).
% 1.46/1.65 tff(2323,plain,
% 1.46/1.65 (c3_1(a37)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[516, 2322])).
% 1.46/1.65 tff(2324,plain,
% 1.46/1.65 (c1_1(a37)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[524, 2322])).
% 1.46/1.65 tff(2325,plain,
% 1.46/1.65 (~c2_1(a37)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[529, 101, 526, 48, 2324, 2323, 10])).
% 1.46/1.65 tff(2326,plain,
% 1.46/1.65 (hskp9),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2285, 101, 2324, 2323, 2060, 1749, 444, 827, 2325])).
% 1.46/1.65 tff(2327,plain,
% 1.46/1.65 (~c3_1(a16)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[839, 2326])).
% 1.46/1.65 tff(2328,plain,
% 1.46/1.65 (c1_1(a16)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[847, 2326])).
% 1.46/1.65 tff(2329,plain,
% 1.46/1.65 (c0_1(a16)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[855, 2326])).
% 1.46/1.65 tff(2330,plain,
% 1.46/1.65 (hskp10),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[862, 101, 757, 2329, 2328, 2327, 813])).
% 1.46/1.65 tff(2331,plain,
% 1.46/1.65 (~c1_1(a18)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[868, 2330])).
% 1.46/1.65 tff(2332,plain,
% 1.46/1.65 (~c0_1(a18)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[874, 2330])).
% 1.46/1.65 tff(2333,plain,
% 1.46/1.65 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c2_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c2_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a58)))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2334,plain,
% 1.46/1.65 ((hskp2 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (hskp2 | c2_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a58)))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2335,plain,
% 1.46/1.65 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c2_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a58))))),
% 1.46/1.65 inference(monotonicity,[status(thm)],[2334])).
% 1.46/1.65 tff(2336,plain,
% 1.46/1.65 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c2_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a58)))),
% 1.46/1.65 inference(transitivity,[status(thm)],[2335, 2333])).
% 1.46/1.65 tff(2337,plain,
% 1.46/1.65 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c3_1(a58)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 1.46/1.65 inference(quant_inst,[status(thm)],[])).
% 1.46/1.65 tff(2338,plain,
% 1.46/1.65 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c2_1(a58) | c1_1(a58) | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a58))),
% 1.46/1.65 inference(modus_ponens,[status(thm)],[2337, 2336])).
% 1.46/1.65 tff(2339,plain,
% 1.46/1.65 (~c2_1(a18)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2338, 101, 1044, 726, 26, 2332, 2331, 1455, 2314])).
% 1.46/1.65 tff(2340,plain,
% 1.46/1.65 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a58) | c0_1(a58) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a58) | c0_1(a58) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a58)))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2341,plain,
% 1.46/1.65 ((hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58))) <=> (hskp12 | c2_1(a58) | c0_1(a58) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a58)))),
% 1.46/1.65 inference(rewrite,[status(thm)],[])).
% 1.46/1.65 tff(2342,plain,
% 1.46/1.65 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a58) | c0_1(a58) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a58))))),
% 1.46/1.65 inference(monotonicity,[status(thm)],[2341])).
% 1.46/1.65 tff(2343,plain,
% 1.46/1.65 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a58) | c0_1(a58) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a58)))),
% 1.46/1.65 inference(transitivity,[status(thm)],[2342, 2340])).
% 1.46/1.65 tff(2344,plain,
% 1.46/1.65 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a16) | (~c1_1(a16)) | (~c0_1(a16)) | c2_1(a58) | c0_1(a58) | (~c3_1(a58)))),
% 1.46/1.65 inference(quant_inst,[status(thm)],[])).
% 1.46/1.65 tff(2345,plain,
% 1.46/1.65 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a58) | c0_1(a58) | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a58))),
% 1.46/1.65 inference(modus_ponens,[status(thm)],[2344, 2343])).
% 1.46/1.65 tff(2346,plain,
% 1.46/1.65 (hskp12),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2345, 101, 726, 2329, 2328, 37, 2327, 918, 2314])).
% 1.46/1.65 tff(2347,plain,
% 1.46/1.65 (~c3_1(a20)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[930, 2346])).
% 1.46/1.65 tff(2348,plain,
% 1.46/1.65 (~c1_1(a20)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[936, 2346])).
% 1.46/1.65 tff(2349,plain,
% 1.46/1.65 (c2_1(a20)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[944, 2346])).
% 1.46/1.65 tff(2350,plain,
% 1.46/1.65 (hskp5),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[951, 101, 2349, 2348, 2347, 226, 224, 275, 334])).
% 1.46/1.65 tff(2351,plain,
% 1.46/1.65 (~c2_1(a11)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[291, 2350])).
% 1.46/1.65 tff(2352,plain,
% 1.46/1.65 (~c1_1(a11)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[297, 2350])).
% 1.46/1.65 tff(2353,plain,
% 1.46/1.65 (c0_1(a11)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[305, 2350])).
% 1.46/1.65 tff(2354,plain,
% 1.46/1.65 (c3_1(a18)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[962, 2330])).
% 1.46/1.65 tff(2355,plain,
% 1.46/1.65 ($false),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[1842, 101, 2354, 2353, 37, 26, 2332, 2352, 2351, 697, 2314, 2339])).
% 1.46/1.65 tff(2356,plain,(hskp21 | c0_1(a58) | c1_1(a58) | (~c3_1(a58)) | hskp2 | c2_1(a58) | c0_1(a13) | c3_1(a13) | c2_1(a13) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | hskp24 | hskp3 | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.65 tff(2357,plain,
% 1.46/1.65 (hskp21),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[2356, 2313, 26, 37, 1044, 726, 2271, 2270, 2272, 2049, 2221, 444, 526, 48, 2269])).
% 1.46/1.65 tff(2358,plain,
% 1.46/1.65 (c0_1(a38)),
% 1.46/1.65 inference(unit_resolution,[status(thm)],[595, 2357])).
% 1.46/1.65 tff(2359,plain,
% 1.46/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a58) | c1_1(a58) | c2_1(a38) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a58) | c1_1(a58) | c2_1(a38) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2360,plain,
% 1.46/1.66 (((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a38) | (~c3_1(a38)) | (~c0_1(a38)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | c1_1(a58) | c2_1(a38) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2361,plain,
% 1.46/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a38) | (~c3_1(a38)) | (~c0_1(a38)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a58) | c1_1(a58) | c2_1(a38) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58))))),
% 1.46/1.66 inference(monotonicity,[status(thm)],[2360])).
% 1.46/1.66 tff(2362,plain,
% 1.46/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a38) | (~c3_1(a38)) | (~c0_1(a38)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a58) | c1_1(a58) | c2_1(a38) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58)))),
% 1.46/1.66 inference(transitivity,[status(thm)],[2361, 2359])).
% 1.46/1.66 tff(2363,plain,
% 1.46/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c2_1(a38) | (~c3_1(a38)) | (~c0_1(a38)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))),
% 1.46/1.66 inference(quant_inst,[status(thm)],[])).
% 1.46/1.66 tff(2364,plain,
% 1.46/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a58) | c1_1(a58) | c2_1(a38) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58))),
% 1.46/1.66 inference(modus_ponens,[status(thm)],[2363, 2362])).
% 1.46/1.66 tff(2365,plain,
% 1.46/1.66 ((~c3_1(a38)) | (~c0_1(a38)) | (~c3_1(a58))),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2364, 101, 726, 26, 450, 2049, 2221, 444, 264])).
% 1.46/1.66 tff(2366,plain,
% 1.46/1.66 (~c3_1(a38)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2365, 2358, 2313])).
% 1.46/1.66 tff(2367,plain,
% 1.46/1.66 (c1_1(a38)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[603, 2357])).
% 1.46/1.66 tff(2368,plain,
% 1.46/1.66 (hskp27),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[624, 2357, 450, 13, 12, 14])).
% 1.46/1.66 tff(2369,plain,
% 1.46/1.66 (c3_1(a12)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[560, 2368])).
% 1.46/1.66 tff(2370,plain,
% 1.46/1.66 (c1_1(a12)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[568, 2368])).
% 1.46/1.66 tff(2371,plain,
% 1.46/1.66 (c0_1(a12)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[1114, 2368])).
% 1.46/1.66 tff(2372,plain,
% 1.46/1.66 ($false),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2198, 101, 2089, 2371, 2370, 2369, 2358, 2367, 2187, 2366])).
% 1.46/1.66 tff(2373,plain,(c2_1(a58) | c1_1(a58) | c2_1(a38) | c3_1(a15) | c2_1(a2) | c3_1(a2) | c0_1(a2) | c0_1(a58) | hskp2 | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.46/1.66 tff(2374,plain,
% 1.46/1.66 (hskp2),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2373, 2274, 450, 444, 13, 12, 14, 37, 2273, 26, 48])).
% 1.46/1.66 tff(2375,plain,
% 1.46/1.66 (~c2_1(a3)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[197, 2374])).
% 1.46/1.66 tff(2376,plain,
% 1.46/1.66 (c3_1(a3)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[205, 2374])).
% 1.46/1.66 tff(2377,plain,
% 1.46/1.66 (c1_1(a3)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[213, 2374])).
% 1.46/1.66 tff(2378,plain,
% 1.46/1.66 (hskp9),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2228, 101, 2377, 2376, 2049, 2221, 444, 2375, 827])).
% 1.46/1.66 tff(2379,plain,
% 1.46/1.66 (~c3_1(a16)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[839, 2378])).
% 1.46/1.66 tff(2380,plain,
% 1.46/1.66 (c1_1(a16)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[847, 2378])).
% 1.46/1.66 tff(2381,plain,
% 1.46/1.66 (c0_1(a16)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[855, 2378])).
% 1.46/1.66 tff(2382,plain,
% 1.46/1.66 (hskp12),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2345, 101, 2273, 2381, 2380, 37, 2379, 918, 2312])).
% 1.46/1.66 tff(2383,plain,
% 1.46/1.66 (~c3_1(a20)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[930, 2382])).
% 1.46/1.66 tff(2384,plain,
% 1.46/1.66 (~c1_1(a20)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[936, 2382])).
% 1.46/1.66 tff(2385,plain,
% 1.46/1.66 (c2_1(a20)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[944, 2382])).
% 1.46/1.66 tff(2386,plain,
% 1.46/1.66 (hskp5),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[951, 101, 2385, 2384, 2383, 2271, 2270, 275, 2272])).
% 1.46/1.66 tff(2387,plain,
% 1.46/1.66 (~c2_1(a11)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[291, 2386])).
% 1.46/1.66 tff(2388,plain,
% 1.46/1.66 (~c1_1(a11)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[297, 2386])).
% 1.46/1.66 tff(2389,plain,
% 1.46/1.66 (c0_1(a11)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[305, 2386])).
% 1.46/1.66 tff(2390,plain,
% 1.46/1.66 ($false),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[1742, 101, 2273, 2389, 37, 26, 2388, 2387, 697, 2312])).
% 1.46/1.66 tff(2391,plain,(c0_1(a2) | c0_1(a58) | c1_1(a58) | c3_1(a15) | c2_1(a38) | c2_1(a2) | c3_1(a2) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.46/1.66 tff(2392,plain,
% 1.46/1.66 ($false),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2391, 2250, 2249, 26, 444, 450, 37, 2248, 48])).
% 1.46/1.66 tff(2393,plain,(c3_1(a15) | c1_1(a58) | c2_1(a38) | c0_1(a58) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.46/1.66 tff(2394,plain,
% 1.46/1.66 (c2_1(a38)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2393, 444, 26, 37, 48])).
% 1.46/1.66 tff(2395,plain,
% 1.46/1.66 (((~hskp21) | (~c2_1(a38))) <=> ((~hskp21) | (~c2_1(a38)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2396,plain,
% 1.46/1.66 (((~c2_1(a38)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a38)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2397,axiom,((~c2_1(a38)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.46/1.66 tff(2398,plain,
% 1.46/1.66 ((~hskp21) | (~c2_1(a38))),
% 1.46/1.66 inference(modus_ponens,[status(thm)],[2397, 2396])).
% 1.46/1.66 tff(2399,plain,
% 1.46/1.66 ((~hskp21) | (~c2_1(a38))),
% 1.46/1.66 inference(modus_ponens,[status(thm)],[2398, 2395])).
% 1.46/1.66 tff(2400,plain,
% 1.46/1.66 (~hskp21),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2399, 2394])).
% 1.46/1.66 tff(2401,plain,
% 1.46/1.66 (hskp13),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[768, 2400, 449])).
% 1.46/1.66 tff(2402,plain,
% 1.46/1.66 (c0_1(a21)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[790, 2401])).
% 1.46/1.66 tff(2403,plain,
% 1.46/1.66 (~c3_1(a21)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[774, 2401])).
% 1.46/1.66 tff(2404,plain,
% 1.46/1.66 (c2_1(a21)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[782, 2401])).
% 1.46/1.66 tff(2405,assumption,(c1_1(a13)), introduced(assumption)).
% 1.46/1.66 tff(2406,plain,
% 1.46/1.66 (~hskp6),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[183, 2405])).
% 1.46/1.66 tff(2407,plain,
% 1.46/1.66 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a13) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a13) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2408,plain,
% 1.46/1.66 ((hskp6 | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a13)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13))) <=> (hskp6 | c0_1(a13) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2409,plain,
% 1.46/1.66 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a13)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a13) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13))))),
% 1.46/1.66 inference(monotonicity,[status(thm)],[2408])).
% 1.46/1.66 tff(2410,plain,
% 1.46/1.66 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a13)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a13) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 1.46/1.66 inference(transitivity,[status(thm)],[2409, 2407])).
% 1.46/1.66 tff(2411,plain,
% 1.46/1.66 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a13) | (~c2_1(a13)) | (~c1_1(a13)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)))),
% 1.46/1.66 inference(quant_inst,[status(thm)],[])).
% 1.46/1.66 tff(2412,plain,
% 1.46/1.66 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a13) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13))),
% 1.46/1.66 inference(modus_ponens,[status(thm)],[2411, 2410])).
% 1.46/1.66 tff(2413,plain,
% 1.46/1.66 (hskp6 | c0_1(a13) | (~c1_1(a13)) | (~c2_1(a13))),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2412, 101, 224, 162])).
% 1.46/1.66 tff(2414,plain,
% 1.46/1.66 (~c2_1(a13)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2413, 2406, 226, 2405])).
% 1.46/1.66 tff(2415,assumption,(~c3_1(a21)), introduced(assumption)).
% 1.46/1.66 tff(2416,assumption,(c2_1(a21)), introduced(assumption)).
% 1.46/1.66 tff(2417,assumption,(c0_1(a21)), introduced(assumption)).
% 1.46/1.66 tff(2418,plain,
% 1.46/1.66 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2419,plain,
% 1.46/1.66 ((hskp6 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21))) <=> (hskp6 | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2420,plain,
% 1.46/1.66 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21))))),
% 1.46/1.66 inference(monotonicity,[status(thm)],[2419])).
% 1.46/1.66 tff(2421,plain,
% 1.46/1.66 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.46/1.66 inference(transitivity,[status(thm)],[2420, 2418])).
% 1.46/1.66 tff(2422,plain,
% 1.46/1.66 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))),
% 1.46/1.66 inference(quant_inst,[status(thm)],[])).
% 1.46/1.66 tff(2423,plain,
% 1.46/1.66 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a21) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21))),
% 1.46/1.66 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 1.46/1.66 tff(2424,plain,
% 1.46/1.66 (hskp6 | (~c1_1(a21))),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2423, 101, 2417, 2416, 2415, 141])).
% 1.46/1.66 tff(2425,plain,
% 1.46/1.66 (~c1_1(a21)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2424, 2406])).
% 1.46/1.66 tff(2426,plain,
% 1.46/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2427,plain,
% 1.46/1.66 (((~ndr1_0) | c3_1(a13) | c2_1(a13) | (~c1_1(a13)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2428,plain,
% 1.46/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a13) | c2_1(a13) | (~c1_1(a13)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21))))),
% 1.46/1.66 inference(monotonicity,[status(thm)],[2427])).
% 1.46/1.66 tff(2429,plain,
% 1.46/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a13) | c2_1(a13) | (~c1_1(a13)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))),
% 1.46/1.66 inference(transitivity,[status(thm)],[2428, 2426])).
% 1.46/1.66 tff(2430,plain,
% 1.46/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a13) | c2_1(a13) | (~c1_1(a13)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 1.46/1.66 inference(quant_inst,[status(thm)],[])).
% 1.46/1.66 tff(2431,plain,
% 1.46/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a21) | (~c1_1(a13)) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21))),
% 1.46/1.66 inference(modus_ponens,[status(thm)],[2430, 2429])).
% 1.46/1.66 tff(2432,plain,
% 1.46/1.66 ((~c1_1(a13)) | c2_1(a13) | c1_1(a21)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2431, 101, 726, 2416, 37, 26, 2415, 224, 362])).
% 1.46/1.66 tff(2433,plain,
% 1.46/1.66 ($false),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2432, 2425, 2414, 2405])).
% 1.46/1.66 tff(2434,plain,((~c1_1(a13)) | c2_1(a58) | (~c2_1(a21)) | c0_1(a58) | c1_1(a58) | c3_1(a21) | c3_1(a13) | (~c0_1(a21)) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.66 tff(2435,plain,
% 1.46/1.66 (~c1_1(a13)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2434, 2404, 448, 37, 26, 2403, 224, 2402, 226])).
% 1.46/1.66 tff(2436,plain,
% 1.46/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2437,plain,
% 1.46/1.66 (((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2438,plain,
% 1.46/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13))))),
% 1.46/1.66 inference(monotonicity,[status(thm)],[2437])).
% 1.46/1.66 tff(2439,plain,
% 1.46/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 1.46/1.66 inference(transitivity,[status(thm)],[2438, 2436])).
% 1.46/1.66 tff(2440,plain,
% 1.46/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 1.46/1.66 inference(quant_inst,[status(thm)],[])).
% 1.46/1.66 tff(2441,plain,
% 1.46/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13))),
% 1.46/1.66 inference(modus_ponens,[status(thm)],[2440, 2439])).
% 1.46/1.66 tff(2442,plain,
% 1.46/1.66 ((~c1_1(a15)) | c2_1(a15) | c1_1(a13) | (~c2_1(a13))),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2441, 101, 448, 37, 26, 444, 224, 362])).
% 1.46/1.66 tff(2443,plain,
% 1.46/1.66 (~c2_1(a13)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2442, 2060, 225, 698])).
% 1.46/1.66 tff(2444,plain,
% 1.46/1.66 (hskp21 | hskp20 | c1_1(a13) | c2_1(a13)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2320, 101, 224, 654])).
% 1.46/1.66 tff(2445,plain,
% 1.46/1.66 (hskp20),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2444, 2443, 2400, 225])).
% 1.46/1.66 tff(2446,plain,
% 1.46/1.66 (c3_1(a37)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[516, 2445])).
% 1.46/1.66 tff(2447,plain,
% 1.46/1.66 (c1_1(a37)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[524, 2445])).
% 1.46/1.66 tff(2448,plain,
% 1.46/1.66 (~c2_1(a37)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[529, 101, 449, 48, 2447, 2446, 10])).
% 1.46/1.66 tff(2449,plain,
% 1.46/1.66 ((~c1_1(a15)) | c2_1(a15) | c1_1(a21)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2119, 101, 448, 2404, 37, 26, 2403, 444, 362])).
% 1.46/1.66 tff(2450,plain,
% 1.46/1.66 (c1_1(a21)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2449, 2060, 698])).
% 1.46/1.66 tff(2451,plain,
% 1.46/1.66 (~c0_1(a37)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[631, 2445])).
% 1.46/1.66 tff(2452,plain,
% 1.46/1.66 ($false),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2216, 101, 2446, 2404, 2451, 2403, 2060, 698, 444, 680, 2450, 2448])).
% 1.46/1.66 tff(2453,plain,((~c1_1(a15)) | c2_1(a15) | c3_1(a15) | hskp3 | c1_1(a13) | c3_1(a13) | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.66 tff(2454,plain,
% 1.46/1.66 (~c1_1(a15)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2453, 698, 444, 48, 225, 224, 37, 26])).
% 1.46/1.66 tff(2455,plain,
% 1.46/1.66 (hskp20 | c1_1(a15) | c2_1(a15)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[747, 101, 2400, 444, 654])).
% 1.46/1.66 tff(2456,plain,
% 1.46/1.66 (hskp20),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2455, 451, 698])).
% 1.46/1.66 tff(2457,assumption,(hskp0), introduced(assumption)).
% 1.46/1.66 tff(2458,plain,
% 1.46/1.66 (~c3_1(a1)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[114, 2457])).
% 1.46/1.66 tff(2459,plain,
% 1.46/1.66 (c1_1(a1)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[130, 2457])).
% 1.46/1.66 tff(2460,plain,
% 1.46/1.66 (c2_1(a1)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[122, 2457])).
% 1.46/1.66 tff(2461,plain,
% 1.46/1.66 ($false),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[1095, 2460, 2459, 444, 757, 12, 13, 698, 14, 451, 2458, 526, 48])).
% 1.46/1.66 tff(2462,plain,((~hskp0) | c3_1(a15) | hskp21 | c3_1(a2) | c2_1(a2) | c2_1(a15) | c0_1(a2) | c1_1(a15) | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.46/1.66 tff(2463,plain,
% 1.46/1.66 (~hskp0),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2462, 451, 2400, 12, 13, 698, 14, 444, 449, 48])).
% 1.46/1.66 tff(2464,plain,
% 1.46/1.66 (~hskp28),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[496, 2463, 48, 37, 26])).
% 1.46/1.66 tff(2465,plain,
% 1.46/1.66 ($false),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[643, 2464, 2463, 12, 13, 14, 2456])).
% 1.46/1.66 tff(2466,plain,(c1_1(a15) | c3_1(a2) | c2_1(a2) | c0_1(a2) | hskp3 | c0_1(a58) | c1_1(a58) | c2_1(a15) | c3_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.66 tff(2467,plain,
% 1.46/1.66 (c0_1(a2)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2466, 2454, 13, 12, 48, 37, 26, 698, 444])).
% 1.46/1.66 tff(2468,plain,
% 1.46/1.66 (~hskp1),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[253, 2467])).
% 1.46/1.66 tff(2469,plain,
% 1.46/1.66 (hskp0),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[548, 2468, 48, 37, 26])).
% 1.46/1.66 tff(2470,plain,
% 1.46/1.66 (c1_1(a1)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[130, 2469])).
% 1.46/1.66 tff(2471,plain,
% 1.46/1.66 (c2_1(a1)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[122, 2469])).
% 1.46/1.66 tff(2472,plain,
% 1.46/1.66 (~c3_1(a1)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[114, 2469])).
% 1.46/1.66 tff(2473,plain,
% 1.46/1.66 ($false),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[971, 2472, 2471, 444, 2400, 698, 2454, 48, 2468, 2470, 449])).
% 1.46/1.66 tff(2474,plain,(c2_1(a15) | c3_1(a15) | hskp3 | c0_1(a58) | c1_1(a58) | c2_1(a2) | c3_1(a2) | c1_1(a13) | c3_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.66 tff(2475,plain,
% 1.46/1.66 (c2_1(a15)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2474, 225, 48, 37, 26, 13, 12, 444, 224])).
% 1.46/1.66 tff(2476,plain,
% 1.46/1.66 ($false),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[1844, 2460, 2459, 26, 37, 444, 12, 13, 1749, 451, 2458])).
% 1.46/1.66 tff(2477,plain,((~hskp0) | c1_1(a58) | c0_1(a58) | c3_1(a15) | c3_1(a2) | c2_1(a2) | (~c2_1(a15)) | c1_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.66 tff(2478,plain,
% 1.46/1.66 (~hskp0),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2477, 451, 37, 444, 12, 13, 1749, 26])).
% 1.46/1.66 tff(2479,plain,
% 1.46/1.66 (~hskp28),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[496, 2478, 48, 37, 26])).
% 1.46/1.66 tff(2480,plain,
% 1.46/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2481,plain,
% 1.46/1.66 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2482,plain,
% 1.46/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2))))),
% 1.46/1.66 inference(monotonicity,[status(thm)],[2481])).
% 1.46/1.66 tff(2483,plain,
% 1.46/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)))),
% 1.46/1.66 inference(transitivity,[status(thm)],[2482, 2480])).
% 1.46/1.66 tff(2484,plain,
% 1.46/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a15) | c1_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 1.46/1.66 inference(quant_inst,[status(thm)],[])).
% 1.46/1.66 tff(2485,plain,
% 1.46/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a15) | (~c2_1(a15)) | c3_1(a15) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2))),
% 1.46/1.66 inference(modus_ponens,[status(thm)],[2484, 2483])).
% 1.46/1.66 tff(2486,plain,
% 1.46/1.66 (c1_1(a15) | (~c2_1(a15)) | c2_1(a2) | (~c1_1(a2))),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2485, 101, 448, 37, 26, 444, 12, 362])).
% 1.46/1.66 tff(2487,plain,
% 1.46/1.66 (~c1_1(a2)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2486, 451, 13, 1749])).
% 1.46/1.66 tff(2488,plain,
% 1.46/1.66 (hskp20),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[661, 2487, 2400, 13])).
% 1.46/1.66 tff(2489,plain,
% 1.46/1.66 (c3_1(a37)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[516, 2488])).
% 1.46/1.66 tff(2490,plain,
% 1.46/1.66 (c1_1(a37)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[524, 2488])).
% 1.46/1.66 tff(2491,plain,
% 1.46/1.66 (~c2_1(a37)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[529, 101, 449, 48, 2490, 2489, 10])).
% 1.46/1.66 tff(2492,plain,
% 1.46/1.66 (hskp28 | hskp0),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[543, 101, 2490, 2489, 540, 2491])).
% 1.46/1.66 tff(2493,plain,
% 1.46/1.66 ($false),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2492, 2479, 2478])).
% 1.46/1.66 tff(2494,plain,(c1_1(a15) | hskp3 | c0_1(a58) | c1_1(a58) | c3_1(a15) | c3_1(a2) | c2_1(a2) | (~c2_1(a15))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.66 tff(2495,plain,
% 1.46/1.66 (c1_1(a15)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2494, 2475, 37, 26, 444, 12, 13, 48])).
% 1.46/1.66 tff(2496,plain,
% 1.46/1.66 (hskp1),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2246, 2495, 444, 2475, 48, 37, 26])).
% 1.46/1.66 tff(2497,plain,
% 1.46/1.66 (~c0_1(a2)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[253, 2496])).
% 1.46/1.66 tff(2498,plain,
% 1.46/1.66 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2499,plain,
% 1.46/1.66 ((hskp3 | hskp0 | (~ndr1_0) | c1_1(a13) | c0_1(a13) | (~c2_1(a13))) <=> (hskp3 | hskp0 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 1.46/1.66 inference(rewrite,[status(thm)],[])).
% 1.46/1.66 tff(2500,plain,
% 1.46/1.66 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a13) | c0_1(a13) | (~c2_1(a13)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13))))),
% 1.46/1.66 inference(monotonicity,[status(thm)],[2499])).
% 1.46/1.66 tff(2501,plain,
% 1.46/1.66 (((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a13) | c0_1(a13) | (~c2_1(a13)))) <=> ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 1.46/1.66 inference(transitivity,[status(thm)],[2500, 2498])).
% 1.46/1.66 tff(2502,plain,
% 1.46/1.66 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp0 | (~ndr1_0) | c1_1(a13) | c0_1(a13) | (~c2_1(a13)))),
% 1.46/1.66 inference(quant_inst,[status(thm)],[])).
% 1.46/1.66 tff(2503,plain,
% 1.46/1.66 ((~![U: $i] : (hskp3 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp0 | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13))),
% 1.46/1.66 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 1.46/1.66 tff(2504,plain,
% 1.46/1.66 (hskp0 | c1_1(a13) | (~c2_1(a13))),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2503, 101, 48, 226, 69])).
% 1.46/1.66 tff(2505,plain,
% 1.46/1.66 (~c2_1(a13)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2504, 11, 225])).
% 1.46/1.66 tff(2506,plain,
% 1.46/1.66 ($false),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[643, 497, 11, 12, 13, 14, 626])).
% 1.46/1.66 tff(2507,plain,(hskp0 | c3_1(a2) | c2_1(a2) | c0_1(a2) | (~hskp20) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.66 tff(2508,plain,
% 1.46/1.66 (~hskp20),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2507, 11, 13, 12, 14, 48, 37, 26])).
% 1.46/1.66 tff(2509,plain,
% 1.46/1.66 ($false),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2444, 2508, 2505, 757, 225])).
% 1.46/1.66 tff(2510,plain,(hskp0 | hskp21 | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | c0_1(a2) | hskp3 | c0_1(a58) | c1_1(a58) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.66 tff(2511,plain,
% 1.46/1.66 (hskp0),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2510, 225, 2400, 224, 13, 12, 2497, 48, 37, 26, 226])).
% 1.46/1.66 tff(2512,plain,
% 1.46/1.66 (~c3_1(a1)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[114, 2511])).
% 1.46/1.66 tff(2513,plain,
% 1.46/1.66 (c2_1(a1)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[122, 2511])).
% 1.46/1.66 tff(2514,plain,
% 1.46/1.66 (c1_1(a1)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[130, 2511])).
% 1.46/1.66 tff(2515,plain,
% 1.46/1.66 (~c2_1(a13)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[332, 2513, 2497, 2512, 2514, 13, 12])).
% 1.46/1.66 tff(2516,plain,
% 1.46/1.66 (hskp20),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2444, 2515, 2400, 225])).
% 1.46/1.66 tff(2517,plain,
% 1.46/1.66 (c3_1(a37)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[516, 2516])).
% 1.46/1.66 tff(2518,plain,
% 1.46/1.66 (c1_1(a37)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[524, 2516])).
% 1.46/1.66 tff(2519,plain,
% 1.46/1.66 (~c2_1(a37)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[529, 101, 449, 48, 2518, 2517, 10])).
% 1.46/1.66 tff(2520,plain,
% 1.46/1.66 (hskp9),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[2285, 101, 2518, 2517, 2495, 2475, 444, 827, 2519])).
% 1.46/1.66 tff(2521,plain,
% 1.46/1.66 (~c3_1(a16)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[839, 2520])).
% 1.46/1.66 tff(2522,plain,
% 1.46/1.66 (~c0_1(a37)),
% 1.46/1.66 inference(unit_resolution,[status(thm)],[631, 2516])).
% 1.46/1.67 tff(2523,plain,
% 1.46/1.67 (c1_1(a16)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[847, 2520])).
% 1.46/1.67 tff(2524,plain,
% 1.46/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2525,plain,
% 1.46/1.67 (((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37))) <=> (c0_1(a37) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2526,plain,
% 1.46/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37))))),
% 1.46/1.67 inference(monotonicity,[status(thm)],[2525])).
% 1.46/1.67 tff(2527,plain,
% 1.46/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))),
% 1.46/1.67 inference(transitivity,[status(thm)],[2526, 2524])).
% 1.46/1.67 tff(2528,plain,
% 1.46/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a15) | (~c2_1(a15)) | (~c1_1(a15)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))),
% 1.46/1.67 inference(quant_inst,[status(thm)],[])).
% 1.46/1.67 tff(2529,plain,
% 1.46/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37))),
% 1.46/1.67 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 1.46/1.67 tff(2530,plain,
% 1.46/1.67 (c2_1(a16)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2529, 101, 2517, 2523, 2522, 2521, 2495, 2475, 444, 680, 2519])).
% 1.46/1.67 tff(2531,plain,
% 1.46/1.67 (c0_1(a16)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[855, 2520])).
% 1.46/1.67 tff(2532,plain,
% 1.46/1.67 (hskp12),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[1079, 101, 2517, 2531, 2523, 2522, 2521, 918, 2519])).
% 1.46/1.67 tff(2533,plain,
% 1.46/1.67 (~c3_1(a20)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[930, 2532])).
% 1.46/1.67 tff(2534,plain,
% 1.46/1.67 (c2_1(a20)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[944, 2532])).
% 1.46/1.67 tff(2535,plain,
% 1.46/1.67 (~c1_1(a20)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[936, 2532])).
% 1.46/1.67 tff(2536,plain,
% 1.46/1.67 (~c2_1(a13)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[332, 14, 143, 142, 144, 13, 12])).
% 1.46/1.67 tff(2537,assumption,(~c3_1(a20)), introduced(assumption)).
% 1.46/1.67 tff(2538,assumption,(~c1_1(a20)), introduced(assumption)).
% 1.46/1.67 tff(2539,assumption,(c2_1(a16)), introduced(assumption)).
% 1.46/1.67 tff(2540,assumption,(~c3_1(a16)), introduced(assumption)).
% 1.46/1.67 tff(2541,assumption,(c1_1(a16)), introduced(assumption)).
% 1.46/1.67 tff(2542,assumption,(c2_1(a20)), introduced(assumption)).
% 1.46/1.67 tff(2543,plain,
% 1.46/1.67 (c0_1(a2) | (~c0_1(a20))),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[1444, 101, 2542, 2541, 2538, 2540, 13, 12, 1264, 2539])).
% 1.46/1.67 tff(2544,plain,
% 1.46/1.67 (~c0_1(a20)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2543, 14])).
% 1.46/1.67 tff(2545,plain,
% 1.46/1.67 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | c3_1(a20) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c3_1(a20) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2546,plain,
% 1.46/1.67 ((hskp18 | hskp3 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c2_1(a20))) <=> (hskp18 | hskp3 | c3_1(a20) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2547,plain,
% 1.46/1.67 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | c3_1(a20) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20))))),
% 1.46/1.67 inference(monotonicity,[status(thm)],[2546])).
% 1.46/1.67 tff(2548,plain,
% 1.46/1.67 (((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c3_1(a20) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20)))),
% 1.46/1.67 inference(transitivity,[status(thm)],[2547, 2545])).
% 1.46/1.67 tff(2549,plain,
% 1.46/1.67 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp18 | hskp3 | (~ndr1_0) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)))),
% 1.46/1.67 inference(quant_inst,[status(thm)],[])).
% 1.46/1.67 tff(2550,plain,
% 1.46/1.67 ((~![U: $i] : (hskp18 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp18 | hskp3 | c3_1(a20) | (~ndr1_0) | c0_1(a20) | (~c2_1(a20))),
% 1.46/1.67 inference(modus_ponens,[status(thm)],[2549, 2548])).
% 1.46/1.67 tff(2551,plain,
% 1.46/1.67 (hskp18 | c0_1(a20)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2550, 101, 48, 2542, 2537, 372])).
% 1.46/1.67 tff(2552,plain,
% 1.46/1.67 (hskp18),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2551, 2544])).
% 1.46/1.67 tff(2553,plain,
% 1.46/1.67 (~c3_1(a31)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[385, 2552])).
% 1.46/1.67 tff(2554,plain,
% 1.46/1.67 (c1_1(a31)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[393, 2552])).
% 1.46/1.67 tff(2555,plain,
% 1.46/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a31) | c1_1(a20) | c3_1(a20) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)) | (~c1_1(a31)) | c2_1(a31))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a31) | c1_1(a20) | c3_1(a20) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)) | (~c1_1(a31)) | c2_1(a31))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2556,plain,
% 1.46/1.67 (((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c0_1(a13)) <=> (c3_1(a31) | c1_1(a20) | c3_1(a20) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)) | (~c1_1(a31)) | c2_1(a31))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2557,plain,
% 1.46/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a31) | c1_1(a20) | c3_1(a20) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)) | (~c1_1(a31)) | c2_1(a31)))),
% 1.46/1.67 inference(monotonicity,[status(thm)],[2556])).
% 1.46/1.67 tff(2558,plain,
% 1.46/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a31) | c1_1(a20) | c3_1(a20) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)) | (~c1_1(a31)) | c2_1(a31))),
% 1.46/1.67 inference(transitivity,[status(thm)],[2557, 2555])).
% 1.46/1.67 tff(2559,plain,
% 1.46/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c0_1(a13))),
% 1.46/1.67 inference(quant_inst,[status(thm)],[])).
% 1.46/1.67 tff(2560,plain,
% 1.46/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a31) | c1_1(a20) | c3_1(a20) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c2_1(a20)) | (~c1_1(a31)) | c2_1(a31)),
% 1.46/1.67 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 1.46/1.67 tff(2561,plain,
% 1.46/1.67 (c2_1(a31)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2560, 101, 2554, 2542, 2553, 2538, 2537, 324, 278, 362, 2536])).
% 1.46/1.67 tff(2562,plain,
% 1.46/1.67 (hskp5 | c0_1(a2) | c2_1(a2)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[1089, 101, 2542, 2538, 2537, 12, 275])).
% 1.46/1.67 tff(2563,plain,
% 1.46/1.67 (hskp5),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2562, 14, 13])).
% 1.46/1.67 tff(2564,plain,
% 1.46/1.67 (~c2_1(a11)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[291, 2563])).
% 1.46/1.67 tff(2565,plain,
% 1.46/1.67 (~c1_1(a11)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[297, 2563])).
% 1.46/1.67 tff(2566,plain,
% 1.46/1.67 (c0_1(a11)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[305, 2563])).
% 1.46/1.67 tff(2567,plain,
% 1.46/1.67 (~c3_1(a11)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[417, 101, 2554, 2566, 2553, 2565, 2564, 264, 2561])).
% 1.46/1.67 tff(2568,plain,
% 1.46/1.67 (~c2_1(a58)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[432, 2536, 324, 277, 26, 278, 48, 37, 14, 13, 12])).
% 1.46/1.67 tff(2569,plain,
% 1.46/1.67 (~c3_1(a58)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[1742, 101, 2568, 2566, 37, 26, 2565, 2564, 697])).
% 1.46/1.67 tff(2570,plain,
% 1.46/1.67 (~c0_1(a31)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[423, 2552])).
% 1.46/1.67 tff(2571,plain,
% 1.46/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | c1_1(a58) | c0_1(a31) | c3_1(a31) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | c1_1(a58) | c0_1(a31) | c3_1(a31) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)) | c3_1(a58))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2572,plain,
% 1.46/1.67 (((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a58) | c1_1(a58) | c3_1(a58)) <=> (c2_1(a58) | c1_1(a58) | c0_1(a31) | c3_1(a31) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)) | c3_1(a58))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2573,plain,
% 1.46/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | c1_1(a58) | c0_1(a31) | c3_1(a31) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)) | c3_1(a58)))),
% 1.46/1.67 inference(monotonicity,[status(thm)],[2572])).
% 1.46/1.67 tff(2574,plain,
% 1.46/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | c1_1(a58) | c0_1(a31) | c3_1(a31) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)) | c3_1(a58))),
% 1.46/1.67 inference(transitivity,[status(thm)],[2573, 2571])).
% 1.46/1.67 tff(2575,plain,
% 1.46/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a11) | c1_1(a11) | (~c0_1(a11)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a58) | c1_1(a58) | c3_1(a58))),
% 1.46/1.67 inference(quant_inst,[status(thm)],[])).
% 1.46/1.67 tff(2576,plain,
% 1.46/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | c1_1(a58) | c0_1(a31) | c3_1(a31) | c1_1(a11) | (~ndr1_0) | c3_1(a11) | (~c0_1(a11)) | (~c2_1(a31)) | c3_1(a58)),
% 1.46/1.67 inference(modus_ponens,[status(thm)],[2575, 2574])).
% 1.46/1.67 tff(2577,plain,
% 1.46/1.67 ($false),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2576, 101, 2568, 2566, 26, 2570, 2553, 2565, 323, 2569, 2567, 2561])).
% 1.46/1.67 tff(2578,plain,(c0_1(a2) | c1_1(a58) | (~c2_1(a20)) | c1_1(a20) | c3_1(a20) | c0_1(a58) | hskp3 | c2_1(a2) | c3_1(a2) | (~c1_1(a16)) | c3_1(a16) | (~c2_1(a16)) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.67 tff(2579,plain,
% 1.46/1.67 ($false),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2578, 2535, 2534, 2497, 2514, 2533, 37, 48, 13, 12, 2523, 2521, 2530, 2513, 2512, 26])).
% 1.46/1.67 tff(2580,plain,(c1_1(a13) | c0_1(a58) | hskp3 | c2_1(a2) | c3_1(a2) | c1_1(a58) | c3_1(a15) | c3_1(a13) | c0_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.67 tff(2581,plain,
% 1.46/1.67 (c2_1(a2)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2580, 2435, 48, 37, 12, 26, 444, 224, 226])).
% 1.46/1.67 tff(2582,plain,
% 1.46/1.67 (~hskp1),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[247, 2581])).
% 1.46/1.67 tff(2583,plain,
% 1.46/1.67 (hskp2 | hskp1 | c0_1(a13) | c1_1(a13)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[232, 101, 224, 47])).
% 1.46/1.67 tff(2584,plain,
% 1.46/1.67 (hskp2),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2583, 2582, 226, 2435])).
% 1.46/1.67 tff(2585,plain,
% 1.46/1.67 (~c2_1(a3)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[197, 2584])).
% 1.46/1.67 tff(2586,plain,
% 1.46/1.67 (c3_1(a3)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[205, 2584])).
% 1.46/1.67 tff(2587,plain,
% 1.46/1.67 (c1_1(a3)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[213, 2584])).
% 1.46/1.67 tff(2588,plain,
% 1.46/1.67 (~c2_1(a13)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[1253, 101, 2582, 2587, 2586, 226, 2435, 2585, 58])).
% 1.46/1.67 tff(2589,plain,
% 1.46/1.67 (hskp20),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2444, 2588, 2400, 2435])).
% 1.46/1.67 tff(2590,plain,
% 1.46/1.67 (c3_1(a37)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[516, 2589])).
% 1.46/1.67 tff(2591,plain,
% 1.46/1.67 (c1_1(a37)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[524, 2589])).
% 1.46/1.67 tff(2592,plain,
% 1.46/1.67 (~c2_1(a37)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[529, 101, 449, 48, 2591, 2590, 10])).
% 1.46/1.67 tff(2593,plain,
% 1.46/1.67 (hskp0),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[548, 2582, 48, 37, 26])).
% 1.46/1.67 tff(2594,plain,
% 1.46/1.67 (~c3_1(a1)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[114, 2593])).
% 1.46/1.67 tff(2595,plain,
% 1.46/1.67 (c2_1(a1)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[122, 2593])).
% 1.46/1.67 tff(2596,plain,
% 1.46/1.67 (c1_1(a1)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[130, 2593])).
% 1.46/1.67 tff(2597,plain,
% 1.46/1.67 (hskp9),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[1218, 101, 2587, 2586, 2596, 2595, 2585, 2594, 827])).
% 1.46/1.67 tff(2598,plain,
% 1.46/1.67 (~c3_1(a16)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[839, 2597])).
% 1.46/1.67 tff(2599,plain,
% 1.46/1.67 (c1_1(a16)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[847, 2597])).
% 1.46/1.67 tff(2600,plain,
% 1.46/1.67 (c0_1(a16)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[855, 2597])).
% 1.46/1.67 tff(2601,plain,
% 1.46/1.67 (hskp10),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[862, 101, 2400, 2600, 2599, 2598, 813])).
% 1.46/1.67 tff(2602,plain,
% 1.46/1.67 (~c1_1(a18)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[868, 2601])).
% 1.46/1.67 tff(2603,plain,
% 1.46/1.67 (~c0_1(a18)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[874, 2601])).
% 1.46/1.67 tff(2604,plain,
% 1.46/1.67 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2605,plain,
% 1.46/1.67 ((hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18))) <=> (hskp1 | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2606,plain,
% 1.46/1.67 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))))),
% 1.46/1.67 inference(monotonicity,[status(thm)],[2605])).
% 1.46/1.67 tff(2607,plain,
% 1.46/1.67 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.46/1.67 inference(transitivity,[status(thm)],[2606, 2604])).
% 1.46/1.67 tff(2608,plain,
% 1.46/1.67 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c0_1(a18) | c1_1(a18) | (~c2_1(a18)))),
% 1.46/1.67 inference(quant_inst,[status(thm)],[])).
% 1.46/1.67 tff(2609,plain,
% 1.46/1.67 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a18) | c1_1(a18) | (~ndr1_0) | (~c2_1(a18)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 1.46/1.67 inference(modus_ponens,[status(thm)],[2608, 2607])).
% 1.46/1.67 tff(2610,plain,
% 1.46/1.67 (~c2_1(a18)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2609, 101, 2582, 2591, 2590, 2603, 2602, 58, 2592])).
% 1.46/1.67 tff(2611,plain,
% 1.46/1.67 (~c0_1(a3)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[1954, 101, 2587, 2586, 226, 2435, 224, 2585, 36])).
% 1.46/1.67 tff(2612,plain,
% 1.46/1.67 (hskp12),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[924, 101, 2600, 2599, 2586, 2598, 2585, 918, 2611])).
% 1.46/1.67 tff(2613,plain,
% 1.46/1.67 (~c3_1(a20)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[930, 2612])).
% 1.46/1.67 tff(2614,plain,
% 1.46/1.67 (~c1_1(a20)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[936, 2612])).
% 1.46/1.67 tff(2615,plain,
% 1.46/1.67 (c2_1(a20)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[944, 2612])).
% 1.46/1.67 tff(2616,plain,
% 1.46/1.67 (hskp5),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[951, 101, 2615, 2614, 2613, 226, 224, 275, 2588])).
% 1.46/1.67 tff(2617,plain,
% 1.46/1.67 (~c2_1(a11)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[291, 2616])).
% 1.46/1.67 tff(2618,plain,
% 1.46/1.67 (~c1_1(a11)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[297, 2616])).
% 1.46/1.67 tff(2619,plain,
% 1.46/1.67 (c0_1(a11)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[305, 2616])).
% 1.46/1.67 tff(2620,plain,
% 1.46/1.67 (c3_1(a18)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[962, 2601])).
% 1.46/1.67 tff(2621,plain,
% 1.46/1.67 ($false),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[969, 101, 2620, 2619, 2603, 2602, 2618, 2617, 697, 2610])).
% 1.46/1.67 tff(2622,plain,(c3_1(a15) | c0_1(a13) | c3_1(a13) | hskp3 | c0_1(a58) | c1_1(a58) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.67 tff(2623,plain,
% 1.46/1.67 ($false),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2622, 447, 446, 12, 48, 37, 26, 444])).
% 1.46/1.67 tff(2624,plain,((~hskp6) | c3_1(a2) | hskp3 | c0_1(a58) | c1_1(a58) | c3_1(a15)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.67 tff(2625,plain,
% 1.46/1.67 (~hskp6),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2624, 444, 48, 37, 26, 12])).
% 1.46/1.67 tff(2626,plain,
% 1.46/1.67 (hskp13),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[768, 2400, 443])).
% 1.46/1.67 tff(2627,plain,
% 1.46/1.67 (~c3_1(a21)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[774, 2626])).
% 1.46/1.67 tff(2628,plain,
% 1.46/1.67 (c2_1(a21)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[782, 2626])).
% 1.46/1.67 tff(2629,plain,
% 1.46/1.67 (c0_1(a21)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[790, 2626])).
% 1.46/1.67 tff(2630,plain,
% 1.46/1.67 (hskp6 | (~c1_1(a21))),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2423, 101, 2629, 2628, 2627, 141])).
% 1.46/1.67 tff(2631,plain,
% 1.46/1.67 (~c1_1(a21)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2630, 2625])).
% 1.46/1.67 tff(2632,plain,
% 1.46/1.67 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.46/1.67 inference(bind,[status(th)],[])).
% 1.46/1.67 tff(2633,plain,
% 1.46/1.67 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.46/1.67 inference(quant_intro,[status(thm)],[2632])).
% 1.46/1.67 tff(2634,plain,
% 1.46/1.67 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2635,plain,
% 1.46/1.67 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp18) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.46/1.67 inference(bind,[status(th)],[])).
% 1.46/1.67 tff(2636,plain,
% 1.46/1.67 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.46/1.67 inference(quant_intro,[status(thm)],[2635])).
% 1.46/1.67 tff(2637,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.46/1.67 tff(2638,plain,
% 1.46/1.67 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.46/1.67 inference(modus_ponens,[status(thm)],[2637, 2636])).
% 1.46/1.67 tff(2639,plain,
% 1.46/1.67 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.46/1.67 inference(modus_ponens,[status(thm)],[2638, 2634])).
% 1.46/1.67 tff(2640,plain,(
% 1.46/1.67 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.46/1.67 inference(skolemize,[status(sab)],[2639])).
% 1.46/1.67 tff(2641,plain,
% 1.46/1.67 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.46/1.67 inference(modus_ponens,[status(thm)],[2640, 2633])).
% 1.46/1.67 tff(2642,plain,
% 1.46/1.67 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2643,plain,
% 1.46/1.67 ((hskp18 | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21))) <=> (hskp18 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2644,plain,
% 1.46/1.67 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21))))),
% 1.46/1.67 inference(monotonicity,[status(thm)],[2643])).
% 1.46/1.67 tff(2645,plain,
% 1.46/1.67 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.46/1.67 inference(transitivity,[status(thm)],[2644, 2642])).
% 1.46/1.67 tff(2646,plain,
% 1.46/1.67 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))),
% 1.46/1.67 inference(quant_inst,[status(thm)],[])).
% 1.46/1.67 tff(2647,plain,
% 1.46/1.67 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21))),
% 1.46/1.67 inference(modus_ponens,[status(thm)],[2646, 2645])).
% 1.46/1.67 tff(2648,plain,
% 1.46/1.67 (hskp18),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[2647, 101, 2629, 2628, 2627, 2641, 2631])).
% 1.46/1.67 tff(2649,plain,
% 1.46/1.67 (~c3_1(a31)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[385, 2648])).
% 1.46/1.67 tff(2650,plain,
% 1.46/1.67 (c1_1(a31)),
% 1.46/1.67 inference(unit_resolution,[status(thm)],[393, 2648])).
% 1.46/1.67 tff(2651,plain,
% 1.46/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c1_1(a31)) | c2_1(a31))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c1_1(a31)) | c2_1(a31))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2652,plain,
% 1.46/1.67 (((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c1_1(a31)) | c2_1(a31))),
% 1.46/1.67 inference(rewrite,[status(thm)],[])).
% 1.46/1.67 tff(2653,plain,
% 1.46/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c1_1(a31)) | c2_1(a31)))),
% 1.46/1.67 inference(monotonicity,[status(thm)],[2652])).
% 1.46/1.67 tff(2654,plain,
% 1.46/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c1_1(a31)) | c2_1(a31))),
% 1.46/1.67 inference(transitivity,[status(thm)],[2653, 2651])).
% 1.46/1.67 tff(2655,plain,
% 1.46/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 1.46/1.68 inference(quant_inst,[status(thm)],[])).
% 1.46/1.68 tff(2656,plain,
% 1.46/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | (~c1_1(a31)) | c2_1(a31)),
% 1.46/1.68 inference(modus_ponens,[status(thm)],[2655, 2654])).
% 1.46/1.68 tff(2657,plain,
% 1.46/1.68 (c2_1(a31)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2656, 101, 435, 2650, 2628, 37, 26, 2649, 2627, 362, 2631])).
% 1.46/1.68 tff(2658,plain,
% 1.46/1.68 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a31) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a31) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2659,plain,
% 1.46/1.68 ((hskp6 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21))) <=> (hskp6 | c3_1(a31) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2660,plain,
% 1.46/1.68 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | c3_1(a31) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31))))),
% 1.46/1.68 inference(monotonicity,[status(thm)],[2659])).
% 1.46/1.68 tff(2661,plain,
% 1.46/1.68 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a31) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.46/1.68 inference(transitivity,[status(thm)],[2660, 2658])).
% 1.46/1.68 tff(2662,plain,
% 1.46/1.68 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)))),
% 1.46/1.68 inference(quant_inst,[status(thm)],[])).
% 1.46/1.68 tff(2663,plain,
% 1.46/1.68 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp6 | c3_1(a31) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31))),
% 1.46/1.68 inference(modus_ponens,[status(thm)],[2662, 2661])).
% 1.46/1.68 tff(2664,plain,
% 1.46/1.68 ($false),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2663, 101, 2625, 2650, 2629, 2628, 2649, 2627, 141, 2657])).
% 1.46/1.68 tff(2665,plain,(c3_1(a15) | c0_1(a58) | c1_1(a58) | hskp3 | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.68 tff(2666,plain,
% 1.46/1.68 (c3_1(a15)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2665, 12, 26, 48, 37])).
% 1.46/1.68 tff(2667,plain,
% 1.46/1.68 (c1_1(a15)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[1632, 698, 449, 48, 1174, 12, 37, 26])).
% 1.46/1.68 tff(2668,plain,
% 1.46/1.68 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2669,plain,
% 1.46/1.68 ((hskp28 | hskp0 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15))) <=> (hskp28 | hskp0 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2670,plain,
% 1.46/1.68 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0)))),
% 1.46/1.68 inference(monotonicity,[status(thm)],[2669])).
% 1.46/1.68 tff(2671,plain,
% 1.46/1.68 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0))),
% 1.46/1.68 inference(transitivity,[status(thm)],[2670, 2668])).
% 1.46/1.68 tff(2672,plain,
% 1.46/1.68 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))),
% 1.46/1.68 inference(quant_inst,[status(thm)],[])).
% 1.46/1.68 tff(2673,plain,
% 1.46/1.68 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~ndr1_0)),
% 1.46/1.68 inference(modus_ponens,[status(thm)],[2672, 2671])).
% 1.46/1.68 tff(2674,plain,
% 1.46/1.68 (hskp28 | hskp0 | c2_1(a15) | (~c3_1(a15))),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2673, 101, 2060, 540])).
% 1.46/1.68 tff(2675,plain,
% 1.46/1.68 ($false),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2674, 497, 11, 1174, 698])).
% 1.46/1.68 tff(2676,plain,(hskp0 | (~c3_1(a15)) | c2_1(a15) | (~c1_1(a15)) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.68 tff(2677,plain,
% 1.46/1.68 (hskp0),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2676, 698, 1174, 2060, 48, 37, 26])).
% 1.46/1.68 tff(2678,plain,
% 1.46/1.68 (c1_1(a1)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[130, 2677])).
% 1.46/1.68 tff(2679,plain,
% 1.46/1.68 (~c3_1(a1)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[114, 2677])).
% 1.46/1.68 tff(2680,plain,
% 1.46/1.68 (c2_1(a1)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[122, 2677])).
% 1.46/1.68 tff(2681,plain,
% 1.46/1.68 (hskp6),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[171, 2678, 2680, 2679])).
% 1.46/1.68 tff(2682,plain,
% 1.46/1.68 (~c3_1(a13)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[177, 2681])).
% 1.46/1.68 tff(2683,plain,
% 1.46/1.68 (~c1_1(a13)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[183, 2681])).
% 1.46/1.68 tff(2684,plain,
% 1.46/1.68 (~c0_1(a13)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[189, 2681])).
% 1.46/1.68 tff(2685,plain,
% 1.46/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c0_1(a15)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2686,plain,
% 1.46/1.68 (((~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c2_1(a15) | (~c0_1(a15)) | (~c1_1(a15)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> ((~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c0_1(a15)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2687,plain,
% 1.46/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c2_1(a15) | (~c0_1(a15)) | (~c1_1(a15)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c0_1(a15))))),
% 1.46/1.68 inference(monotonicity,[status(thm)],[2686])).
% 1.46/1.68 tff(2688,plain,
% 1.46/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c2_1(a15) | (~c0_1(a15)) | (~c1_1(a15)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c0_1(a15)))),
% 1.46/1.68 inference(transitivity,[status(thm)],[2687, 2685])).
% 1.46/1.68 tff(2689,plain,
% 1.46/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c2_1(a15) | (~c0_1(a15)) | (~c1_1(a15)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.46/1.68 inference(quant_inst,[status(thm)],[])).
% 1.46/1.68 tff(2690,plain,
% 1.46/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c0_1(a15))),
% 1.46/1.68 inference(modus_ponens,[status(thm)],[2689, 2688])).
% 1.46/1.68 tff(2691,plain,
% 1.46/1.68 (~c0_1(a15)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2690, 101, 2060, 698, 1174, 2684, 2683, 2682, 36])).
% 1.46/1.68 tff(2692,plain,
% 1.46/1.68 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2693,plain,
% 1.46/1.68 ((hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15))) <=> (hskp9 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2694,plain,
% 1.46/1.68 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))))),
% 1.46/1.68 inference(monotonicity,[status(thm)],[2693])).
% 1.46/1.68 tff(2695,plain,
% 1.46/1.68 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 1.46/1.68 inference(transitivity,[status(thm)],[2694, 2692])).
% 1.46/1.68 tff(2696,plain,
% 1.46/1.68 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))),
% 1.46/1.68 inference(quant_inst,[status(thm)],[])).
% 1.46/1.68 tff(2697,plain,
% 1.46/1.68 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))),
% 1.46/1.68 inference(modus_ponens,[status(thm)],[2696, 2695])).
% 1.46/1.68 tff(2698,plain,
% 1.46/1.68 (hskp9),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2697, 101, 2678, 2680, 2060, 698, 1174, 2679, 827])).
% 1.46/1.68 tff(2699,plain,
% 1.46/1.68 (~c3_1(a16)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[839, 2698])).
% 1.46/1.68 tff(2700,plain,
% 1.46/1.68 (c1_1(a16)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[847, 2698])).
% 1.46/1.68 tff(2701,plain,
% 1.46/1.68 (c2_1(a16)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[1227, 101, 2700, 2678, 2680, 2699, 698, 1174, 2679, 680, 2691])).
% 1.46/1.68 tff(2702,plain,
% 1.46/1.68 (c0_1(a16)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[855, 2698])).
% 1.46/1.68 tff(2703,assumption,(c0_1(a16)), introduced(assumption)).
% 1.46/1.68 tff(2704,plain,
% 1.46/1.68 (~c0_1(a3)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[907, 101, 2703, 2541, 1947, 1946, 2540, 1945, 901])).
% 1.46/1.68 tff(2705,plain,
% 1.46/1.68 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2706,plain,
% 1.46/1.68 ((hskp1 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13))) <=> (hskp1 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2707,plain,
% 1.46/1.68 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13))))),
% 1.46/1.68 inference(monotonicity,[status(thm)],[2706])).
% 1.46/1.68 tff(2708,plain,
% 1.46/1.68 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13)))),
% 1.46/1.68 inference(transitivity,[status(thm)],[2707, 2705])).
% 1.46/1.68 tff(2709,plain,
% 1.46/1.68 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)) | c0_1(a13) | c1_1(a13) | (~c2_1(a13)))),
% 1.46/1.68 inference(quant_inst,[status(thm)],[])).
% 1.46/1.68 tff(2710,plain,
% 1.46/1.68 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | (~c2_1(a13))),
% 1.46/1.68 inference(modus_ponens,[status(thm)],[2709, 2708])).
% 1.46/1.68 tff(2711,plain,
% 1.46/1.68 (hskp1 | (~c2_1(a13))),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2710, 101, 2060, 698, 1174, 226, 225, 58])).
% 1.46/1.68 tff(2712,plain,
% 1.46/1.68 (~c2_1(a13)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2711, 191])).
% 1.46/1.68 tff(2713,plain,
% 1.46/1.68 (~c0_1(a15)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2690, 101, 2060, 698, 1174, 226, 225, 224, 36])).
% 1.46/1.68 tff(2714,plain,
% 1.46/1.68 (hskp12),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[1272, 101, 2703, 2541, 2540, 698, 1174, 918, 2713])).
% 1.46/1.68 tff(2715,plain,
% 1.46/1.68 (~c3_1(a20)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[930, 2714])).
% 1.46/1.68 tff(2716,plain,
% 1.46/1.68 (~c1_1(a20)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[936, 2714])).
% 1.46/1.68 tff(2717,plain,
% 1.46/1.68 (c2_1(a20)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[944, 2714])).
% 1.46/1.68 tff(2718,plain,
% 1.46/1.68 (hskp5 | c2_1(a13)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[951, 101, 2717, 2716, 2715, 226, 224, 275])).
% 1.46/1.68 tff(2719,plain,
% 1.46/1.68 (hskp5),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2718, 2712])).
% 1.46/1.68 tff(2720,plain,
% 1.46/1.68 (~c2_1(a11)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[291, 2719])).
% 1.46/1.68 tff(2721,plain,
% 1.46/1.68 (~c1_1(a11)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[297, 2719])).
% 1.46/1.68 tff(2722,plain,
% 1.46/1.68 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c1_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a20)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2723,plain,
% 1.46/1.68 ((hskp10 | hskp1 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20))) <=> (hskp10 | hskp1 | c1_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a20)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2724,plain,
% 1.46/1.68 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c1_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a20))))),
% 1.46/1.68 inference(monotonicity,[status(thm)],[2723])).
% 1.46/1.68 tff(2725,plain,
% 1.46/1.68 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a20)))),
% 1.46/1.68 inference(transitivity,[status(thm)],[2724, 2722])).
% 1.46/1.68 tff(2726,plain,
% 1.46/1.68 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)))),
% 1.46/1.68 inference(quant_inst,[status(thm)],[])).
% 1.46/1.68 tff(2727,plain,
% 1.46/1.68 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a20) | c3_1(a20) | (~ndr1_0) | (~c2_1(a20))),
% 1.46/1.68 inference(modus_ponens,[status(thm)],[2726, 2725])).
% 1.46/1.68 tff(2728,plain,
% 1.46/1.68 (hskp10 | hskp1),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2727, 101, 2717, 2716, 2715, 1786])).
% 1.46/1.68 tff(2729,plain,
% 1.46/1.68 (hskp10),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2728, 191])).
% 1.46/1.68 tff(2730,plain,
% 1.46/1.68 (~c1_1(a18)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[868, 2729])).
% 1.46/1.68 tff(2731,plain,
% 1.46/1.68 (~c0_1(a18)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[874, 2729])).
% 1.46/1.68 tff(2732,plain,
% 1.46/1.68 (c0_1(a11)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[305, 2719])).
% 1.46/1.68 tff(2733,plain,
% 1.46/1.68 (c3_1(a18)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[962, 2729])).
% 1.46/1.68 tff(2734,plain,
% 1.46/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c0_1(a11)) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c0_1(a11)) | (~c3_1(a18)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2735,plain,
% 1.46/1.68 (((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18))) <=> (c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c0_1(a11)) | (~c3_1(a18)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2736,plain,
% 1.46/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c0_1(a11)) | (~c3_1(a18))))),
% 1.46/1.68 inference(monotonicity,[status(thm)],[2735])).
% 1.46/1.68 tff(2737,plain,
% 1.46/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c0_1(a11)) | (~c3_1(a18)))),
% 1.46/1.68 inference(transitivity,[status(thm)],[2736, 2734])).
% 1.46/1.68 tff(2738,plain,
% 1.46/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a11) | c2_1(a11) | (~c0_1(a11)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))),
% 1.46/1.68 inference(quant_inst,[status(thm)],[])).
% 1.46/1.68 tff(2739,plain,
% 1.46/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a18) | c1_1(a18) | c1_1(a11) | c2_1(a11) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3) | (~c0_1(a11)) | (~c3_1(a18))),
% 1.46/1.68 inference(modus_ponens,[status(thm)],[2738, 2737])).
% 1.46/1.68 tff(2740,plain,
% 1.46/1.68 ($false),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2739, 101, 2733, 2732, 1946, 2731, 2730, 2721, 2720, 1945, 697, 2704])).
% 1.46/1.68 tff(2741,plain,(hskp1 | (~c0_1(a16)) | (~c1_1(a16)) | c3_1(a16) | c0_1(a13) | c3_1(a13) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | c1_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.68 tff(2742,plain,
% 1.46/1.68 (hskp1),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2741, 2702, 2700, 2699, 2684, 2682, 2060, 698, 1174, 2683])).
% 1.46/1.68 tff(2743,plain,
% 1.46/1.68 (~c3_1(a2)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[241, 2742])).
% 1.46/1.68 tff(2744,plain,
% 1.46/1.68 (hskp12),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[1272, 101, 2702, 2700, 2699, 698, 1174, 918, 2691])).
% 1.46/1.68 tff(2745,plain,
% 1.46/1.68 (~c3_1(a20)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[930, 2744])).
% 1.46/1.68 tff(2746,plain,
% 1.46/1.68 (~c1_1(a20)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[936, 2744])).
% 1.46/1.68 tff(2747,plain,
% 1.46/1.68 (c2_1(a20)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[944, 2744])).
% 1.46/1.68 tff(2748,plain,
% 1.46/1.68 (~c0_1(a2)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[253, 2742])).
% 1.46/1.68 tff(2749,plain,
% 1.46/1.68 (~c2_1(a2)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[247, 2742])).
% 1.46/1.68 tff(2750,plain,
% 1.46/1.68 ($false),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2578, 2749, 2748, 2747, 2746, 2745, 37, 48, 26, 2743, 2700, 2699, 2701, 2680, 2679, 2678])).
% 1.46/1.68 tff(2751,plain,(c2_1(a15) | c0_1(a58) | hskp3 | c1_1(a58) | (~c1_1(a15)) | (~c3_1(a15))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.68 tff(2752,plain,
% 1.46/1.68 ($false),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2751, 2667, 698, 48, 26, 37, 1174])).
% 1.46/1.68 tff(2753,plain,(c2_1(a15) | hskp3 | c1_1(a58) | c0_1(a58) | (~c3_1(a15)) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.68 tff(2754,plain,
% 1.46/1.68 (c2_1(a15)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2753, 2666, 26, 37, 48, 12])).
% 1.46/1.68 tff(2755,plain,
% 1.46/1.68 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~c1_1(a15)) | (~c2_1(a15)) | (~c3_1(a15)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~c1_1(a15)) | (~c2_1(a15)) | (~c3_1(a15)) | (~ndr1_0))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2756,plain,
% 1.46/1.68 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15))) <=> (hskp24 | hskp3 | (~c1_1(a15)) | (~c2_1(a15)) | (~c3_1(a15)) | (~ndr1_0))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2757,plain,
% 1.46/1.68 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~c1_1(a15)) | (~c2_1(a15)) | (~c3_1(a15)) | (~ndr1_0)))),
% 1.46/1.68 inference(monotonicity,[status(thm)],[2756])).
% 1.46/1.68 tff(2758,plain,
% 1.46/1.68 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~c1_1(a15)) | (~c2_1(a15)) | (~c3_1(a15)) | (~ndr1_0))),
% 1.46/1.68 inference(transitivity,[status(thm)],[2757, 2755])).
% 1.46/1.68 tff(2759,plain,
% 1.46/1.68 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)))),
% 1.46/1.68 inference(quant_inst,[status(thm)],[])).
% 1.46/1.68 tff(2760,plain,
% 1.46/1.68 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp3 | (~c1_1(a15)) | (~c2_1(a15)) | (~c3_1(a15)) | (~ndr1_0)),
% 1.46/1.68 inference(modus_ponens,[status(thm)],[2759, 2758])).
% 1.46/1.68 tff(2761,plain,
% 1.46/1.68 (~c1_1(a15)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2760, 101, 443, 48, 2754, 2666, 10])).
% 1.46/1.68 tff(2762,plain,
% 1.46/1.68 (c2_1(a38)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2031, 2761, 26, 37, 12, 48])).
% 1.46/1.68 tff(2763,plain,
% 1.46/1.68 (~hskp21),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2399, 2762])).
% 1.46/1.68 tff(2764,plain,
% 1.46/1.68 (hskp13),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[768, 2763, 443])).
% 1.46/1.68 tff(2765,plain,
% 1.46/1.68 (c0_1(a21)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[790, 2764])).
% 1.46/1.68 tff(2766,plain,
% 1.46/1.68 (c2_1(a21)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[782, 2764])).
% 1.46/1.68 tff(2767,plain,
% 1.46/1.68 (~c3_1(a21)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[774, 2764])).
% 1.46/1.68 tff(2768,plain,
% 1.46/1.68 (hskp6 | (~c1_1(a21))),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2423, 101, 2765, 2766, 2767, 141])).
% 1.46/1.68 tff(2769,plain,
% 1.46/1.68 (~c1_1(a21)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2768, 25])).
% 1.46/1.68 tff(2770,plain,
% 1.46/1.68 (c2_1(a2) | (~c1_1(a2)) | c1_1(a21)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[1937, 101, 435, 2766, 37, 26, 2767, 12, 362])).
% 1.46/1.68 tff(2771,plain,
% 1.46/1.68 (~c1_1(a2)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2770, 2769, 13])).
% 1.46/1.68 tff(2772,plain,
% 1.46/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2773,plain,
% 1.46/1.68 (((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2774,plain,
% 1.46/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2)))),
% 1.46/1.68 inference(monotonicity,[status(thm)],[2773])).
% 1.46/1.68 tff(2775,plain,
% 1.46/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2))),
% 1.46/1.68 inference(transitivity,[status(thm)],[2774, 2772])).
% 1.46/1.68 tff(2776,plain,
% 1.46/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a2) | c2_1(a2) | c1_1(a2) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 1.46/1.68 inference(quant_inst,[status(thm)],[])).
% 1.46/1.68 tff(2777,plain,
% 1.46/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a2)),
% 1.46/1.68 inference(modus_ponens,[status(thm)],[2776, 2775])).
% 1.46/1.68 tff(2778,plain,
% 1.46/1.68 (c0_1(a2) | c1_1(a2)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2777, 101, 2761, 2754, 2666, 13, 12, 344])).
% 1.46/1.68 tff(2779,plain,
% 1.46/1.68 (c0_1(a2)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2778, 2771])).
% 1.46/1.68 tff(2780,plain,
% 1.46/1.68 (~hskp1),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[253, 2779])).
% 1.46/1.68 tff(2781,plain,
% 1.46/1.68 (hskp0),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[548, 2780, 48, 37, 26])).
% 1.46/1.68 tff(2782,plain,
% 1.46/1.68 (~c3_1(a1)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[114, 2781])).
% 1.46/1.68 tff(2783,plain,
% 1.46/1.68 (c1_1(a1)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[130, 2781])).
% 1.46/1.68 tff(2784,plain,
% 1.46/1.68 (c2_1(a1)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[122, 2781])).
% 1.46/1.68 tff(2785,plain,
% 1.46/1.68 ($false),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[171, 2784, 2783, 25, 2782])).
% 1.46/1.68 tff(2786,plain,(hskp6 | hskp3 | c0_1(a58) | c1_1(a58) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.68 tff(2787,plain,
% 1.46/1.68 (hskp6),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2786, 13, 37, 26, 48, 12])).
% 1.46/1.68 tff(2788,plain,
% 1.46/1.68 (~c0_1(a13)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[189, 2787])).
% 1.46/1.68 tff(2789,plain,
% 1.46/1.68 (~c3_1(a13)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[177, 2787])).
% 1.46/1.68 tff(2790,plain,
% 1.46/1.68 (~c1_1(a13)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2434, 226, 726, 37, 26, 2415, 2416, 2417, 224])).
% 1.46/1.68 tff(2791,plain,
% 1.46/1.68 (hskp1),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[1982, 2790, 1174, 1749, 12, 451, 13, 224, 226])).
% 1.46/1.68 tff(2792,plain,
% 1.46/1.68 (~c0_1(a2)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[253, 2791])).
% 1.46/1.68 tff(2793,plain,
% 1.46/1.68 (c0_1(a2) | c1_1(a2)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2777, 101, 451, 1749, 1174, 13, 12, 344])).
% 1.46/1.68 tff(2794,plain,
% 1.46/1.68 (c1_1(a2)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2793, 2792])).
% 1.46/1.68 tff(2795,plain,
% 1.46/1.68 (c1_1(a13) | c0_1(a2) | c2_1(a13)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[1979, 101, 451, 1749, 1174, 224, 13, 12, 344])).
% 1.46/1.68 tff(2796,plain,
% 1.46/1.68 (c2_1(a13)),
% 1.46/1.68 inference(unit_resolution,[status(thm)],[2795, 2792, 2790])).
% 1.46/1.68 tff(2797,plain,
% 1.46/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a13)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a13)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2798,plain,
% 1.46/1.68 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a13)))),
% 1.46/1.68 inference(rewrite,[status(thm)],[])).
% 1.46/1.68 tff(2799,plain,
% 1.46/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a13))))),
% 1.46/1.68 inference(monotonicity,[status(thm)],[2798])).
% 1.46/1.68 tff(2800,plain,
% 1.46/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a13)))),
% 1.46/1.68 inference(transitivity,[status(thm)],[2799, 2797])).
% 1.46/1.68 tff(2801,plain,
% 1.46/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c1_1(a2)) | c3_1(a13) | c1_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c0_1(a58))),
% 1.46/1.69 inference(quant_inst,[status(thm)],[])).
% 1.46/1.69 tff(2802,plain,
% 1.46/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a13) | c3_1(a13) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a13))),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2801, 2800])).
% 1.46/1.69 tff(2803,plain,
% 1.46/1.69 (c1_1(a13) | (~c1_1(a2)) | (~c2_1(a13))),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2802, 101, 726, 37, 26, 224, 13, 12, 362])).
% 1.46/1.69 tff(2804,plain,
% 1.46/1.69 ($false),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2803, 2796, 2794, 2790])).
% 1.46/1.69 tff(2805,plain,(c0_1(a13) | c2_1(a58) | c0_1(a58) | c1_1(a58) | c3_1(a13) | c2_1(a2) | c3_1(a2) | c1_1(a15) | (~c2_1(a15)) | (~c3_1(a15)) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.69 tff(2806,plain,
% 1.46/1.69 ($false),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2805, 2789, 2788, 37, 26, 435, 13, 12, 2761, 2754, 2666, 2767, 2766, 2765])).
% 1.46/1.69 tff(2807,plain,(c2_1(a2) | c0_1(a58) | c1_1(a58) | c3_1(a2) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.46/1.69 tff(2808,plain,
% 1.46/1.69 (c2_1(a2)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2807, 12, 26, 37, 48])).
% 1.46/1.69 tff(2809,plain,
% 1.46/1.69 (~hskp1),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[247, 2808])).
% 1.46/1.69 tff(2810,plain,
% 1.46/1.69 (hskp0),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[548, 2809, 48, 37, 26])).
% 1.46/1.69 tff(2811,plain,
% 1.46/1.69 (~c3_1(a1)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[114, 2810])).
% 1.46/1.69 tff(2812,plain,
% 1.46/1.69 (c1_1(a1)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[130, 2810])).
% 1.46/1.69 tff(2813,plain,
% 1.46/1.69 (c2_1(a1)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[122, 2810])).
% 1.46/1.69 tff(2814,plain,
% 1.46/1.69 (hskp6),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[171, 2813, 2812, 2811])).
% 1.46/1.69 tff(2815,plain,
% 1.46/1.69 (~c3_1(a13)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[177, 2814])).
% 1.46/1.69 tff(2816,plain,
% 1.46/1.69 (~c1_1(a13)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[183, 2814])).
% 1.46/1.69 tff(2817,plain,
% 1.46/1.69 (~c0_1(a13)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[189, 2814])).
% 1.46/1.69 tff(2818,plain,
% 1.46/1.69 (hskp2),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[232, 101, 2809, 2817, 2816, 2815, 47])).
% 1.46/1.69 tff(2819,plain,
% 1.46/1.69 (~c2_1(a3)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[197, 2818])).
% 1.46/1.69 tff(2820,plain,
% 1.46/1.69 (c3_1(a3)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[205, 2818])).
% 1.46/1.69 tff(2821,plain,
% 1.46/1.69 (c1_1(a3)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[213, 2818])).
% 1.46/1.69 tff(2822,plain,
% 1.46/1.69 (~c2_1(a13)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[1253, 101, 2809, 2821, 2820, 2817, 2816, 2819, 58])).
% 1.46/1.69 tff(2823,plain,
% 1.46/1.69 ($false),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2029, 101, 2761, 2754, 2666, 2817, 2816, 2815, 344, 2822])).
% 1.46/1.69 tff(2824,plain,(c3_1(a2) | hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.69 tff(2825,plain,
% 1.46/1.69 (c3_1(a2)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2824, 48, 37, 26])).
% 1.46/1.69 tff(2826,plain,
% 1.46/1.69 (~hskp1),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[241, 2825])).
% 1.46/1.69 tff(2827,plain,
% 1.46/1.69 (hskp0),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[548, 2826, 48, 37, 26])).
% 1.46/1.69 tff(2828,plain,
% 1.46/1.69 (~c3_1(a1)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[114, 2827])).
% 1.46/1.69 tff(2829,plain,
% 1.46/1.69 (c1_1(a1)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[130, 2827])).
% 1.46/1.69 tff(2830,plain,
% 1.46/1.69 (c2_1(a1)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[122, 2827])).
% 1.46/1.69 tff(2831,plain,
% 1.46/1.69 (hskp6),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[171, 2830, 2829, 2828])).
% 1.46/1.69 tff(2832,plain,
% 1.46/1.69 (~c3_1(a13)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[177, 2831])).
% 1.46/1.69 tff(2833,plain,
% 1.46/1.69 (~c1_1(a13)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[183, 2831])).
% 1.46/1.69 tff(2834,plain,
% 1.46/1.69 (~c0_1(a13)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[189, 2831])).
% 1.46/1.69 tff(2835,plain,
% 1.46/1.69 (hskp2),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[232, 101, 2826, 2834, 2833, 2832, 47])).
% 1.46/1.69 tff(2836,plain,
% 1.46/1.69 (~c2_1(a3)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[197, 2835])).
% 1.46/1.69 tff(2837,plain,
% 1.46/1.69 (c3_1(a3)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[205, 2835])).
% 1.46/1.69 tff(2838,plain,
% 1.46/1.69 (c1_1(a3)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[213, 2835])).
% 1.46/1.69 tff(2839,plain,
% 1.46/1.69 (~c0_1(a3)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[1954, 101, 2838, 2837, 2834, 2833, 2832, 2836, 36])).
% 1.46/1.69 tff(2840,plain,
% 1.46/1.69 (hskp9),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[1218, 101, 2838, 2837, 2829, 2830, 2836, 2828, 827])).
% 1.46/1.69 tff(2841,plain,
% 1.46/1.69 (~c3_1(a16)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[839, 2840])).
% 1.46/1.69 tff(2842,plain,
% 1.46/1.69 (c1_1(a16)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[847, 2840])).
% 1.46/1.69 tff(2843,plain,
% 1.46/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a16) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2844,plain,
% 1.46/1.69 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (c3_1(a16) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2845,plain,
% 1.46/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a16) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16)))),
% 1.46/1.69 inference(monotonicity,[status(thm)],[2844])).
% 1.46/1.69 tff(2846,plain,
% 1.46/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16))),
% 1.46/1.69 inference(transitivity,[status(thm)],[2845, 2843])).
% 1.46/1.69 tff(2847,plain,
% 1.46/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.46/1.69 inference(quant_inst,[status(thm)],[])).
% 1.46/1.69 tff(2848,plain,
% 1.46/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a16) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a3)) | c0_1(a3) | (~c1_1(a16)) | c2_1(a16)),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2847, 2846])).
% 1.46/1.69 tff(2849,plain,
% 1.46/1.69 (c2_1(a16)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2848, 101, 2842, 2837, 2829, 2830, 2841, 2836, 2828, 680, 2839])).
% 1.46/1.69 tff(2850,plain,
% 1.46/1.69 (~c2_1(a13)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[1253, 101, 2826, 2838, 2837, 2834, 2833, 2836, 58])).
% 1.46/1.69 tff(2851,plain,
% 1.46/1.69 (c0_1(a16)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[855, 2840])).
% 1.46/1.69 tff(2852,plain,
% 1.46/1.69 (hskp12),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[924, 101, 2851, 2842, 2837, 2841, 2836, 918, 2839])).
% 1.46/1.69 tff(2853,plain,
% 1.46/1.69 (~c1_1(a20)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[936, 2852])).
% 1.46/1.69 tff(2854,plain,
% 1.46/1.69 (c2_1(a20)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[944, 2852])).
% 1.46/1.69 tff(2855,plain,
% 1.46/1.69 (~c0_1(a20)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[1281, 101, 2854, 2842, 2853, 2841, 2834, 2832, 1264, 2850, 2849])).
% 1.46/1.69 tff(2856,plain,
% 1.46/1.69 ($false),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[1288, 101, 2826, 2854, 2838, 2837, 2853, 2836, 58, 2855])).
% 1.46/1.69 tff(2857,plain,(hskp3 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.69 tff(2858,plain,
% 1.46/1.69 (hskp3),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2857, 37, 26])).
% 1.46/1.69 tff(2859,plain,
% 1.46/1.69 (((~hskp3) | (~c2_1(a7))) <=> ((~hskp3) | (~c2_1(a7)))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2860,plain,
% 1.46/1.69 (((~c2_1(a7)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a7)))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2861,axiom,((~c2_1(a7)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.46/1.69 tff(2862,plain,
% 1.46/1.69 ((~hskp3) | (~c2_1(a7))),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2861, 2860])).
% 1.46/1.69 tff(2863,plain,
% 1.46/1.69 ((~hskp3) | (~c2_1(a7))),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2862, 2859])).
% 1.46/1.69 tff(2864,plain,
% 1.46/1.69 (~c2_1(a7)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2863, 2858])).
% 1.46/1.69 tff(2865,plain,
% 1.46/1.69 (~hskp24),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[442, 726])).
% 1.46/1.69 tff(2866,assumption,(~c1_1(a7)), introduced(assumption)).
% 1.46/1.69 tff(2867,plain,
% 1.46/1.69 (((~hskp3) | c3_1(a7)) <=> ((~hskp3) | c3_1(a7))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2868,axiom,((~hskp3) | c3_1(a7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.46/1.69 tff(2869,plain,
% 1.46/1.69 ((~hskp3) | c3_1(a7)),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2868, 2867])).
% 1.46/1.69 tff(2870,plain,
% 1.46/1.69 ((~hskp3) | c3_1(a7)),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2869, 2867])).
% 1.46/1.69 tff(2871,plain,
% 1.46/1.69 ((~hskp3) | c3_1(a7)),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2870, 2867])).
% 1.46/1.69 tff(2872,plain,
% 1.46/1.69 ((~hskp3) | c3_1(a7)),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2871, 2867])).
% 1.46/1.69 tff(2873,plain,
% 1.46/1.69 ((~hskp3) | c3_1(a7)),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2872, 2867])).
% 1.46/1.69 tff(2874,plain,
% 1.46/1.69 (c3_1(a7)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2873, 2858])).
% 1.46/1.69 tff(2875,plain,
% 1.46/1.69 (((~hskp3) | c0_1(a7)) <=> ((~hskp3) | c0_1(a7))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2876,axiom,((~hskp3) | c0_1(a7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.46/1.69 tff(2877,plain,
% 1.46/1.69 ((~hskp3) | c0_1(a7)),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2876, 2875])).
% 1.46/1.69 tff(2878,plain,
% 1.46/1.69 ((~hskp3) | c0_1(a7)),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2877, 2875])).
% 1.46/1.69 tff(2879,plain,
% 1.46/1.69 ((~hskp3) | c0_1(a7)),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2878, 2875])).
% 1.46/1.69 tff(2880,plain,
% 1.46/1.69 ((~hskp3) | c0_1(a7)),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2879, 2875])).
% 1.46/1.69 tff(2881,plain,
% 1.46/1.69 ((~hskp3) | c0_1(a7)),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2880, 2875])).
% 1.46/1.69 tff(2882,plain,
% 1.46/1.69 (c0_1(a7)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2881, 2858])).
% 1.46/1.69 tff(2883,plain,
% 1.46/1.69 (((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))) <=> ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp13 | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2884,plain,
% 1.46/1.69 ((hskp24 | hskp13 | (~ndr1_0) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7))) <=> (hskp24 | hskp13 | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2885,plain,
% 1.46/1.69 (((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7)))) <=> ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7)))),
% 1.46/1.69 inference(monotonicity,[status(thm)],[2884])).
% 1.46/1.69 tff(2886,plain,
% 1.46/1.69 (((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7)))) <=> ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp13 | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))),
% 1.46/1.69 inference(transitivity,[status(thm)],[2885, 2883])).
% 1.46/1.69 tff(2887,plain,
% 1.46/1.69 ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp13 | (~ndr1_0) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7)))),
% 1.46/1.69 inference(quant_inst,[status(thm)],[])).
% 1.46/1.69 tff(2888,plain,
% 1.46/1.69 ((~![U: $i] : (hskp24 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp13 | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7)),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2887, 2886])).
% 1.46/1.69 tff(2889,plain,
% 1.46/1.69 (hskp24 | hskp13 | c1_1(a7)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2888, 101, 2882, 2874, 1914])).
% 1.46/1.69 tff(2890,plain,
% 1.46/1.69 (hskp13),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2889, 2865, 2866])).
% 1.46/1.69 tff(2891,plain,
% 1.46/1.69 (~c3_1(a21)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[774, 2890])).
% 1.46/1.69 tff(2892,plain,
% 1.46/1.69 (c2_1(a21)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[782, 2890])).
% 1.46/1.69 tff(2893,plain,
% 1.46/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a21) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a21)) | (~c2_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a21) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a21)) | (~c2_1(a21)))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2894,plain,
% 1.46/1.69 (((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> (c3_1(a21) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a21)) | (~c2_1(a21)))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2895,plain,
% 1.46/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a21) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a21)) | (~c2_1(a21))))),
% 1.46/1.69 inference(monotonicity,[status(thm)],[2894])).
% 1.46/1.69 tff(2896,plain,
% 1.46/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a21) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a21)) | (~c2_1(a21)))),
% 1.46/1.69 inference(transitivity,[status(thm)],[2895, 2893])).
% 1.46/1.69 tff(2897,plain,
% 1.46/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 1.46/1.69 inference(quant_inst,[status(thm)],[])).
% 1.46/1.69 tff(2898,plain,
% 1.46/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a21) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a21)) | (~c2_1(a21))),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2897, 2896])).
% 1.46/1.69 tff(2899,plain,
% 1.46/1.69 (~c1_1(a21)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2898, 101, 2892, 2882, 2874, 2891, 2864, 264, 2866])).
% 1.46/1.69 tff(2900,plain,
% 1.46/1.69 (c0_1(a21)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[790, 2890])).
% 1.46/1.69 tff(2901,plain,
% 1.46/1.69 (hskp18),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2647, 101, 2900, 2892, 2891, 2641, 2899])).
% 1.46/1.69 tff(2902,plain,
% 1.46/1.69 (~c3_1(a31)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[385, 2901])).
% 1.46/1.69 tff(2903,plain,
% 1.46/1.69 (c1_1(a31)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[393, 2901])).
% 1.46/1.69 tff(2904,plain,
% 1.46/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a31) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a31)) | (~c2_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a31) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2905,plain,
% 1.46/1.69 (((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> (c3_1(a31) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2906,plain,
% 1.46/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a31) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a31)) | (~c2_1(a31))))),
% 1.46/1.69 inference(monotonicity,[status(thm)],[2905])).
% 1.46/1.69 tff(2907,plain,
% 1.46/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a31) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.46/1.69 inference(transitivity,[status(thm)],[2906, 2904])).
% 1.46/1.69 tff(2908,plain,
% 1.46/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 1.46/1.69 inference(quant_inst,[status(thm)],[])).
% 1.46/1.69 tff(2909,plain,
% 1.46/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a31) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c1_1(a31)) | (~c2_1(a31))),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2908, 2907])).
% 1.46/1.69 tff(2910,plain,
% 1.46/1.69 (~c2_1(a31)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2909, 101, 2903, 2882, 2874, 2902, 2864, 264, 2866])).
% 1.46/1.69 tff(2911,plain,
% 1.46/1.69 ($false),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2656, 101, 726, 2903, 2892, 37, 26, 2902, 2891, 362, 2899, 2910])).
% 1.46/1.69 tff(2912,plain,(c2_1(a58) | c0_1(a58) | c1_1(a58) | c1_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.69 tff(2913,plain,
% 1.46/1.69 (c1_1(a7)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2912, 726, 26, 37])).
% 1.46/1.69 tff(2914,plain,
% 1.46/1.69 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | c2_1(a7) | (~ndr1_0) | (~c0_1(a7)) | (~c1_1(a7)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a7) | (~ndr1_0) | (~c0_1(a7)) | (~c1_1(a7)))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2915,plain,
% 1.46/1.69 ((hskp24 | hskp6 | (~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7))) <=> (hskp24 | hskp6 | c2_1(a7) | (~ndr1_0) | (~c0_1(a7)) | (~c1_1(a7)))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2916,plain,
% 1.46/1.69 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | c2_1(a7) | (~ndr1_0) | (~c0_1(a7)) | (~c1_1(a7))))),
% 1.46/1.69 inference(monotonicity,[status(thm)],[2915])).
% 1.46/1.69 tff(2917,plain,
% 1.46/1.69 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a7) | (~ndr1_0) | (~c0_1(a7)) | (~c1_1(a7)))),
% 1.46/1.69 inference(transitivity,[status(thm)],[2916, 2914])).
% 1.46/1.69 tff(2918,plain,
% 1.46/1.69 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7)))),
% 1.46/1.69 inference(quant_inst,[status(thm)],[])).
% 1.46/1.69 tff(2919,plain,
% 1.46/1.69 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a7) | (~ndr1_0) | (~c0_1(a7)) | (~c1_1(a7))),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2918, 2917])).
% 1.46/1.69 tff(2920,plain,
% 1.46/1.69 (hskp24 | hskp6 | (~c1_1(a7))),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2919, 101, 2882, 2864, 984])).
% 1.46/1.69 tff(2921,plain,
% 1.46/1.69 ($false),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2920, 2913, 2865, 25])).
% 1.46/1.69 tff(2922,plain,(c2_1(a58) | hskp6 | c1_1(a58) | c0_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.69 tff(2923,plain,
% 1.46/1.69 (hskp6),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2922, 726, 26, 37])).
% 1.46/1.69 tff(2924,plain,
% 1.46/1.69 (~c1_1(a13)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[183, 2923])).
% 1.46/1.69 tff(2925,plain,
% 1.46/1.69 (~c0_1(a13)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[189, 2923])).
% 1.46/1.69 tff(2926,plain,
% 1.46/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2927,plain,
% 1.46/1.69 (((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2928,plain,
% 1.46/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7))))),
% 1.46/1.69 inference(monotonicity,[status(thm)],[2927])).
% 1.46/1.69 tff(2929,plain,
% 1.46/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))),
% 1.46/1.69 inference(transitivity,[status(thm)],[2928, 2926])).
% 1.46/1.69 tff(2930,plain,
% 1.46/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.46/1.69 inference(quant_inst,[status(thm)],[])).
% 1.46/1.69 tff(2931,plain,
% 1.46/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7))),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2930, 2929])).
% 1.46/1.69 tff(2932,plain,
% 1.46/1.69 ($false),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2931, 101, 2882, 2874, 2925, 2924, 224, 2864, 36, 2913])).
% 1.46/1.69 tff(2933,plain,(c2_1(a58) | c3_1(a13) | c1_1(a58) | c0_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.69 tff(2934,plain,
% 1.46/1.69 (c3_1(a13)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2933, 726, 26, 37])).
% 1.46/1.69 tff(2935,plain,
% 1.46/1.69 ($false),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[177, 2934, 2923])).
% 1.46/1.69 tff(2936,plain,(c2_1(a58) | c1_1(a58) | c0_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.69 tff(2937,plain,
% 1.46/1.69 (c2_1(a58)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2936, 37, 26])).
% 1.46/1.69 tff(2938,plain,
% 1.46/1.69 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a58)))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2939,plain,
% 1.46/1.69 ((hskp1 | (~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58))) <=> (hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a58)))),
% 1.46/1.69 inference(rewrite,[status(thm)],[])).
% 1.46/1.69 tff(2940,plain,
% 1.46/1.69 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a58))))),
% 1.46/1.69 inference(monotonicity,[status(thm)],[2939])).
% 1.46/1.69 tff(2941,plain,
% 1.46/1.69 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a58)))),
% 1.46/1.69 inference(transitivity,[status(thm)],[2940, 2938])).
% 1.46/1.69 tff(2942,plain,
% 1.46/1.69 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))),
% 1.46/1.69 inference(quant_inst,[status(thm)],[])).
% 1.46/1.69 tff(2943,plain,
% 1.46/1.69 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c1_1(a7)) | (~c2_1(a58))),
% 1.46/1.69 inference(modus_ponens,[status(thm)],[2942, 2941])).
% 1.46/1.69 tff(2944,plain,
% 1.46/1.69 (hskp1 | (~c1_1(a7)) | (~c2_1(a58))),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2943, 101, 2874, 37, 26, 2864, 58])).
% 1.46/1.69 tff(2945,plain,
% 1.46/1.69 (~c1_1(a7)),
% 1.46/1.69 inference(unit_resolution,[status(thm)],[2944, 191, 59])).
% 1.46/1.69 tff(2946,plain,
% 1.46/1.69 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | (~c2_1(a58)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(2947,plain,
% 1.46/1.70 ((hskp2 | (~ndr1_0) | c1_1(a7) | c2_1(a7) | (~c3_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58))) <=> (hskp2 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | (~c2_1(a58)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(2948,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a7) | c2_1(a7) | (~c3_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | (~c2_1(a58))))),
% 1.46/1.70 inference(monotonicity,[status(thm)],[2947])).
% 1.46/1.70 tff(2949,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a7) | c2_1(a7) | (~c3_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | (~c2_1(a58)))),
% 1.46/1.70 inference(transitivity,[status(thm)],[2948, 2946])).
% 1.46/1.70 tff(2950,plain,
% 1.46/1.70 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c1_1(a7) | c2_1(a7) | (~c3_1(a7)) | c0_1(a58) | c1_1(a58) | (~c2_1(a58)))),
% 1.46/1.70 inference(quant_inst,[status(thm)],[])).
% 1.46/1.70 tff(2951,plain,
% 1.46/1.70 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp2 | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | (~c2_1(a58))),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[2950, 2949])).
% 1.46/1.70 tff(2952,plain,
% 1.46/1.70 ($false),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2951, 101, 223, 59, 2874, 37, 26, 2864, 1455, 2945])).
% 1.46/1.70 tff(2953,plain,(hskp1 | (~c2_1(a58)) | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.70 tff(2954,plain,
% 1.46/1.70 (hskp1),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2953, 2937, 37, 26])).
% 1.46/1.70 tff(2955,plain,
% 1.46/1.70 (~c3_1(a2)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[241, 2954])).
% 1.46/1.70 tff(2956,plain,
% 1.46/1.70 (~c2_1(a2)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[247, 2954])).
% 1.46/1.70 tff(2957,plain,
% 1.46/1.70 (~c0_1(a2)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[253, 2954])).
% 1.46/1.70 tff(2958,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(2959,plain,
% 1.46/1.70 ((hskp0 | (~ndr1_0) | c0_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp0 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(2960,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58))))),
% 1.46/1.70 inference(monotonicity,[status(thm)],[2959])).
% 1.46/1.70 tff(2961,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.46/1.70 inference(transitivity,[status(thm)],[2960, 2958])).
% 1.46/1.70 tff(2962,plain,
% 1.46/1.70 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.46/1.70 inference(quant_inst,[status(thm)],[])).
% 1.46/1.70 tff(2963,plain,
% 1.46/1.70 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58))),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[2962, 2961])).
% 1.46/1.70 tff(2964,plain,
% 1.46/1.70 (hskp0 | (~c3_1(a58))),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2963, 101, 2937, 37, 2957, 2956, 2955, 24])).
% 1.46/1.70 tff(2965,plain,
% 1.46/1.70 (~c3_1(a58)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2964, 11])).
% 1.46/1.70 tff(2966,plain,
% 1.46/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)) | c3_1(a58))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(2967,plain,
% 1.46/1.70 (((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a58) | c0_1(a58) | c3_1(a58)) <=> (c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)) | c3_1(a58))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(2968,plain,
% 1.46/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)) | c3_1(a58)))),
% 1.46/1.70 inference(monotonicity,[status(thm)],[2967])).
% 1.46/1.70 tff(2969,plain,
% 1.46/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)) | c3_1(a58))),
% 1.46/1.70 inference(transitivity,[status(thm)],[2968, 2966])).
% 1.46/1.70 tff(2970,plain,
% 1.46/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a7) | (~c3_1(a7)) | (~c1_1(a7)) | c2_1(a7) | (~c0_1(a7)) | (~c1_1(a7)) | c1_1(a58) | c0_1(a58) | c3_1(a58))),
% 1.46/1.70 inference(quant_inst,[status(thm)],[])).
% 1.46/1.70 tff(2971,plain,
% 1.46/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a58) | c1_1(a58) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)) | c3_1(a58)),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[2970, 2969])).
% 1.46/1.70 tff(2972,plain,
% 1.46/1.70 ((~c1_1(a7)) | c3_1(a58)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2971, 101, 2882, 2874, 37, 26, 2864, 36])).
% 1.46/1.70 tff(2973,plain,
% 1.46/1.70 (~c1_1(a7)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2972, 2965])).
% 1.46/1.70 tff(2974,plain,
% 1.46/1.70 (hskp2),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2951, 101, 2937, 2874, 37, 26, 2864, 1455, 2973])).
% 1.46/1.70 tff(2975,plain,
% 1.46/1.70 (~c2_1(a3)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[197, 2974])).
% 1.46/1.70 tff(2976,plain,
% 1.46/1.70 (c3_1(a3)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[205, 2974])).
% 1.46/1.70 tff(2977,plain,
% 1.46/1.70 (c1_1(a3)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[213, 2974])).
% 1.46/1.70 tff(2978,plain,
% 1.46/1.70 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(2979,plain,
% 1.46/1.70 ((hskp28 | hskp0 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3))) <=> (hskp28 | hskp0 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(2980,plain,
% 1.46/1.70 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3))))),
% 1.46/1.70 inference(monotonicity,[status(thm)],[2979])).
% 1.46/1.70 tff(2981,plain,
% 1.46/1.70 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.46/1.70 inference(transitivity,[status(thm)],[2980, 2978])).
% 1.46/1.70 tff(2982,plain,
% 1.46/1.70 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)))),
% 1.46/1.70 inference(quant_inst,[status(thm)],[])).
% 1.46/1.70 tff(2983,plain,
% 1.46/1.70 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp0 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3))),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[2982, 2981])).
% 1.46/1.70 tff(2984,plain,
% 1.46/1.70 (hskp28),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2983, 101, 11, 2977, 2976, 2975, 540])).
% 1.46/1.70 tff(2985,plain,
% 1.46/1.70 (c3_1(a25)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[460, 2984])).
% 1.46/1.70 tff(2986,plain,
% 1.46/1.70 (c1_1(a25)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[468, 2984])).
% 1.46/1.70 tff(2987,plain,
% 1.46/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a7) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | c1_1(a7) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | c1_1(a7) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(2988,plain,
% 1.46/1.70 (((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> (c2_1(a7) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | c1_1(a7) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(2989,plain,
% 1.46/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a7) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | c1_1(a7) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25))))),
% 1.46/1.70 inference(monotonicity,[status(thm)],[2988])).
% 1.46/1.70 tff(2990,plain,
% 1.46/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | c1_1(a7) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.46/1.70 inference(transitivity,[status(thm)],[2989, 2987])).
% 1.46/1.70 tff(2991,plain,
% 1.46/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 1.46/1.70 inference(quant_inst,[status(thm)],[])).
% 1.46/1.70 tff(2992,plain,
% 1.46/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c3_1(a7)) | c1_1(a7) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25))),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[2991, 2990])).
% 1.46/1.70 tff(2993,plain,
% 1.46/1.70 (~c0_1(a25)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2992, 101, 2986, 2985, 2874, 2977, 2976, 2864, 2975, 1676, 2973])).
% 1.46/1.70 tff(2994,plain,
% 1.46/1.70 (c2_1(a25)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[476, 2984])).
% 1.46/1.70 tff(2995,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(2996,plain,
% 1.46/1.70 ((hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(2997,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25)))),
% 1.46/1.70 inference(monotonicity,[status(thm)],[2996])).
% 1.46/1.70 tff(2998,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))),
% 1.46/1.70 inference(transitivity,[status(thm)],[2997, 2995])).
% 1.46/1.70 tff(2999,plain,
% 1.46/1.70 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.46/1.70 inference(quant_inst,[status(thm)],[])).
% 1.46/1.70 tff(3000,plain,
% 1.46/1.70 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25)),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[2999, 2998])).
% 1.46/1.70 tff(3001,plain,
% 1.46/1.70 ($false),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[3000, 101, 11, 2994, 2985, 2957, 2956, 2955, 24, 2993])).
% 1.46/1.70 tff(3002,plain,(hskp0 | c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.70 tff(3003,plain,
% 1.46/1.70 (hskp0),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[3002, 37, 26])).
% 1.46/1.70 tff(3004,plain,
% 1.46/1.70 (~c3_1(a1)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[114, 3003])).
% 1.46/1.70 tff(3005,plain,
% 1.46/1.70 (c1_1(a1)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[130, 3003])).
% 1.46/1.70 tff(3006,plain,
% 1.46/1.70 (c2_1(a1)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[122, 3003])).
% 1.46/1.70 tff(3007,plain,
% 1.46/1.70 (hskp6),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[171, 3006, 3005, 3004])).
% 1.46/1.70 tff(3008,plain,
% 1.46/1.70 (~c3_1(a13)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[177, 3007])).
% 1.46/1.70 tff(3009,plain,
% 1.46/1.70 (~c1_1(a13)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[183, 3007])).
% 1.46/1.70 tff(3010,plain,
% 1.46/1.70 (~c0_1(a13)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[189, 3007])).
% 1.46/1.70 tff(3011,plain,
% 1.46/1.70 (~c1_1(a7)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2931, 101, 2882, 2874, 3010, 3009, 3008, 2864, 36])).
% 1.46/1.70 tff(3012,plain,
% 1.46/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(3013,plain,
% 1.46/1.70 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> (c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(3014,plain,
% 1.46/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7)))),
% 1.46/1.70 inference(monotonicity,[status(thm)],[3013])).
% 1.46/1.70 tff(3015,plain,
% 1.46/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7))),
% 1.46/1.70 inference(transitivity,[status(thm)],[3014, 3012])).
% 1.46/1.70 tff(3016,plain,
% 1.46/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 1.46/1.70 inference(quant_inst,[status(thm)],[])).
% 1.46/1.70 tff(3017,plain,
% 1.46/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7)),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[3016, 3015])).
% 1.46/1.70 tff(3018,plain,
% 1.46/1.70 ($false),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[3017, 101, 2882, 2874, 3005, 3006, 2864, 3004, 264, 3011])).
% 1.46/1.70 tff(3019,plain,(c0_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.70 tff(3020,plain,
% 1.46/1.70 (c0_1(a58)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[3019, 26])).
% 1.46/1.70 tff(3021,plain,
% 1.46/1.70 (((~hskp24) | (~c0_1(a58))) <=> ((~hskp24) | (~c0_1(a58)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(3022,plain,
% 1.46/1.70 (((~c0_1(a58)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a58)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(3023,axiom,((~c0_1(a58)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.46/1.70 tff(3024,plain,
% 1.46/1.70 ((~hskp24) | (~c0_1(a58))),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[3023, 3022])).
% 1.46/1.70 tff(3025,plain,
% 1.46/1.70 ((~hskp24) | (~c0_1(a58))),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[3024, 3021])).
% 1.46/1.70 tff(3026,plain,
% 1.46/1.70 (~hskp24),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[3025, 3020])).
% 1.46/1.70 tff(3027,plain,
% 1.46/1.70 ($false),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[489, 101, 526, 48, 469, 477, 461, 10])).
% 1.46/1.70 tff(3028,plain,((~hskp28) | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.46/1.70 tff(3029,plain,
% 1.46/1.70 (~hskp28),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[3028, 48, 3026])).
% 1.46/1.70 tff(3030,plain,
% 1.46/1.70 (~c2_1(a37)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[529, 101, 526, 48, 641, 633, 10])).
% 1.46/1.70 tff(3031,plain,
% 1.46/1.70 (~hskp28),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[3028, 48, 526])).
% 1.46/1.70 tff(3032,plain,
% 1.46/1.70 ($false),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[543, 101, 3031, 11, 641, 633, 540, 3030])).
% 1.46/1.70 tff(3033,plain,((~hskp20) | hskp0 | hskp24 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.46/1.70 tff(3034,plain,
% 1.46/1.70 (~hskp20),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[3033, 11, 3026, 48])).
% 1.46/1.70 tff(3035,plain,
% 1.46/1.70 (hskp1),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[508, 3034, 3029])).
% 1.46/1.70 tff(3036,plain,
% 1.46/1.70 (~c0_1(a2)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[253, 3035])).
% 1.46/1.70 tff(3037,plain,
% 1.46/1.70 (~c2_1(a2)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[247, 3035])).
% 1.46/1.70 tff(3038,plain,
% 1.46/1.70 (~hskp27),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[585, 11, 3029, 3026, 48])).
% 1.46/1.70 tff(3039,plain,
% 1.46/1.70 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.46/1.70 inference(bind,[status(th)],[])).
% 1.46/1.70 tff(3040,plain,
% 1.46/1.70 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.46/1.70 inference(quant_intro,[status(thm)],[3039])).
% 1.46/1.70 tff(3041,plain,
% 1.46/1.70 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(3042,plain,
% 1.46/1.70 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_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))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_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))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~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))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.46/1.70 inference(bind,[status(th)],[])).
% 1.46/1.70 tff(3043,plain,
% 1.46/1.70 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.46/1.70 inference(quant_intro,[status(thm)],[3042])).
% 1.46/1.70 tff(3044,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 1.46/1.70 tff(3045,plain,
% 1.46/1.70 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[3044, 3043])).
% 1.46/1.70 tff(3046,plain,
% 1.46/1.70 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[3045, 3041])).
% 1.46/1.70 tff(3047,plain,(
% 1.46/1.70 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.46/1.70 inference(skolemize,[status(sab)],[3046])).
% 1.46/1.70 tff(3048,plain,
% 1.46/1.70 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[3047, 3040])).
% 1.46/1.70 tff(3049,plain,
% 1.46/1.70 (hskp13),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[768, 757, 3026])).
% 1.46/1.70 tff(3050,plain,
% 1.46/1.70 (~c3_1(a21)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[774, 3049])).
% 1.46/1.70 tff(3051,plain,
% 1.46/1.70 (c2_1(a21)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[782, 3049])).
% 1.46/1.70 tff(3052,plain,
% 1.46/1.70 (~c2_1(a38)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2399, 588])).
% 1.46/1.70 tff(3053,plain,
% 1.46/1.70 ($false),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[990, 101, 526, 25, 596, 604, 3052, 984])).
% 1.46/1.70 tff(3054,plain,((~hskp21) | hskp24 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.46/1.70 tff(3055,plain,
% 1.46/1.70 (~hskp21),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[3054, 25, 3026])).
% 1.46/1.70 tff(3056,plain,
% 1.46/1.70 (hskp13),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[768, 3055, 3026])).
% 1.46/1.70 tff(3057,plain,
% 1.46/1.70 (~c3_1(a21)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[774, 3056])).
% 1.46/1.70 tff(3058,plain,
% 1.46/1.70 (c2_1(a21)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[782, 3056])).
% 1.46/1.70 tff(3059,plain,
% 1.46/1.70 (c0_1(a21)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[790, 3056])).
% 1.46/1.70 tff(3060,plain,
% 1.46/1.70 (~c1_1(a21)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2423, 101, 25, 3059, 3058, 3057, 141])).
% 1.46/1.70 tff(3061,plain,
% 1.46/1.70 (hskp18),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2647, 101, 3059, 3058, 3057, 2641, 3060])).
% 1.46/1.70 tff(3062,plain,
% 1.46/1.70 (~c3_1(a31)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[385, 3061])).
% 1.46/1.70 tff(3063,plain,
% 1.46/1.70 (c1_1(a31)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[393, 3061])).
% 1.46/1.70 tff(3064,plain,
% 1.46/1.70 (~c2_1(a31)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[2663, 101, 25, 3063, 3059, 3058, 3062, 3057, 141])).
% 1.46/1.70 tff(3065,plain,
% 1.46/1.70 (~c0_1(a31)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[423, 3061])).
% 1.46/1.70 tff(3066,assumption,(~hskp20), introduced(assumption)).
% 1.46/1.70 tff(3067,plain,
% 1.46/1.70 (c3_1(a58)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[669, 3066, 726, 757])).
% 1.46/1.70 tff(3068,plain,
% 1.46/1.70 (c0_1(a21)),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[790, 3049])).
% 1.46/1.70 tff(3069,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(3070,plain,
% 1.46/1.70 ((hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58))) <=> (hskp20 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(3071,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c3_1(a58))))),
% 1.46/1.70 inference(monotonicity,[status(thm)],[3070])).
% 1.46/1.70 tff(3072,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c3_1(a58)))),
% 1.46/1.70 inference(transitivity,[status(thm)],[3071, 3069])).
% 1.46/1.70 tff(3073,plain,
% 1.46/1.70 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))),
% 1.46/1.70 inference(quant_inst,[status(thm)],[])).
% 1.46/1.70 tff(3074,plain,
% 1.46/1.70 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | (~c0_1(a21)) | (~c2_1(a21)) | (~c3_1(a58))),
% 1.46/1.70 inference(modus_ponens,[status(thm)],[3073, 3072])).
% 1.46/1.70 tff(3075,plain,
% 1.46/1.70 (hskp20 | (~c3_1(a58))),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[3074, 101, 3068, 3051, 3020, 26, 3050, 3048])).
% 1.46/1.70 tff(3076,plain,
% 1.46/1.70 ($false),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[3075, 3067, 3066])).
% 1.46/1.70 tff(3077,plain,(hskp20 | c1_1(a58) | c2_1(a58) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.46/1.70 tff(3078,plain,
% 1.46/1.70 (hskp20),
% 1.46/1.70 inference(unit_resolution,[status(thm)],[3077, 3055, 726, 26])).
% 1.46/1.70 tff(3079,assumption,(~c2_1(a31)), introduced(assumption)).
% 1.46/1.70 tff(3080,assumption,(~c3_1(a31)), introduced(assumption)).
% 1.46/1.70 tff(3081,assumption,(~c0_1(a31)), introduced(assumption)).
% 1.46/1.70 tff(3082,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a37) | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c2_1(a37)) | (~c3_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a37) | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c2_1(a37)) | (~c3_1(a37)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(3083,plain,
% 1.46/1.70 ((hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31)) <=> (hskp0 | c0_1(a37) | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c2_1(a37)) | (~c3_1(a37)))),
% 1.46/1.70 inference(rewrite,[status(thm)],[])).
% 1.46/1.70 tff(3084,plain,
% 1.46/1.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a37) | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c2_1(a37)) | (~c3_1(a37))))),
% 1.46/1.71 inference(monotonicity,[status(thm)],[3083])).
% 1.46/1.71 tff(3085,plain,
% 1.46/1.71 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a37) | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c2_1(a37)) | (~c3_1(a37)))),
% 1.46/1.71 inference(transitivity,[status(thm)],[3084, 3082])).
% 1.46/1.71 tff(3086,plain,
% 1.46/1.71 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a37) | (~c2_1(a37)) | (~c3_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31))),
% 1.46/1.71 inference(quant_inst,[status(thm)],[])).
% 1.46/1.71 tff(3087,plain,
% 1.46/1.71 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a37) | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c2_1(a37)) | (~c3_1(a37))),
% 1.46/1.71 inference(modus_ponens,[status(thm)],[3086, 3085])).
% 1.46/1.71 tff(3088,plain,
% 1.46/1.71 (~c2_1(a37)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[3087, 101, 11, 633, 632, 3081, 3080, 24, 3079])).
% 1.46/1.71 tff(3089,plain,
% 1.46/1.71 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.46/1.71 inference(rewrite,[status(thm)],[])).
% 1.46/1.71 tff(3090,plain,
% 1.46/1.71 ((hskp6 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31)) <=> (hskp6 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.46/1.71 inference(rewrite,[status(thm)],[])).
% 1.46/1.71 tff(3091,plain,
% 1.46/1.71 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))))),
% 1.46/1.71 inference(monotonicity,[status(thm)],[3090])).
% 1.46/1.71 tff(3092,plain,
% 1.46/1.71 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.46/1.71 inference(transitivity,[status(thm)],[3091, 3089])).
% 1.46/1.71 tff(3093,plain,
% 1.46/1.71 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c3_1(a31) | c2_1(a31) | c0_1(a31))),
% 1.46/1.71 inference(quant_inst,[status(thm)],[])).
% 1.46/1.71 tff(3094,plain,
% 1.46/1.71 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 1.46/1.71 inference(modus_ponens,[status(thm)],[3093, 3092])).
% 1.46/1.71 tff(3095,plain,
% 1.46/1.71 ($false),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[3094, 101, 25, 641, 633, 3081, 3080, 1238, 3079, 3088])).
% 1.46/1.71 tff(3096,plain,((~hskp20) | hskp6 | c0_1(a31) | c3_1(a31) | c2_1(a31) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.46/1.71 tff(3097,plain,
% 1.46/1.71 (hskp0),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[3096, 3078, 3065, 3062, 3064, 25])).
% 1.46/1.71 tff(3098,plain,
% 1.46/1.71 (~c3_1(a1)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[114, 3097])).
% 1.46/1.71 tff(3099,plain,
% 1.46/1.71 (c1_1(a1)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[130, 3097])).
% 1.46/1.71 tff(3100,plain,
% 1.46/1.71 (c2_1(a1)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[122, 3097])).
% 1.46/1.71 tff(3101,plain,
% 1.46/1.71 ($false),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[171, 3100, 3099, 25, 3098])).
% 1.46/1.71 tff(3102,plain,(hskp6 | c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.46/1.71 tff(3103,plain,
% 1.46/1.71 (hskp6),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[3102, 726, 26])).
% 1.46/1.71 tff(3104,plain,
% 1.46/1.71 (~c3_1(a13)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[177, 3103])).
% 1.46/1.71 tff(3105,plain,
% 1.46/1.71 (~c1_1(a13)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[183, 3103])).
% 1.46/1.71 tff(3106,plain,
% 1.46/1.71 (~c0_1(a13)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[189, 3103])).
% 1.46/1.71 tff(3107,plain,
% 1.46/1.71 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))),
% 1.46/1.71 inference(rewrite,[status(thm)],[])).
% 1.46/1.71 tff(3108,plain,
% 1.46/1.71 ((hskp1 | hskp0 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13)) <=> (hskp1 | hskp0 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))),
% 1.46/1.71 inference(rewrite,[status(thm)],[])).
% 1.46/1.71 tff(3109,plain,
% 1.46/1.71 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0)))),
% 1.46/1.71 inference(monotonicity,[status(thm)],[3108])).
% 1.46/1.71 tff(3110,plain,
% 1.46/1.71 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0))),
% 1.46/1.71 inference(transitivity,[status(thm)],[3109, 3107])).
% 1.46/1.71 tff(3111,plain,
% 1.46/1.71 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp1 | hskp0 | (~ndr1_0) | c3_1(a13) | c1_1(a13) | c0_1(a13))),
% 1.46/1.71 inference(quant_inst,[status(thm)],[])).
% 1.46/1.71 tff(3112,plain,
% 1.46/1.71 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp1 | hskp0 | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0)),
% 1.46/1.71 inference(modus_ponens,[status(thm)],[3111, 3110])).
% 1.46/1.71 tff(3113,plain,
% 1.46/1.71 (hskp1 | hskp0),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[3112, 101, 3106, 3105, 3104, 709])).
% 1.46/1.71 tff(3114,plain,
% 1.46/1.71 (hskp1),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[3113, 11])).
% 1.46/1.71 tff(3115,plain,
% 1.46/1.71 (~c2_1(a2)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[247, 3114])).
% 1.46/1.71 tff(3116,plain,
% 1.46/1.71 (~c0_1(a2)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[253, 3114])).
% 1.46/1.71 tff(3117,plain,
% 1.46/1.71 (~hskp27),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[585, 3029, 11, 3026, 48])).
% 1.46/1.71 tff(3118,plain,
% 1.46/1.71 (~hskp20),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[643, 3029, 12, 3115, 11, 3116])).
% 1.46/1.71 tff(3119,plain,
% 1.46/1.71 (hskp21),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[3077, 3118, 726, 26])).
% 1.46/1.71 tff(3120,plain,
% 1.46/1.71 (~c2_1(a38)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[2399, 3119])).
% 1.46/1.71 tff(3121,plain,
% 1.46/1.71 ($false),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[624, 3120, 3119, 3117, 3115, 12, 3116])).
% 1.46/1.71 tff(3122,plain,(hskp3 | c3_1(a2) | c2_1(a58) | c1_1(a58) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.46/1.71 tff(3123,plain,
% 1.46/1.71 (hskp3),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[3122, 11, 726, 26, 12])).
% 1.46/1.71 tff(3124,plain,
% 1.46/1.71 (~c2_1(a7)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[2863, 3123])).
% 1.46/1.71 tff(3125,plain,
% 1.46/1.71 (c3_1(a7)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[2873, 3123])).
% 1.46/1.71 tff(3126,plain,
% 1.46/1.71 (c0_1(a7)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[2881, 3123])).
% 1.46/1.71 tff(3127,plain,
% 1.46/1.71 (~c1_1(a7)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[2931, 101, 3126, 3125, 3106, 3105, 3104, 3124, 36])).
% 1.46/1.71 tff(3128,plain,
% 1.46/1.71 (hskp13 | c1_1(a7)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[2888, 101, 3026, 3126, 3125, 1914])).
% 1.46/1.71 tff(3129,plain,
% 1.46/1.71 (hskp13),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[3128, 3127])).
% 1.46/1.71 tff(3130,plain,
% 1.46/1.71 (~c3_1(a21)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[774, 3129])).
% 1.46/1.71 tff(3131,plain,
% 1.46/1.71 (c2_1(a21)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[782, 3129])).
% 1.46/1.71 tff(3132,plain,
% 1.46/1.71 (c0_1(a21)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[790, 3129])).
% 1.46/1.71 tff(3133,plain,
% 1.46/1.71 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c3_1(a21) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c0_1(a21)) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c3_1(a21) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.46/1.71 inference(rewrite,[status(thm)],[])).
% 1.46/1.71 tff(3134,plain,
% 1.46/1.71 ((hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7))) <=> (hskp20 | c3_1(a21) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.46/1.71 inference(rewrite,[status(thm)],[])).
% 1.46/1.71 tff(3135,plain,
% 1.46/1.71 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c3_1(a21) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c0_1(a21)) | (~c2_1(a21))))),
% 1.46/1.71 inference(monotonicity,[status(thm)],[3134])).
% 1.46/1.71 tff(3136,plain,
% 1.46/1.71 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c3_1(a21) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.46/1.71 inference(transitivity,[status(thm)],[3135, 3133])).
% 1.46/1.71 tff(3137,plain,
% 1.46/1.71 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a7) | (~c3_1(a7)) | (~c0_1(a7)))),
% 1.46/1.71 inference(quant_inst,[status(thm)],[])).
% 1.46/1.71 tff(3138,plain,
% 1.46/1.71 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c3_1(a21) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c0_1(a21)) | (~c2_1(a21))),
% 1.46/1.71 inference(modus_ponens,[status(thm)],[3137, 3136])).
% 1.46/1.71 tff(3139,plain,
% 1.46/1.71 (hskp20),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[3138, 101, 3132, 3131, 3126, 3125, 3130, 3048, 3127])).
% 1.46/1.71 tff(3140,plain,
% 1.46/1.71 (~c0_1(a37)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[631, 3139])).
% 1.46/1.71 tff(3141,plain,
% 1.46/1.71 (c3_1(a37)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[516, 3139])).
% 1.46/1.71 tff(3142,plain,
% 1.46/1.71 (~c2_1(a37)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[639, 101, 11, 3141, 3140, 3116, 3115, 12, 24])).
% 1.46/1.71 tff(3143,plain,
% 1.46/1.71 (c1_1(a37)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[524, 3139])).
% 1.46/1.71 tff(3144,plain,
% 1.46/1.71 (hskp28),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[643, 3139, 12, 3115, 11, 3116])).
% 1.46/1.71 tff(3145,plain,
% 1.46/1.71 (c3_1(a25)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[460, 3144])).
% 1.46/1.71 tff(3146,plain,
% 1.46/1.71 (c1_1(a25)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[468, 3144])).
% 1.46/1.71 tff(3147,plain,
% 1.46/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.46/1.71 inference(rewrite,[status(thm)],[])).
% 1.46/1.71 tff(3148,plain,
% 1.46/1.71 (((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> (c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.46/1.71 inference(rewrite,[status(thm)],[])).
% 1.46/1.71 tff(3149,plain,
% 1.46/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25))))),
% 1.46/1.71 inference(monotonicity,[status(thm)],[3148])).
% 1.46/1.71 tff(3150,plain,
% 1.46/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)))),
% 1.46/1.71 inference(transitivity,[status(thm)],[3149, 3147])).
% 1.46/1.71 tff(3151,plain,
% 1.46/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 1.46/1.71 inference(quant_inst,[status(thm)],[])).
% 1.46/1.71 tff(3152,plain,
% 1.46/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | c1_1(a7) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c0_1(a25))),
% 1.46/1.71 inference(modus_ponens,[status(thm)],[3151, 3150])).
% 1.46/1.71 tff(3153,plain,
% 1.46/1.71 (~c0_1(a25)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[3152, 101, 3146, 3145, 3143, 3141, 3125, 3124, 1676, 3127, 3142])).
% 1.46/1.71 tff(3154,plain,
% 1.46/1.71 (~c1_1(a21)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[2898, 101, 3131, 3126, 3125, 3130, 3124, 264, 3127])).
% 1.46/1.71 tff(3155,plain,
% 1.46/1.71 (hskp18),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[2647, 101, 3132, 3131, 3130, 2641, 3154])).
% 1.46/1.71 tff(3156,plain,
% 1.46/1.71 (~c3_1(a31)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[385, 3155])).
% 1.46/1.71 tff(3157,plain,
% 1.46/1.71 (c1_1(a31)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[393, 3155])).
% 1.46/1.71 tff(3158,plain,
% 1.46/1.71 (~c2_1(a31)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[2909, 101, 3157, 3126, 3125, 3156, 3124, 264, 3127])).
% 1.46/1.71 tff(3159,plain,
% 1.46/1.71 (~c0_1(a31)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[423, 3155])).
% 1.46/1.71 tff(3160,plain,
% 1.46/1.71 (c2_1(a25)),
% 1.46/1.71 inference(unit_resolution,[status(thm)],[476, 3144])).
% 1.46/1.71 tff(3161,plain,
% 1.46/1.71 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))),
% 1.46/1.71 inference(rewrite,[status(thm)],[])).
% 1.46/1.71 tff(3162,plain,
% 1.46/1.71 ((hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a31) | c2_1(a31) | c0_1(a31)) <=> (hskp0 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3163,plain,
% 1.54/1.71 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3162])).
% 1.54/1.71 tff(3164,plain,
% 1.54/1.71 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3163, 3161])).
% 1.54/1.71 tff(3165,plain,
% 1.54/1.71 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a25) | (~c2_1(a25)) | (~c3_1(a25)) | c3_1(a31) | c2_1(a31) | c0_1(a31))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3166,plain,
% 1.54/1.71 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a31) | c3_1(a31) | (~ndr1_0) | c2_1(a31) | (~c3_1(a25)) | (~c2_1(a25)) | c0_1(a25)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3165, 3164])).
% 1.54/1.71 tff(3167,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3166, 101, 11, 3160, 3145, 3159, 3156, 24, 3158, 3153])).
% 1.54/1.71 tff(3168,plain,(hskp0 | c3_1(a2) | c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3169,plain,
% 1.54/1.71 (hskp0),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3168, 12, 726, 26])).
% 1.54/1.71 tff(3170,plain,
% 1.54/1.71 (~c3_1(a1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[114, 3169])).
% 1.54/1.71 tff(3171,plain,
% 1.54/1.71 (c2_1(a1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[122, 3169])).
% 1.54/1.71 tff(3172,plain,
% 1.54/1.71 (c1_1(a1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[130, 3169])).
% 1.54/1.71 tff(3173,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3174,plain,
% 1.54/1.71 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58))) <=> (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3175,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3174])).
% 1.54/1.71 tff(3176,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3175, 3173])).
% 1.54/1.71 tff(3177,plain,
% 1.54/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3178,plain,
% 1.54/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a58))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3177, 3176])).
% 1.54/1.71 tff(3179,plain,
% 1.54/1.71 (~c3_1(a58)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3178, 101, 726, 3172, 3171, 3020, 26, 3170, 264])).
% 1.54/1.71 tff(3180,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c3_1(a58))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3181,plain,
% 1.54/1.71 (((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a58) | c1_1(a58) | c3_1(a58)) <=> (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c3_1(a58))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3182,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c3_1(a58)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3181])).
% 1.54/1.71 tff(3183,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c3_1(a58))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3182, 3180])).
% 1.54/1.71 tff(3184,plain,
% 1.54/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a58) | c1_1(a58) | c3_1(a58))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3185,plain,
% 1.54/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c3_1(a58)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3184, 3183])).
% 1.54/1.71 tff(3186,plain,
% 1.54/1.71 (c0_1(a1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3185, 101, 726, 3171, 3020, 26, 3170, 323, 3179])).
% 1.54/1.71 tff(3187,assumption,(c0_1(a1)), introduced(assumption)).
% 1.54/1.71 tff(3188,assumption,(hskp3), introduced(assumption)).
% 1.54/1.71 tff(3189,plain,
% 1.54/1.71 (~c2_1(a7)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2863, 3188])).
% 1.54/1.71 tff(3190,plain,
% 1.54/1.71 (c3_1(a7)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2873, 3188])).
% 1.54/1.71 tff(3191,plain,
% 1.54/1.71 (c0_1(a7)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2881, 3188])).
% 1.54/1.71 tff(3192,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3193,plain,
% 1.54/1.71 (((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7))) <=> (c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3194,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3193])).
% 1.54/1.71 tff(3195,plain,
% 1.54/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3194, 3192])).
% 1.54/1.71 tff(3196,plain,
% 1.54/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | (~c1_1(a7)) | (~c0_1(a7)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3197,plain,
% 1.54/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a7) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a7)) | (~c0_1(a7)) | (~c1_1(a7))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3196, 3195])).
% 1.54/1.71 tff(3198,plain,
% 1.54/1.71 (~c1_1(a7)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3197, 101, 3191, 3190, 144, 3189, 142, 901, 3187])).
% 1.54/1.71 tff(3199,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3017, 101, 3191, 3190, 144, 143, 3189, 142, 264, 3198])).
% 1.54/1.71 tff(3200,plain,((~hskp3) | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3201,plain,
% 1.54/1.71 (~hskp3),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3200, 3172, 3171, 3170, 3186])).
% 1.54/1.71 tff(3202,plain,
% 1.54/1.71 (~hskp28),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3028, 3201, 3026])).
% 1.54/1.71 tff(3203,plain,
% 1.54/1.71 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.54/1.71 inference(bind,[status(th)],[])).
% 1.54/1.71 tff(3204,plain,
% 1.54/1.71 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.72 inference(quant_intro,[status(thm)],[3203])).
% 1.54/1.72 tff(3205,plain,
% 1.54/1.72 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3206,plain,
% 1.54/1.72 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(3207,plain,
% 1.54/1.72 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.72 inference(quant_intro,[status(thm)],[3206])).
% 1.54/1.72 tff(3208,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.54/1.72 tff(3209,plain,
% 1.54/1.72 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3208, 3207])).
% 1.54/1.72 tff(3210,plain,
% 1.54/1.72 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3209, 3205])).
% 1.54/1.72 tff(3211,plain,(
% 1.54/1.72 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.72 inference(skolemize,[status(sab)],[3210])).
% 1.54/1.72 tff(3212,plain,
% 1.54/1.72 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3211, 3204])).
% 1.54/1.72 tff(3213,assumption,(c0_1(a2)), introduced(assumption)).
% 1.54/1.72 tff(3214,plain,
% 1.54/1.72 (~hskp1),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[253, 3213])).
% 1.54/1.72 tff(3215,plain,
% 1.54/1.72 (hskp20),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[508, 3214, 3029])).
% 1.54/1.72 tff(3216,plain,
% 1.54/1.72 (c3_1(a37)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[516, 3215])).
% 1.54/1.72 tff(3217,plain,
% 1.54/1.72 (c1_1(a37)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[524, 3215])).
% 1.54/1.72 tff(3218,plain,
% 1.54/1.72 (~c2_1(a37)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[529, 101, 3026, 48, 3217, 3216, 10])).
% 1.54/1.72 tff(3219,plain,
% 1.54/1.72 (hskp2 | hskp1),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[232, 101, 3106, 3105, 3104, 47])).
% 1.54/1.72 tff(3220,plain,
% 1.54/1.72 (hskp2),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3219, 3214])).
% 1.54/1.72 tff(3221,plain,
% 1.54/1.72 (~c2_1(a3)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[197, 3220])).
% 1.54/1.72 tff(3222,plain,
% 1.54/1.72 (c3_1(a3)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[205, 3220])).
% 1.54/1.72 tff(3223,plain,
% 1.54/1.72 (c1_1(a3)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[213, 3220])).
% 1.54/1.72 tff(3224,plain,
% 1.54/1.72 (hskp9),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1218, 101, 3223, 3222, 3172, 3171, 3221, 3170, 827])).
% 1.54/1.72 tff(3225,plain,
% 1.54/1.72 (~c3_1(a16)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[839, 3224])).
% 1.54/1.72 tff(3226,plain,
% 1.54/1.72 (~c0_1(a37)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[631, 3215])).
% 1.54/1.72 tff(3227,plain,
% 1.54/1.72 (c1_1(a16)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[847, 3224])).
% 1.54/1.72 tff(3228,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a16) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3229,plain,
% 1.54/1.72 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37))) <=> (c0_1(a37) | c3_1(a16) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3230,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a16) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3229])).
% 1.54/1.72 tff(3231,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3230, 3228])).
% 1.54/1.72 tff(3232,plain,
% 1.54/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c3_1(a16) | c2_1(a16) | (~c1_1(a16)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3233,plain,
% 1.54/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a16)) | c2_1(a16) | c2_1(a37) | (~c3_1(a37))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3232, 3231])).
% 1.54/1.72 tff(3234,plain,
% 1.54/1.72 (c2_1(a16)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3233, 101, 3216, 3227, 3172, 3171, 3226, 3225, 3170, 680, 3218])).
% 1.54/1.72 tff(3235,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a58))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3236,plain,
% 1.54/1.72 (((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c3_1(a58)) <=> (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a58))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3237,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a58)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3236])).
% 1.54/1.72 tff(3238,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a58))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3237, 3235])).
% 1.54/1.72 tff(3239,plain,
% 1.54/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a58) | c1_1(a58) | c3_1(a58))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3240,plain,
% 1.54/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a58)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3239, 3238])).
% 1.54/1.72 tff(3241,plain,
% 1.54/1.72 (~c2_1(a13)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3240, 101, 726, 3020, 26, 3106, 3104, 323, 3179])).
% 1.54/1.72 tff(3242,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3243,plain,
% 1.54/1.72 (((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_1(a3)) | (~c0_1(a3))) <=> (c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3244,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_1(a3)) | (~c0_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3243])).
% 1.54/1.72 tff(3245,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_1(a3)) | (~c0_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3244, 3242])).
% 1.54/1.72 tff(3246,plain,
% 1.54/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | (~c3_1(a3)) | (~c0_1(a3)) | c2_1(a3) | (~c1_1(a3)) | (~c0_1(a3)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3247,plain,
% 1.54/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | (~c0_1(a3)) | (~c1_1(a3))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3246, 3245])).
% 1.54/1.72 tff(3248,plain,
% 1.54/1.72 (~c0_1(a3)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3247, 101, 3223, 3222, 3172, 3221, 3170, 901, 3186])).
% 1.54/1.72 tff(3249,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3250,plain,
% 1.54/1.72 ((hskp12 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3))) <=> (hskp12 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3251,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3250])).
% 1.54/1.72 tff(3252,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3251, 3249])).
% 1.54/1.72 tff(3253,plain,
% 1.54/1.72 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a3) | c0_1(a3) | (~c3_1(a3)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3254,plain,
% 1.54/1.72 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a3) | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)) | (~c3_1(a3)) | c0_1(a3)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3253, 3252])).
% 1.54/1.72 tff(3255,plain,
% 1.54/1.72 (hskp12),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3254, 101, 3222, 3172, 3221, 3170, 918, 3186, 3248])).
% 1.54/1.72 tff(3256,plain,
% 1.54/1.72 (~c1_1(a20)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[936, 3255])).
% 1.54/1.72 tff(3257,plain,
% 1.54/1.72 (c2_1(a20)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[944, 3255])).
% 1.54/1.72 tff(3258,plain,
% 1.54/1.72 (~c0_1(a20)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1281, 101, 3257, 3227, 3256, 3225, 3106, 3104, 1264, 3241, 3234])).
% 1.54/1.72 tff(3259,plain,
% 1.54/1.72 (~c1_1(a2)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1703, 101, 3222, 3172, 3171, 3221, 13, 12, 3170, 680, 3248])).
% 1.54/1.72 tff(3260,plain,
% 1.54/1.72 (~c3_1(a20)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[930, 3255])).
% 1.54/1.72 tff(3261,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | c1_1(a58) | c3_1(a20) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a20) | (~c2_1(a20)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | c1_1(a58) | c3_1(a20) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a20) | (~c2_1(a20)) | c3_1(a58))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3262,plain,
% 1.54/1.72 (((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a58) | c1_1(a58) | c3_1(a58)) <=> (c2_1(a58) | c1_1(a58) | c3_1(a20) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a20) | (~c2_1(a20)) | c3_1(a58))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3263,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | c1_1(a58) | c3_1(a20) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a20) | (~c2_1(a20)) | c3_1(a58)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3262])).
% 1.54/1.72 tff(3264,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | c1_1(a58) | c3_1(a20) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a20) | (~c2_1(a20)) | c3_1(a58))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3263, 3261])).
% 1.54/1.72 tff(3265,plain,
% 1.54/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a58) | c1_1(a58) | c3_1(a58))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3266,plain,
% 1.54/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | c1_1(a58) | c3_1(a20) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c0_1(a20) | (~c2_1(a20)) | c3_1(a58)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3265, 3264])).
% 1.54/1.72 tff(3267,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3266, 101, 726, 3257, 26, 3260, 3213, 12, 323, 3179, 3259, 3258])).
% 1.54/1.72 tff(3268,plain,((~c0_1(a2)) | c2_1(a58) | c1_1(a58) | c3_1(a2) | c2_1(a2) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3269,plain,
% 1.54/1.72 (~c0_1(a2)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3268, 48, 26, 12, 13, 726])).
% 1.54/1.72 tff(3270,plain,
% 1.54/1.72 (c2_1(a38)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1123, 451, 2460, 526, 444, 698, 12, 14, 13, 48, 2458, 2459])).
% 1.54/1.72 tff(3271,plain,
% 1.54/1.72 (hskp21),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2462, 451, 526, 12, 2457, 13, 14, 444, 698, 48])).
% 1.54/1.72 tff(3272,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2399, 3271, 3270])).
% 1.54/1.72 tff(3273,plain,(c1_1(a15) | hskp24 | c3_1(a2) | (~hskp0) | c2_1(a2) | c0_1(a2) | c3_1(a15) | c2_1(a15) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3274,plain,
% 1.54/1.72 (c1_1(a15)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3273, 698, 12, 3169, 13, 14, 444, 3026, 48])).
% 1.54/1.72 tff(3275,plain,
% 1.54/1.72 (~hskp8),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2088, 3274])).
% 1.54/1.72 tff(3276,plain,
% 1.54/1.72 (hskp8 | hskp7 | c0_1(a2) | c2_1(a2)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1323, 101, 12, 1311])).
% 1.54/1.72 tff(3277,plain,
% 1.54/1.72 (hskp7),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3276, 3275, 14, 13])).
% 1.54/1.72 tff(3278,plain,
% 1.54/1.72 (~c2_1(a14)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1330, 3277])).
% 1.54/1.72 tff(3279,plain,
% 1.54/1.72 (~c0_1(a14)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1352, 3277])).
% 1.54/1.72 tff(3280,plain,
% 1.54/1.72 (c1_1(a14)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1338, 3277])).
% 1.54/1.72 tff(3281,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | (~c1_1(a14)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3282,plain,
% 1.54/1.72 ((hskp9 | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14))) <=> (hskp9 | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | (~c1_1(a14)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3283,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | (~c1_1(a14))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3282])).
% 1.54/1.72 tff(3284,plain,
% 1.54/1.72 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | (~c1_1(a14)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3283, 3281])).
% 1.54/1.72 tff(3285,plain,
% 1.54/1.72 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3286,plain,
% 1.54/1.72 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c0_1(a1)) | (~c1_1(a14))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3285, 3284])).
% 1.54/1.72 tff(3287,plain,
% 1.54/1.72 (hskp9),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3286, 101, 3280, 3172, 3171, 3279, 3278, 3212, 3186])).
% 1.54/1.72 tff(3288,plain,
% 1.54/1.72 (~c3_1(a16)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[839, 3287])).
% 1.54/1.72 tff(3289,plain,
% 1.54/1.72 (c1_1(a16)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[847, 3287])).
% 1.54/1.72 tff(3290,plain,
% 1.54/1.72 (c0_1(a16)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[855, 3287])).
% 1.54/1.72 tff(3291,plain,
% 1.54/1.72 (hskp20),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3077, 757, 726, 26])).
% 1.54/1.72 tff(3292,plain,
% 1.54/1.72 (c3_1(a37)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[516, 3291])).
% 1.54/1.72 tff(3293,plain,
% 1.54/1.72 (c1_1(a37)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[524, 3291])).
% 1.54/1.72 tff(3294,plain,
% 1.54/1.72 (~c2_1(a37)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[529, 101, 3026, 48, 3293, 3292, 10])).
% 1.54/1.72 tff(3295,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3296,plain,
% 1.54/1.72 (((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a13) | c1_1(a13) | c0_1(a13)) <=> (c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3297,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3296])).
% 1.54/1.72 tff(3298,plain,
% 1.54/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3297, 3295])).
% 1.54/1.72 tff(3299,plain,
% 1.54/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a15) | c2_1(a15) | (~c1_1(a15)) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c2_1(a13) | c1_1(a13) | c0_1(a13))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3300,plain,
% 1.54/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a21) | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | c1_1(a21) | (~c2_1(a21))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3299, 3298])).
% 1.54/1.72 tff(3301,plain,
% 1.54/1.72 (c1_1(a21)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3300, 101, 3051, 3050, 2060, 698, 444, 3106, 3105, 362, 334])).
% 1.54/1.72 tff(3302,plain,
% 1.54/1.72 (~c0_1(a37)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[631, 3291])).
% 1.54/1.72 tff(3303,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2216, 101, 3292, 3051, 3302, 3050, 2060, 698, 444, 680, 3301, 3294])).
% 1.54/1.72 tff(3304,plain,(hskp21 | (~c1_1(a15)) | c2_1(a15) | c3_1(a15) | c2_1(a13) | hskp3 | c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3305,plain,
% 1.54/1.72 (hskp21),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3304, 3274, 698, 444, 3241, 48, 726, 26])).
% 1.54/1.72 tff(3306,plain,
% 1.54/1.72 (~c2_1(a38)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2399, 3305])).
% 1.54/1.73 tff(3307,plain,
% 1.54/1.73 (hskp27),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[624, 3306, 3305, 13, 12, 14])).
% 1.54/1.73 tff(3308,plain,
% 1.54/1.73 (c3_1(a12)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[560, 3307])).
% 1.54/1.73 tff(3309,plain,
% 1.54/1.73 (c1_1(a12)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[568, 3307])).
% 1.54/1.73 tff(3310,plain,
% 1.54/1.73 (c0_1(a12)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1114, 3307])).
% 1.54/1.73 tff(3311,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3312,plain,
% 1.54/1.73 ((hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16))) <=> (hskp8 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3313,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3312])).
% 1.54/1.73 tff(3314,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3313, 3311])).
% 1.54/1.73 tff(3315,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a16) | (~c0_1(a16)) | (~c1_1(a16)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3316,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | c3_1(a16) | (~ndr1_0) | (~c1_1(a16)) | (~c0_1(a16)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3315, 3314])).
% 1.54/1.73 tff(3317,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3316, 101, 3275, 3310, 3309, 3308, 3290, 3289, 3288, 2187])).
% 1.54/1.73 tff(3318,plain,(c2_1(a15) | c2_1(a2) | c3_1(a2) | c0_1(a2) | c3_1(a15) | hskp3 | c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3319,plain,
% 1.54/1.73 (c2_1(a15)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3318, 14, 12, 13, 444, 48, 726, 26])).
% 1.54/1.73 tff(3320,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | c3_1(a58))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3321,plain,
% 1.54/1.73 (((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c3_1(a58)) <=> (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | c3_1(a58))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3322,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | c3_1(a58)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3321])).
% 1.54/1.73 tff(3323,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | c3_1(a58))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3322, 3320])).
% 1.54/1.73 tff(3324,plain,
% 1.54/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c0_1(a58)) | c3_1(a15) | c0_1(a15) | (~c2_1(a15)) | c2_1(a58) | c1_1(a58) | c3_1(a58))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3325,plain,
% 1.54/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | (~c2_1(a15)) | c3_1(a15) | (~ndr1_0) | c0_1(a15) | c3_1(a58)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3324, 3323])).
% 1.54/1.73 tff(3326,plain,
% 1.54/1.73 ((~c2_1(a15)) | c0_1(a15)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3325, 101, 726, 3020, 26, 444, 323, 3179])).
% 1.54/1.73 tff(3327,plain,
% 1.54/1.73 (c0_1(a15)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3326, 3319])).
% 1.54/1.73 tff(3328,plain,
% 1.54/1.73 (~hskp8),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1997, 3319])).
% 1.54/1.73 tff(3329,plain,
% 1.54/1.73 (hskp7),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3276, 3328, 14, 13])).
% 1.54/1.73 tff(3330,plain,
% 1.54/1.73 (~c2_1(a14)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1330, 3329])).
% 1.54/1.73 tff(3331,plain,
% 1.54/1.73 (~c0_1(a14)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1352, 3329])).
% 1.54/1.73 tff(3332,plain,
% 1.54/1.73 (c1_1(a15)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1771, 3319, 3171, 3170, 13, 444, 14, 3172, 12])).
% 1.54/1.73 tff(3333,plain,
% 1.54/1.73 (c1_1(a14)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1338, 3329])).
% 1.54/1.73 tff(3334,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c0_1(a15)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3335,plain,
% 1.54/1.73 ((hskp9 | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14))) <=> (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c0_1(a15)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3336,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c0_1(a15))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3335])).
% 1.54/1.73 tff(3337,plain,
% 1.54/1.73 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c0_1(a15)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3336, 3334])).
% 1.54/1.73 tff(3338,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3339,plain,
% 1.54/1.73 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | (~c1_1(a15)) | (~c2_1(a15)) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | (~c0_1(a15))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3338, 3337])).
% 1.54/1.73 tff(3340,plain,
% 1.54/1.73 (hskp9),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3339, 101, 3333, 3332, 3319, 3331, 3330, 3212, 3327])).
% 1.54/1.73 tff(3341,plain,
% 1.54/1.73 (~c3_1(a16)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[839, 3340])).
% 1.54/1.73 tff(3342,plain,
% 1.54/1.73 (c1_1(a16)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[847, 3340])).
% 1.54/1.73 tff(3343,plain,
% 1.54/1.73 (c0_1(a16)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[855, 3340])).
% 1.54/1.73 tff(3344,plain,
% 1.54/1.73 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp10 | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3345,plain,
% 1.54/1.73 ((hskp21 | hskp10 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1))) <=> (hskp21 | hskp10 | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3346,plain,
% 1.54/1.73 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3345])).
% 1.54/1.73 tff(3347,plain,
% 1.54/1.73 (((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)))) <=> ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp10 | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3346, 3344])).
% 1.54/1.73 tff(3348,plain,
% 1.54/1.73 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp21 | hskp10 | (~ndr1_0) | c3_1(a1) | (~c1_1(a1)) | (~c0_1(a1)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3349,plain,
% 1.54/1.73 ((~![U: $i] : (hskp21 | hskp10 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp21 | hskp10 | c3_1(a1) | (~ndr1_0) | (~c1_1(a1)) | (~c0_1(a1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3348, 3347])).
% 1.54/1.73 tff(3350,plain,
% 1.54/1.73 (hskp21 | hskp10 | (~c0_1(a1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3349, 101, 144, 142, 813])).
% 1.54/1.73 tff(3351,plain,
% 1.54/1.73 (hskp10),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3350, 757, 3187])).
% 1.54/1.73 tff(3352,plain,
% 1.54/1.73 (~c1_1(a18)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[868, 3351])).
% 1.54/1.73 tff(3353,plain,
% 1.54/1.73 (~c0_1(a18)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[874, 3351])).
% 1.54/1.73 tff(3354,plain,
% 1.54/1.73 (c3_1(a18)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[962, 3351])).
% 1.54/1.73 tff(3355,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a18) | c1_1(a18) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a18) | c1_1(a18) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c3_1(a18)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3356,plain,
% 1.54/1.73 (((~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18))) <=> (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a18) | c1_1(a18) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c3_1(a18)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3357,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a18) | c1_1(a18) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c3_1(a18))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3356])).
% 1.54/1.73 tff(3358,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a18) | c1_1(a18) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c3_1(a18)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3357, 3355])).
% 1.54/1.73 tff(3359,plain,
% 1.54/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)) | c2_1(a14) | c0_1(a14) | (~c3_1(a14)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3360,plain,
% 1.54/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a58) | (~c0_1(a58)) | c1_1(a58) | c0_1(a18) | c1_1(a18) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c3_1(a14)) | (~c3_1(a18))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3359, 3358])).
% 1.54/1.73 tff(3361,plain,
% 1.54/1.73 (~c3_1(a14)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3360, 101, 726, 3354, 3020, 26, 3353, 3352, 2143, 2142, 697])).
% 1.54/1.73 tff(3362,assumption,(c1_1(a14)), introduced(assumption)).
% 1.54/1.73 tff(3363,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | (~c1_1(a16)) | (~c2_1(a16)) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | (~c1_1(a16)) | (~c2_1(a16)) | c2_1(a37) | (~c3_1(a37)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3364,plain,
% 1.54/1.73 (((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37))) <=> (c0_1(a37) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | (~c1_1(a16)) | (~c2_1(a16)) | c2_1(a37) | (~c3_1(a37)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3365,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | (~c1_1(a16)) | (~c2_1(a16)) | c2_1(a37) | (~c3_1(a37))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3364])).
% 1.54/1.73 tff(3366,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | (~c1_1(a16)) | (~c2_1(a16)) | c2_1(a37) | (~c3_1(a37)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3365, 3363])).
% 1.54/1.73 tff(3367,plain,
% 1.54/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a16) | (~c2_1(a16)) | (~c1_1(a16)) | c3_1(a14) | c2_1(a14) | (~c1_1(a14)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3368,plain,
% 1.54/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c3_1(a16) | c2_1(a14) | (~ndr1_0) | c3_1(a14) | (~c1_1(a14)) | (~c1_1(a16)) | (~c2_1(a16)) | c2_1(a37) | (~c3_1(a37))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3367, 3366])).
% 1.54/1.73 tff(3369,plain,
% 1.54/1.73 (~c2_1(a16)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3368, 101, 3292, 2541, 3362, 3302, 2540, 2142, 680, 3361, 3294])).
% 1.54/1.73 tff(3370,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2529, 101, 3292, 2541, 3302, 2540, 2060, 1749, 444, 680, 3369, 3294])).
% 1.54/1.73 tff(3371,plain,(hskp21 | (~c1_1(a16)) | c3_1(a16) | (~c1_1(a15)) | (~c2_1(a15)) | c3_1(a15) | (~c1_1(a14)) | c2_1(a14) | c2_1(a58) | c1_1(a58) | c0_1(a14) | hskp3 | (~c0_1(a1)) | (~c1_1(a1)) | c3_1(a1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3372,plain,
% 1.54/1.73 (hskp21),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3371, 3342, 3341, 3332, 3319, 444, 3333, 3330, 726, 26, 3331, 48, 3186, 3172, 3170])).
% 1.54/1.73 tff(3373,plain,
% 1.54/1.73 (~c2_1(a38)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2399, 3372])).
% 1.54/1.73 tff(3374,plain,
% 1.54/1.73 (hskp27),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[624, 3373, 3372, 13, 12, 14])).
% 1.54/1.73 tff(3375,plain,
% 1.54/1.73 (c3_1(a12)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[560, 3374])).
% 1.54/1.73 tff(3376,plain,
% 1.54/1.73 (c1_1(a12)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[568, 3374])).
% 1.54/1.73 tff(3377,plain,
% 1.54/1.73 (c0_1(a12)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1114, 3374])).
% 1.54/1.73 tff(3378,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3316, 101, 3328, 3377, 3376, 3375, 3343, 3342, 3341, 2187])).
% 1.54/1.73 tff(3379,plain,(c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a15) | c2_1(a58) | c1_1(a58) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3380,plain,
% 1.54/1.73 (c3_1(a15)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3379, 3269, 12, 13, 726, 26, 48])).
% 1.54/1.73 tff(3381,plain,
% 1.54/1.73 (~hskp8),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1316, 3380])).
% 1.54/1.73 tff(3382,plain,
% 1.54/1.73 (hskp7),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3276, 3381, 3269, 13])).
% 1.54/1.73 tff(3383,plain,
% 1.54/1.73 (~c2_1(a14)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1330, 3382])).
% 1.54/1.73 tff(3384,plain,
% 1.54/1.73 (~c0_1(a14)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1352, 3382])).
% 1.54/1.73 tff(3385,plain,
% 1.54/1.73 (c1_1(a14)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1338, 3382])).
% 1.54/1.73 tff(3386,plain,
% 1.54/1.73 (hskp9),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3286, 101, 3385, 3172, 3171, 3384, 3383, 3212, 3186])).
% 1.54/1.73 tff(3387,plain,
% 1.54/1.73 (~c3_1(a16)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[839, 3386])).
% 1.54/1.73 tff(3388,plain,
% 1.54/1.73 (c1_1(a16)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[847, 3386])).
% 1.54/1.73 tff(3389,plain,
% 1.54/1.73 (c0_1(a16)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[855, 3386])).
% 1.54/1.73 tff(3390,plain,
% 1.54/1.73 (~c3_1(a58)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3178, 101, 726, 144, 143, 3020, 26, 142, 264])).
% 1.54/1.73 tff(3391,plain,
% 1.54/1.73 (c0_1(a1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3185, 101, 726, 143, 3020, 26, 142, 323, 3390])).
% 1.54/1.73 tff(3392,plain,
% 1.54/1.73 (hskp10),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3350, 757, 3391])).
% 1.54/1.73 tff(3393,plain,
% 1.54/1.73 (~c1_1(a18)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[868, 3392])).
% 1.54/1.73 tff(3394,plain,
% 1.54/1.73 (~c0_1(a18)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[874, 3392])).
% 1.54/1.73 tff(3395,plain,
% 1.54/1.73 (c3_1(a18)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[962, 3392])).
% 1.54/1.73 tff(3396,plain,
% 1.54/1.73 (~c3_1(a14)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3360, 101, 726, 3395, 3020, 26, 3394, 3393, 2143, 2142, 697])).
% 1.54/1.73 tff(3397,plain,
% 1.54/1.73 (hskp9),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3286, 101, 3362, 144, 143, 2143, 2142, 3212, 3391])).
% 1.54/1.73 tff(3398,plain,
% 1.54/1.73 (~c3_1(a16)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[839, 3397])).
% 1.54/1.73 tff(3399,plain,
% 1.54/1.73 (c1_1(a16)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[847, 3397])).
% 1.54/1.73 tff(3400,plain,
% 1.54/1.73 (~c2_1(a16)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3368, 101, 3292, 3399, 3362, 3302, 3398, 2142, 680, 3396, 3294])).
% 1.54/1.73 tff(3401,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3233, 101, 3292, 3399, 144, 143, 3302, 3398, 142, 680, 3400, 3294])).
% 1.54/1.73 tff(3402,plain,(hskp21 | (~c1_1(a1)) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a14)) | c2_1(a14) | c2_1(a58) | c1_1(a58) | c0_1(a14) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3403,plain,
% 1.54/1.73 (hskp21),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3402, 3385, 3171, 3170, 3172, 3383, 726, 26, 3384, 48])).
% 1.54/1.73 tff(3404,plain,
% 1.54/1.73 (~c2_1(a38)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2399, 3403])).
% 1.54/1.73 tff(3405,plain,
% 1.54/1.73 (hskp27),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[624, 3404, 3403, 13, 12, 3269])).
% 1.54/1.73 tff(3406,plain,
% 1.54/1.73 (c3_1(a12)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[560, 3405])).
% 1.54/1.73 tff(3407,plain,
% 1.54/1.73 (c1_1(a12)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[568, 3405])).
% 1.54/1.73 tff(3408,plain,
% 1.54/1.73 (c0_1(a12)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1114, 3405])).
% 1.54/1.73 tff(3409,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3316, 101, 3381, 3408, 3407, 3406, 3389, 3388, 3387, 2187])).
% 1.54/1.73 tff(3410,plain,(hskp3 | c2_1(a2) | c3_1(a2) | c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3411,plain,
% 1.54/1.73 (c2_1(a2)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3410, 3201, 12, 726, 26])).
% 1.54/1.73 tff(3412,plain,
% 1.54/1.73 (~hskp1),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[247, 3411])).
% 1.54/1.73 tff(3413,plain,
% 1.54/1.73 (hskp20),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[508, 3412, 3202])).
% 1.54/1.73 tff(3414,plain,
% 1.54/1.73 (c3_1(a37)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[516, 3413])).
% 1.54/1.73 tff(3415,plain,
% 1.54/1.73 (c1_1(a37)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[524, 3413])).
% 1.54/1.73 tff(3416,plain,
% 1.54/1.73 (~c2_1(a37)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[529, 101, 3026, 3201, 3415, 3414, 10])).
% 1.54/1.73 tff(3417,plain,
% 1.54/1.73 (hskp2),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3219, 3412])).
% 1.54/1.73 tff(3418,plain,
% 1.54/1.73 (~c2_1(a3)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[197, 3417])).
% 1.54/1.73 tff(3419,plain,
% 1.54/1.73 (c3_1(a3)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[205, 3417])).
% 1.54/1.73 tff(3420,plain,
% 1.54/1.73 (c1_1(a3)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[213, 3417])).
% 1.54/1.73 tff(3421,plain,
% 1.54/1.73 (~c0_1(a3)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3247, 101, 3420, 3419, 3172, 3418, 3170, 901, 3186])).
% 1.54/1.73 tff(3422,plain,
% 1.54/1.73 (^[U: $i] : refl((hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))),
% 1.54/1.73 inference(bind,[status(th)],[])).
% 1.54/1.73 tff(3423,plain,
% 1.54/1.73 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.54/1.73 inference(quant_intro,[status(thm)],[3422])).
% 1.54/1.73 tff(3424,plain,
% 1.54/1.73 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3425,plain,
% 1.54/1.73 (^[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) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp7) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp7) <=> (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp7) <=> (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))))),
% 1.54/1.73 inference(bind,[status(th)],[])).
% 1.54/1.73 tff(3426,plain,
% 1.54/1.73 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp7) <=> ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.54/1.73 inference(quant_intro,[status(thm)],[3425])).
% 1.54/1.73 tff(3427,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 1.54/1.73 tff(3428,plain,
% 1.54/1.73 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3427, 3426])).
% 1.54/1.73 tff(3429,plain,
% 1.54/1.73 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3428, 3424])).
% 1.54/1.73 tff(3430,plain,(
% 1.54/1.73 ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.54/1.73 inference(skolemize,[status(sab)],[3429])).
% 1.54/1.73 tff(3431,plain,
% 1.54/1.73 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3430, 3423])).
% 1.54/1.73 tff(3432,plain,
% 1.54/1.73 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp7 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp7 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3433,plain,
% 1.54/1.73 ((hskp28 | hskp7 | (~ndr1_0) | c0_1(a3) | c2_1(a3) | (~c3_1(a3))) <=> (hskp28 | hskp7 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3434,plain,
% 1.54/1.73 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp7 | (~ndr1_0) | c0_1(a3) | c2_1(a3) | (~c3_1(a3)))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp7 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3433])).
% 1.54/1.73 tff(3435,plain,
% 1.54/1.73 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp7 | (~ndr1_0) | c0_1(a3) | c2_1(a3) | (~c3_1(a3)))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp7 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3434, 3432])).
% 1.54/1.73 tff(3436,plain,
% 1.54/1.73 ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp7 | (~ndr1_0) | c0_1(a3) | c2_1(a3) | (~c3_1(a3)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3437,plain,
% 1.54/1.73 ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp7 | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | c0_1(a3)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3436, 3435])).
% 1.54/1.73 tff(3438,plain,
% 1.54/1.73 (hskp7),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3437, 101, 3202, 3419, 3418, 3431, 3421])).
% 1.54/1.73 tff(3439,plain,
% 1.54/1.73 (~c0_1(a14)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1352, 3438])).
% 1.54/1.73 tff(3440,plain,
% 1.54/1.73 (~c2_1(a14)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1330, 3438])).
% 1.54/1.73 tff(3441,plain,
% 1.54/1.73 (c1_1(a14)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1338, 3438])).
% 1.54/1.73 tff(3442,plain,
% 1.54/1.73 (hskp21),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3402, 3441, 3171, 3170, 3172, 3440, 726, 26, 3439, 3201])).
% 1.54/1.73 tff(3443,plain,
% 1.54/1.73 (~c2_1(a38)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2399, 3442])).
% 1.54/1.73 tff(3444,plain,
% 1.54/1.73 (c1_1(a38)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[603, 3442])).
% 1.54/1.73 tff(3445,plain,
% 1.54/1.73 (c0_1(a38)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[595, 3442])).
% 1.54/1.73 tff(3446,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3447,plain,
% 1.54/1.73 (((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3448,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c0_1(a38)) | (~c1_1(a38))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3447])).
% 1.54/1.73 tff(3449,plain,
% 1.54/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3448, 3446])).
% 1.54/1.73 tff(3450,plain,
% 1.54/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3451,plain,
% 1.54/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | (~c0_1(a38)) | (~c1_1(a38))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3450, 3449])).
% 1.54/1.73 tff(3452,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3451, 101, 3445, 3444, 3415, 3414, 3443, 3106, 3105, 3104, 36, 3416])).
% 1.54/1.73 tff(3453,plain,(c3_1(a2) | c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3454,plain,
% 1.54/1.74 (c3_1(a2)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3453, 726, 26])).
% 1.54/1.74 tff(3455,plain,
% 1.54/1.74 (~hskp1),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[241, 3454])).
% 1.54/1.74 tff(3456,plain,
% 1.54/1.74 (hskp2),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3219, 3455])).
% 1.54/1.74 tff(3457,plain,
% 1.54/1.74 (~c2_1(a3)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[197, 3456])).
% 1.54/1.74 tff(3458,plain,
% 1.54/1.74 (hskp0),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3113, 3455])).
% 1.54/1.74 tff(3459,plain,
% 1.54/1.74 (c1_1(a1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[130, 3458])).
% 1.54/1.74 tff(3460,plain,
% 1.54/1.74 (~c3_1(a1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[114, 3458])).
% 1.54/1.74 tff(3461,plain,
% 1.54/1.74 (c2_1(a1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[122, 3458])).
% 1.54/1.74 tff(3462,plain,
% 1.54/1.74 (~c3_1(a58)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3178, 101, 726, 3459, 3461, 3020, 26, 3460, 264])).
% 1.54/1.74 tff(3463,plain,
% 1.54/1.74 (c0_1(a1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3185, 101, 726, 3461, 3020, 26, 3460, 323, 3462])).
% 1.54/1.74 tff(3464,plain,
% 1.54/1.74 (~hskp3),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3200, 3463, 3461, 3460, 3459])).
% 1.54/1.74 tff(3465,plain,
% 1.54/1.74 (c3_1(a3)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[205, 3456])).
% 1.54/1.74 tff(3466,plain,
% 1.54/1.74 (c1_1(a3)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[213, 3456])).
% 1.54/1.74 tff(3467,plain,
% 1.54/1.74 (~c0_1(a3)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1954, 101, 3466, 3465, 3106, 3105, 3104, 3457, 36])).
% 1.54/1.74 tff(3468,plain,
% 1.54/1.74 (~hskp28),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3028, 3464, 3026])).
% 1.54/1.74 tff(3469,plain,
% 1.54/1.74 (hskp28 | hskp7 | c0_1(a3)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3437, 101, 3465, 3457, 3431])).
% 1.54/1.74 tff(3470,plain,
% 1.54/1.74 (hskp7),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3469, 3468, 3467])).
% 1.54/1.74 tff(3471,plain,
% 1.54/1.74 (~c0_1(a14)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1352, 3470])).
% 1.54/1.74 tff(3472,plain,
% 1.54/1.74 (~c2_1(a14)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1330, 3470])).
% 1.54/1.74 tff(3473,plain,
% 1.54/1.74 (c1_1(a14)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1338, 3470])).
% 1.54/1.74 tff(3474,plain,
% 1.54/1.74 (hskp21),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3402, 3473, 3461, 3460, 3459, 3472, 726, 26, 3471, 3464])).
% 1.54/1.74 tff(3475,plain,
% 1.54/1.74 (~c2_1(a38)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2399, 3474])).
% 1.54/1.74 tff(3476,plain,
% 1.54/1.74 (c1_1(a38)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[603, 3474])).
% 1.54/1.74 tff(3477,plain,
% 1.54/1.74 (c0_1(a38)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[595, 3474])).
% 1.54/1.74 tff(3478,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3479,plain,
% 1.54/1.74 (((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3480,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a38)) | (~c1_1(a38))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3479])).
% 1.54/1.74 tff(3481,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3480, 3478])).
% 1.54/1.74 tff(3482,plain,
% 1.54/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a3) | (~c3_1(a3)) | (~c1_1(a3)) | c2_1(a38) | (~c0_1(a38)) | (~c1_1(a38)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3483,plain,
% 1.54/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a38) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c3_1(a3)) | (~c1_1(a3)) | (~c0_1(a38)) | (~c1_1(a38))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3482, 3481])).
% 1.54/1.74 tff(3484,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3483, 101, 3477, 3476, 3466, 3465, 3475, 3106, 3105, 3104, 3457, 36])).
% 1.54/1.74 tff(3485,plain,(c2_1(a58) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3486,plain,
% 1.54/1.74 (c2_1(a58)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3485, 26])).
% 1.54/1.74 tff(3487,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a58)) | c1_1(a58) | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a58)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3488,plain,
% 1.54/1.74 (((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> ((~c0_1(a58)) | c1_1(a58) | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a58)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3489,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a58)) | c1_1(a58) | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a58))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3488])).
% 1.54/1.74 tff(3490,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a58)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3489, 3487])).
% 1.54/1.74 tff(3491,plain,
% 1.54/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c1_1(a21)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3492,plain,
% 1.54/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a21)) | (~c2_1(a21)) | (~c2_1(a58))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3491, 3490])).
% 1.54/1.74 tff(3493,plain,
% 1.54/1.74 (c0_1(a2) | (~c1_1(a21))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3492, 101, 3486, 3051, 3020, 26, 3050, 13, 12, 1264])).
% 1.54/1.74 tff(3494,plain,
% 1.54/1.74 (~c1_1(a21)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3493, 14])).
% 1.54/1.74 tff(3495,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3496,plain,
% 1.54/1.74 ((hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp5 | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3497,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3496])).
% 1.54/1.74 tff(3498,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3497, 3495])).
% 1.54/1.74 tff(3499,plain,
% 1.54/1.74 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3500,plain,
% 1.54/1.74 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c3_1(a21) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3499, 3498])).
% 1.54/1.74 tff(3501,plain,
% 1.54/1.74 (hskp5 | c0_1(a2) | c1_1(a21)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3500, 101, 3051, 3050, 13, 12, 275])).
% 1.54/1.74 tff(3502,plain,
% 1.54/1.74 (hskp5),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3501, 14, 3494])).
% 1.54/1.74 tff(3503,plain,
% 1.54/1.74 (~c1_1(a11)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[297, 3502])).
% 1.54/1.74 tff(3504,plain,
% 1.54/1.74 (c0_1(a11)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[305, 3502])).
% 1.54/1.74 tff(3505,plain,
% 1.54/1.74 (~hskp20),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[643, 14, 12, 11, 577, 13])).
% 1.54/1.74 tff(3506,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c3_1(a21) | c1_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c0_1(a21)) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c3_1(a21) | c1_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3507,plain,
% 1.54/1.74 ((hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a11) | (~c3_1(a11)) | (~c0_1(a11))) <=> (hskp20 | c3_1(a21) | c1_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3508,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a11) | (~c3_1(a11)) | (~c0_1(a11)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c3_1(a21) | c1_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c0_1(a21)) | (~c2_1(a21))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3507])).
% 1.54/1.74 tff(3509,plain,
% 1.54/1.74 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a11) | (~c3_1(a11)) | (~c0_1(a11)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c3_1(a21) | c1_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3508, 3506])).
% 1.54/1.74 tff(3510,plain,
% 1.54/1.74 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c1_1(a11) | (~c3_1(a11)) | (~c0_1(a11)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3511,plain,
% 1.54/1.74 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c3_1(a21) | c1_1(a11) | (~ndr1_0) | (~c3_1(a11)) | (~c0_1(a11)) | (~c0_1(a21)) | (~c2_1(a21))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3510, 3509])).
% 1.54/1.74 tff(3512,plain,
% 1.54/1.74 (~c3_1(a11)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3511, 101, 3505, 3068, 3051, 3504, 3050, 3503, 3048])).
% 1.54/1.74 tff(3513,plain,
% 1.54/1.74 (~c2_1(a11)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[291, 3502])).
% 1.54/1.74 tff(3514,plain,
% 1.54/1.74 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3515,plain,
% 1.54/1.74 ((hskp21 | hskp20 | (~ndr1_0) | c3_1(a11) | c1_1(a11) | c2_1(a11)) <=> (hskp21 | hskp20 | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3516,plain,
% 1.54/1.74 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a11) | c1_1(a11) | c2_1(a11))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11)))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3515])).
% 1.54/1.74 tff(3517,plain,
% 1.54/1.74 (((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a11) | c1_1(a11) | c2_1(a11))) <=> ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3516, 3514])).
% 1.54/1.74 tff(3518,plain,
% 1.54/1.74 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp21 | hskp20 | (~ndr1_0) | c3_1(a11) | c1_1(a11) | c2_1(a11))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3519,plain,
% 1.54/1.74 ((~![U: $i] : (hskp21 | hskp20 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp21 | hskp20 | c1_1(a11) | c2_1(a11) | (~ndr1_0) | c3_1(a11)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3518, 3517])).
% 1.54/1.74 tff(3520,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3519, 101, 757, 3505, 3503, 3513, 654, 3512])).
% 1.54/1.74 tff(3521,plain,(c0_1(a2) | hskp21 | c2_1(a2) | c3_1(a2) | c1_1(a58) | hskp0 | hskp28), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3522,plain,
% 1.54/1.74 (hskp21),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3521, 3036, 3037, 12, 26, 11, 3029])).
% 1.54/1.74 tff(3523,plain,
% 1.54/1.74 (~c2_1(a38)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2399, 3522])).
% 1.54/1.74 tff(3524,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[624, 3523, 3522, 3038, 3037, 12, 3036])).
% 1.54/1.74 tff(3525,plain,(hskp0 | c3_1(a2) | c1_1(a58) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(3526,plain,
% 1.54/1.74 (hskp0),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3525, 12, 26, 48])).
% 1.54/1.74 tff(3527,plain,
% 1.54/1.74 (~c3_1(a1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[114, 3526])).
% 1.54/1.74 tff(3528,plain,
% 1.54/1.74 (c2_1(a1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[122, 3526])).
% 1.54/1.74 tff(3529,plain,
% 1.54/1.74 (c1_1(a1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[130, 3526])).
% 1.54/1.74 tff(3530,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a58)) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a58)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3531,plain,
% 1.54/1.74 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> ((~c0_1(a58)) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a58)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3532,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a58)) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a58))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3531])).
% 1.54/1.74 tff(3533,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a58)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3532, 3530])).
% 1.54/1.74 tff(3534,plain,
% 1.54/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3535,plain,
% 1.54/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a58))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 1.54/1.74 tff(3536,plain,
% 1.54/1.74 (c0_1(a2)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3535, 101, 3486, 3529, 3528, 3020, 26, 13, 12, 3527, 1264])).
% 1.54/1.74 tff(3537,plain,
% 1.54/1.74 (~hskp1),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[253, 3536])).
% 1.54/1.74 tff(3538,plain,
% 1.54/1.74 (hskp20),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[508, 3537, 3029])).
% 1.54/1.74 tff(3539,plain,
% 1.54/1.74 (c3_1(a37)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[516, 3538])).
% 1.54/1.74 tff(3540,plain,
% 1.54/1.74 (c1_1(a37)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[524, 3538])).
% 1.54/1.74 tff(3541,plain,
% 1.54/1.74 (~c2_1(a37)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[529, 101, 3026, 48, 3540, 3539, 10])).
% 1.54/1.74 tff(3542,plain,
% 1.54/1.74 (hskp6),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[171, 3528, 3529, 3527])).
% 1.54/1.74 tff(3543,plain,
% 1.54/1.74 (~c3_1(a13)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[177, 3542])).
% 1.54/1.74 tff(3544,plain,
% 1.54/1.74 (~c1_1(a13)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[183, 3542])).
% 1.54/1.74 tff(3545,plain,
% 1.54/1.74 (~c0_1(a13)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[189, 3542])).
% 1.54/1.74 tff(3546,plain,
% 1.54/1.74 (hskp2 | hskp1),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[232, 101, 3545, 3544, 3543, 47])).
% 1.54/1.74 tff(3547,plain,
% 1.54/1.74 (hskp2),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3546, 3537])).
% 1.54/1.74 tff(3548,plain,
% 1.54/1.74 (~c2_1(a3)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[197, 3547])).
% 1.54/1.74 tff(3549,plain,
% 1.54/1.74 (c3_1(a3)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[205, 3547])).
% 1.54/1.74 tff(3550,plain,
% 1.54/1.74 (c1_1(a3)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[213, 3547])).
% 1.54/1.74 tff(3551,plain,
% 1.54/1.74 (~c1_1(a2)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1805, 101, 3550, 3549, 3545, 3544, 3543, 3548, 3536, 13, 36])).
% 1.54/1.74 tff(3552,plain,
% 1.54/1.74 (~c0_1(a3)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1954, 101, 3550, 3549, 3545, 3544, 3543, 3548, 36])).
% 1.54/1.74 tff(3553,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a58) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a58) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3554,plain,
% 1.54/1.74 (((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3))) <=> (c1_1(a58) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3555,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a58) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c2_1(a58)) | (~c3_1(a58))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3554])).
% 1.54/1.74 tff(3556,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a58) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c2_1(a58)) | (~c3_1(a58)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3555, 3553])).
% 1.54/1.74 tff(3557,plain,
% 1.54/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a2) | c2_1(a2) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a3) | c0_1(a3) | (~c1_1(a3)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3558,plain,
% 1.54/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a58) | c2_1(a3) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c0_1(a3) | (~c1_1(a3)) | (~c2_1(a58)) | (~c3_1(a58))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3557, 3556])).
% 1.54/1.74 tff(3559,plain,
% 1.54/1.74 (c0_1(a3) | (~c3_1(a58))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3558, 101, 3486, 3550, 26, 3548, 3536, 13, 12, 1965])).
% 1.54/1.74 tff(3560,plain,
% 1.54/1.74 (~c3_1(a58)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3559, 3552])).
% 1.54/1.74 tff(3561,plain,
% 1.54/1.74 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3562,plain,
% 1.54/1.74 ((hskp10 | hskp1 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58))) <=> (hskp10 | hskp1 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3563,plain,
% 1.54/1.74 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3562])).
% 1.54/1.74 tff(3564,plain,
% 1.54/1.74 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 1.54/1.74 inference(transitivity,[status(thm)],[3563, 3561])).
% 1.54/1.74 tff(3565,plain,
% 1.54/1.74 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a58) | c1_1(a58) | (~c2_1(a58)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(3566,plain,
% 1.54/1.74 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[3565, 3564])).
% 1.54/1.74 tff(3567,plain,
% 1.54/1.74 (hskp10 | hskp1 | (~c2_1(a58)) | c3_1(a58)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3566, 101, 26, 1786])).
% 1.54/1.74 tff(3568,plain,
% 1.54/1.74 (hskp10),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3567, 3560, 3486, 3537])).
% 1.54/1.74 tff(3569,plain,
% 1.54/1.74 (~c1_1(a18)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[868, 3568])).
% 1.54/1.74 tff(3570,plain,
% 1.54/1.74 (~c0_1(a18)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[874, 3568])).
% 1.54/1.74 tff(3571,plain,
% 1.54/1.74 (~c0_1(a37)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[631, 3538])).
% 1.54/1.74 tff(3572,plain,
% 1.54/1.74 (c3_1(a18)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[962, 3568])).
% 1.54/1.74 tff(3573,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c0_1(a18) | c1_1(a18) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c0_1(a18) | c1_1(a18) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3574,plain,
% 1.54/1.74 (((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18))) <=> (c0_1(a37) | c0_1(a18) | c1_1(a18) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(3575,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a37) | c0_1(a18) | c1_1(a18) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[3574])).
% 1.54/1.74 tff(3576,plain,
% 1.54/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c0_1(a18) | c1_1(a18) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3575, 3573])).
% 1.54/1.75 tff(3577,plain,
% 1.54/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)) | c2_1(a37) | c0_1(a37) | (~c3_1(a37)) | c1_1(a18) | c0_1(a18) | (~c3_1(a18)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3578,plain,
% 1.54/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a37) | c0_1(a18) | c1_1(a18) | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a18)) | c2_1(a37) | (~c3_1(a37))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3577, 3576])).
% 1.54/1.75 tff(3579,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3578, 101, 3539, 3572, 3571, 3570, 3569, 3536, 13, 697, 3551, 3541])).
% 1.54/1.75 tff(3580,plain,(c2_1(a2) | c1_1(a58) | c3_1(a2) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3581,plain,
% 1.54/1.75 (c2_1(a2)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3580, 12, 26, 48])).
% 1.54/1.75 tff(3582,plain,
% 1.54/1.75 (~hskp1),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[247, 3581])).
% 1.54/1.75 tff(3583,plain,
% 1.54/1.75 (hskp2),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3546, 3582])).
% 1.54/1.75 tff(3584,plain,
% 1.54/1.75 (~c2_1(a3)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[197, 3583])).
% 1.54/1.75 tff(3585,plain,
% 1.54/1.75 (c3_1(a3)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[205, 3583])).
% 1.54/1.75 tff(3586,plain,
% 1.54/1.75 (c1_1(a3)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[213, 3583])).
% 1.54/1.75 tff(3587,plain,
% 1.54/1.75 (~c2_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1253, 101, 3582, 3586, 3585, 3545, 3544, 3584, 58])).
% 1.54/1.75 tff(3588,plain,
% 1.54/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a13) | (~c2_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a13) | (~c2_1(a58)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3589,plain,
% 1.54/1.75 (((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a13) | c0_1(a13) | c3_1(a13)) <=> ((~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a13) | (~c2_1(a58)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3590,plain,
% 1.54/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a13) | (~c2_1(a58))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3589])).
% 1.54/1.75 tff(3591,plain,
% 1.54/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a13) | (~c2_1(a58)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3590, 3588])).
% 1.54/1.75 tff(3592,plain,
% 1.54/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3593,plain,
% 1.54/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (~c0_1(a58)) | c1_1(a58) | c0_1(a13) | c3_1(a13) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c2_1(a13) | (~c2_1(a58))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3592, 3591])).
% 1.54/1.75 tff(3594,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3593, 101, 3486, 3529, 3528, 3020, 26, 3545, 3543, 3527, 1264, 3587])).
% 1.54/1.75 tff(3595,plain,(c3_1(a2) | c1_1(a58) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3596,plain,
% 1.54/1.75 (c3_1(a2)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3595, 48, 26])).
% 1.54/1.75 tff(3597,plain,
% 1.54/1.75 (~hskp1),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[241, 3596])).
% 1.54/1.75 tff(3598,plain,
% 1.54/1.75 (hskp20),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[508, 3597, 3029])).
% 1.54/1.75 tff(3599,plain,
% 1.54/1.75 (c3_1(a37)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[516, 3598])).
% 1.54/1.75 tff(3600,plain,
% 1.54/1.75 (c1_1(a37)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[524, 3598])).
% 1.54/1.75 tff(3601,plain,
% 1.54/1.75 (~c2_1(a37)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[529, 101, 3026, 48, 3600, 3599, 10])).
% 1.54/1.75 tff(3602,plain,
% 1.54/1.75 (hskp0),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3033, 3598, 3026, 48])).
% 1.54/1.75 tff(3603,plain,
% 1.54/1.75 (~c3_1(a1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[114, 3602])).
% 1.54/1.75 tff(3604,plain,
% 1.54/1.75 (c1_1(a1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[130, 3602])).
% 1.54/1.75 tff(3605,plain,
% 1.54/1.75 (c2_1(a1)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[122, 3602])).
% 1.54/1.75 tff(3606,plain,
% 1.54/1.75 (hskp6),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[171, 3605, 3604, 3603])).
% 1.54/1.75 tff(3607,plain,
% 1.54/1.75 (~c1_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[183, 3606])).
% 1.54/1.75 tff(3608,plain,
% 1.54/1.75 (~c0_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[189, 3606])).
% 1.54/1.75 tff(3609,plain,
% 1.54/1.75 (~c2_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[890, 101, 3597, 3600, 3599, 3608, 3607, 58, 3601])).
% 1.54/1.75 tff(3610,plain,
% 1.54/1.75 (~c3_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[177, 3606])).
% 1.54/1.75 tff(3611,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3593, 101, 3486, 3604, 3605, 3020, 26, 3608, 3610, 3603, 1264, 3609])).
% 1.54/1.75 tff(3612,plain,(hskp3 | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3613,plain,
% 1.54/1.75 (hskp3),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3612, 26])).
% 1.54/1.75 tff(3614,plain,
% 1.54/1.75 (~c2_1(a7)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2863, 3613])).
% 1.54/1.75 tff(3615,plain,
% 1.54/1.75 (c3_1(a7)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2873, 3613])).
% 1.54/1.75 tff(3616,plain,
% 1.54/1.75 (c0_1(a7)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2881, 3613])).
% 1.54/1.75 tff(3617,plain,
% 1.54/1.75 (hskp6),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3054, 588, 526])).
% 1.54/1.75 tff(3618,plain,
% 1.54/1.75 (~c3_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[177, 3617])).
% 1.54/1.75 tff(3619,plain,
% 1.54/1.75 (~c1_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[183, 3617])).
% 1.54/1.75 tff(3620,plain,
% 1.54/1.75 (~c0_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[189, 3617])).
% 1.54/1.75 tff(3621,plain,
% 1.54/1.75 (~c3_1(a38)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1001, 101, 596, 604, 3052, 3620, 3619, 3618, 36])).
% 1.54/1.75 tff(3622,assumption,(~c2_1(a7)), introduced(assumption)).
% 1.54/1.75 tff(3623,assumption,(c3_1(a7)), introduced(assumption)).
% 1.54/1.75 tff(3624,assumption,(c0_1(a7)), introduced(assumption)).
% 1.54/1.75 tff(3625,plain,
% 1.54/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a38) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a38) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3626,plain,
% 1.54/1.75 (((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38))) <=> (c2_1(a38) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3627,plain,
% 1.54/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a38) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3626])).
% 1.54/1.75 tff(3628,plain,
% 1.54/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a38) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3627, 3625])).
% 1.54/1.75 tff(3629,plain,
% 1.54/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a38) | (~c1_1(a38)) | (~c0_1(a38)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a38) | (~c1_1(a38)) | (~c0_1(a38)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3630,plain,
% 1.54/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a38) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c3_1(a38) | (~c0_1(a38)) | (~c1_1(a38))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3629, 3628])).
% 1.54/1.75 tff(3631,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3630, 101, 596, 604, 3624, 3623, 3052, 3622, 901, 3621])).
% 1.54/1.75 tff(3632,plain,((~hskp21) | (~c0_1(a7)) | (~c3_1(a7)) | c2_1(a7) | hskp24), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3633,plain,
% 1.54/1.75 (~hskp21),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3632, 3616, 3615, 3614, 3026])).
% 1.54/1.75 tff(3634,plain,
% 1.54/1.75 (hskp13),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[768, 3633, 3026])).
% 1.54/1.75 tff(3635,plain,
% 1.54/1.75 (c0_1(a21)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[790, 3634])).
% 1.54/1.75 tff(3636,plain,
% 1.54/1.75 (hskp6),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[171, 2460, 2459, 2458])).
% 1.54/1.75 tff(3637,plain,
% 1.54/1.75 (~c3_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[177, 3636])).
% 1.54/1.75 tff(3638,plain,
% 1.54/1.75 (~c1_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[183, 3636])).
% 1.54/1.75 tff(3639,plain,
% 1.54/1.75 (~c0_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[189, 3636])).
% 1.54/1.75 tff(3640,plain,
% 1.54/1.75 (~c1_1(a7)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2931, 101, 3624, 3623, 3639, 3638, 3637, 3622, 36])).
% 1.54/1.75 tff(3641,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3017, 101, 3624, 3623, 2459, 2460, 3622, 2458, 264, 3640])).
% 1.54/1.75 tff(3642,plain,((~hskp0) | (~c0_1(a7)) | (~c3_1(a7)) | c2_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3643,plain,
% 1.54/1.75 (~hskp0),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3642, 3616, 3615, 3614])).
% 1.54/1.75 tff(3644,plain,
% 1.54/1.75 (~c1_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[183, 445])).
% 1.54/1.75 tff(3645,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3112, 101, 191, 11, 446, 3644, 447, 709])).
% 1.54/1.75 tff(3646,plain,((~hskp6) | hskp1 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3647,plain,
% 1.54/1.75 (~hskp6),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3646, 191, 3643])).
% 1.54/1.75 tff(3648,plain,
% 1.54/1.75 (~c3_1(a21)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[774, 3634])).
% 1.54/1.75 tff(3649,plain,
% 1.54/1.75 (c2_1(a21)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[782, 3634])).
% 1.54/1.75 tff(3650,plain,
% 1.54/1.75 (hskp6 | (~c1_1(a21))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2423, 101, 3635, 3649, 3648, 141])).
% 1.54/1.75 tff(3651,plain,
% 1.54/1.75 (~c1_1(a21)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3650, 3647])).
% 1.54/1.75 tff(3652,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a58)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3653,plain,
% 1.54/1.75 ((hskp18 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21))) <=> (hskp18 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a58)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3654,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a58))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3653])).
% 1.54/1.75 tff(3655,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a58)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3654, 3652])).
% 1.54/1.75 tff(3656,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3657,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | (~c0_1(a58)) | c1_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a58))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3656, 3655])).
% 1.54/1.75 tff(3658,plain,
% 1.54/1.75 (hskp18 | c1_1(a21)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3657, 101, 3486, 3635, 3020, 26, 3648, 2641])).
% 1.54/1.75 tff(3659,plain,
% 1.54/1.75 (hskp18),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3658, 3651])).
% 1.54/1.75 tff(3660,plain,
% 1.54/1.75 (c1_1(a31)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[393, 3659])).
% 1.54/1.75 tff(3661,plain,
% 1.54/1.75 (~c3_1(a31)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[385, 3659])).
% 1.54/1.75 tff(3662,plain,
% 1.54/1.75 (~c0_1(a31)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[423, 3659])).
% 1.54/1.75 tff(3663,plain,
% 1.54/1.75 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3664,plain,
% 1.54/1.75 ((hskp10 | hskp1 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21))) <=> (hskp10 | hskp1 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3665,plain,
% 1.54/1.75 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3664])).
% 1.54/1.75 tff(3666,plain,
% 1.54/1.75 (((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)))) <=> ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3665, 3663])).
% 1.54/1.75 tff(3667,plain,
% 1.54/1.75 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp10 | hskp1 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3668,plain,
% 1.54/1.75 ((~![U: $i] : (hskp10 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp10 | hskp1 | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3667, 3666])).
% 1.54/1.75 tff(3669,plain,
% 1.54/1.75 (hskp10 | hskp1 | c1_1(a21)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3668, 101, 3649, 3648, 1786])).
% 1.54/1.75 tff(3670,plain,
% 1.54/1.75 (hskp10),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3669, 3651, 191])).
% 1.54/1.75 tff(3671,plain,
% 1.54/1.75 (~c1_1(a18)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[868, 3670])).
% 1.54/1.75 tff(3672,plain,
% 1.54/1.75 (c3_1(a18)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[962, 3670])).
% 1.54/1.75 tff(3673,plain,
% 1.54/1.75 (~c0_1(a18)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[874, 3670])).
% 1.54/1.75 tff(3674,assumption,(c1_1(a31)), introduced(assumption)).
% 1.54/1.75 tff(3675,plain,
% 1.54/1.75 (hskp6 | (~c2_1(a31))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2663, 101, 3674, 2417, 2416, 3080, 2415, 141])).
% 1.54/1.75 tff(3676,plain,
% 1.54/1.75 (~c2_1(a31)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3675, 25])).
% 1.54/1.75 tff(3677,assumption,(~c0_1(a18)), introduced(assumption)).
% 1.54/1.75 tff(3678,assumption,(c3_1(a18)), introduced(assumption)).
% 1.54/1.75 tff(3679,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a31) | c3_1(a31) | c0_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a31) | c3_1(a31) | c0_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a31))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3680,plain,
% 1.54/1.75 ((hskp0 | (~ndr1_0) | c0_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a31) | c2_1(a31) | c0_1(a31)) <=> (hskp0 | c0_1(a31) | c3_1(a31) | c0_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a31))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3681,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | c0_1(a31) | c3_1(a31) | c0_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a31)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3680])).
% 1.54/1.75 tff(3682,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a31) | c3_1(a31) | c0_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a31))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3681, 3679])).
% 1.54/1.75 tff(3683,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c0_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a31) | c2_1(a31) | c0_1(a31))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3684,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp0 | c0_1(a31) | c3_1(a31) | c0_1(a18) | (~ndr1_0) | (~c2_1(a18)) | (~c3_1(a18)) | c2_1(a31)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3683, 3682])).
% 1.54/1.75 tff(3685,plain,
% 1.54/1.75 ((~c2_1(a18)) | c2_1(a31)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3684, 101, 11, 3678, 3081, 3080, 3677, 24])).
% 1.54/1.75 tff(3686,plain,
% 1.54/1.75 (~c2_1(a18)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3685, 3676])).
% 1.54/1.75 tff(3687,plain,
% 1.54/1.75 (~c1_1(a21)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2424, 25])).
% 1.54/1.75 tff(3688,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c0_1(a31) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c2_1(a31))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c0_1(a31) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c2_1(a31))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3689,plain,
% 1.54/1.75 ((hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a31) | c2_1(a31) | c0_1(a31)) <=> (hskp5 | c0_1(a31) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c2_1(a31))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3690,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c0_1(a31) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c2_1(a31)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3689])).
% 1.54/1.75 tff(3691,plain,
% 1.54/1.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a31) | c2_1(a31) | c0_1(a31))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c0_1(a31) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c2_1(a31))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3690, 3688])).
% 1.54/1.75 tff(3692,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a31) | c2_1(a31) | c0_1(a31))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3693,plain,
% 1.54/1.75 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c0_1(a31) | c3_1(a31) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c2_1(a31)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3692, 3691])).
% 1.54/1.75 tff(3694,plain,
% 1.54/1.75 (hskp5 | c1_1(a21) | c2_1(a31)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3693, 101, 2416, 3081, 3080, 2415, 275])).
% 1.54/1.75 tff(3695,plain,
% 1.54/1.75 (hskp5),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3694, 3676, 3687])).
% 1.54/1.75 tff(3696,plain,
% 1.54/1.75 (~c2_1(a11)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[291, 3695])).
% 1.54/1.75 tff(3697,plain,
% 1.54/1.75 (~c1_1(a11)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[297, 3695])).
% 1.54/1.75 tff(3698,assumption,(~c1_1(a18)), introduced(assumption)).
% 1.54/1.75 tff(3699,plain,
% 1.54/1.75 (c0_1(a11)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[305, 3695])).
% 1.54/1.75 tff(3700,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[969, 101, 3678, 3699, 3677, 3698, 3697, 3696, 697, 3686])).
% 1.54/1.75 tff(3701,plain,(hskp6 | (~c3_1(a18)) | c0_1(a18) | c1_1(a18) | (~c2_1(a21)) | c0_1(a31) | c3_1(a31) | c3_1(a21) | hskp0 | (~c1_1(a31)) | (~c0_1(a21))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3702,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3701, 3673, 3672, 3647, 3671, 3649, 3662, 3661, 3648, 3643, 3660, 3635])).
% 1.54/1.75 tff(3703,plain,(hskp1 | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3704,plain,
% 1.54/1.75 (hskp1),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3703, 26])).
% 1.54/1.75 tff(3705,plain,
% 1.54/1.75 (~c3_1(a2)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[241, 3704])).
% 1.54/1.75 tff(3706,plain,
% 1.54/1.75 (~c0_1(a2)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[253, 3704])).
% 1.54/1.75 tff(3707,plain,
% 1.54/1.75 (~c2_1(a2)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[247, 3704])).
% 1.54/1.75 tff(3708,plain,
% 1.54/1.75 (c0_1(a2) | (~c1_1(a21))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3492, 101, 3486, 3649, 3020, 26, 3648, 13, 12, 1264])).
% 1.54/1.75 tff(3709,plain,
% 1.54/1.75 (~c1_1(a21)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3708, 14])).
% 1.54/1.75 tff(3710,plain,
% 1.54/1.75 (~c1_1(a21)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3492, 101, 3486, 3051, 3020, 26, 3050, 14, 13, 12, 1264])).
% 1.54/1.75 tff(3711,plain,
% 1.54/1.75 (hskp5),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3500, 101, 3051, 3050, 14, 13, 12, 275, 3710])).
% 1.54/1.75 tff(3712,plain,
% 1.54/1.75 (~c1_1(a11)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[297, 3711])).
% 1.54/1.75 tff(3713,plain,
% 1.54/1.75 (c0_1(a11)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[305, 3711])).
% 1.54/1.75 tff(3714,plain,
% 1.54/1.75 (~c3_1(a11)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3511, 101, 3066, 3068, 3051, 3713, 3050, 3712, 3048])).
% 1.54/1.75 tff(3715,plain,
% 1.54/1.75 (~c2_1(a11)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[291, 3711])).
% 1.54/1.75 tff(3716,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3519, 101, 757, 3066, 3712, 3715, 654, 3714])).
% 1.54/1.75 tff(3717,plain,(hskp21 | hskp20 | c0_1(a2) | c2_1(a2) | c3_1(a2) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3718,plain,
% 1.54/1.75 (c0_1(a2)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3717, 3066, 3633, 13, 12, 26])).
% 1.54/1.75 tff(3719,plain,
% 1.54/1.75 (hskp20 | c2_1(a2) | c1_1(a2)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[660, 101, 3633, 12, 654])).
% 1.54/1.75 tff(3720,plain,
% 1.54/1.75 (c1_1(a2)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3719, 3066, 13])).
% 1.54/1.75 tff(3721,plain,
% 1.54/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a7) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a7)) | (~c0_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a7) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a7)) | (~c0_1(a7)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3722,plain,
% 1.54/1.75 (((~ndr1_0) | c3_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2))) <=> (c2_1(a7) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a7)) | (~c0_1(a7)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3723,plain,
% 1.54/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c2_1(a7) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a7)) | (~c0_1(a7))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[3722])).
% 1.54/1.75 tff(3724,plain,
% 1.54/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a7) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a7)) | (~c0_1(a7)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[3723, 3721])).
% 1.54/1.75 tff(3725,plain,
% 1.54/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(3726,plain,
% 1.54/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c2_1(a7) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a7)) | (~c0_1(a7))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[3725, 3724])).
% 1.54/1.75 tff(3727,plain,
% 1.54/1.75 ((~c0_1(a2)) | (~c1_1(a2))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3726, 101, 3616, 3615, 3614, 13, 12, 901])).
% 1.54/1.75 tff(3728,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3727, 3720, 3718])).
% 1.54/1.75 tff(3729,plain,(hskp20 | c2_1(a2) | c3_1(a2) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3730,plain,
% 1.54/1.75 (hskp20),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3729, 13, 12, 26])).
% 1.54/1.75 tff(3731,plain,
% 1.54/1.75 (hskp18),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3658, 3709])).
% 1.54/1.75 tff(3732,plain,
% 1.54/1.75 (~c0_1(a31)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[423, 3731])).
% 1.54/1.75 tff(3733,plain,
% 1.54/1.75 (~c3_1(a31)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[385, 3731])).
% 1.54/1.75 tff(3734,plain,
% 1.54/1.75 (hskp0 | c0_1(a2) | (~c2_1(a37))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[639, 101, 633, 632, 13, 12, 24])).
% 1.54/1.75 tff(3735,plain,
% 1.54/1.75 (~c2_1(a37)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3734, 11, 14])).
% 1.54/1.75 tff(3736,plain,
% 1.54/1.75 (hskp6),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3096, 11, 626, 3081, 3080, 3079])).
% 1.54/1.75 tff(3737,plain,
% 1.54/1.75 (~c3_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[177, 3736])).
% 1.54/1.75 tff(3738,plain,
% 1.54/1.75 (~c1_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[183, 3736])).
% 1.54/1.75 tff(3739,plain,
% 1.54/1.75 (~c0_1(a13)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[189, 3736])).
% 1.54/1.75 tff(3740,plain,
% 1.54/1.75 (~c1_1(a7)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2931, 101, 3624, 3623, 3739, 3738, 3737, 3622, 36])).
% 1.54/1.75 tff(3741,plain,
% 1.54/1.75 (hskp28),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[643, 11, 12, 626, 14, 13])).
% 1.54/1.75 tff(3742,plain,
% 1.54/1.75 (c3_1(a25)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[460, 3741])).
% 1.54/1.75 tff(3743,plain,
% 1.54/1.75 (c1_1(a25)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[468, 3741])).
% 1.54/1.75 tff(3744,plain,
% 1.54/1.75 (~c0_1(a25)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3152, 101, 3743, 3742, 641, 633, 3623, 3622, 1676, 3740, 3735])).
% 1.54/1.75 tff(3745,plain,
% 1.54/1.75 (c2_1(a25)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[476, 3741])).
% 1.54/1.75 tff(3746,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3166, 101, 11, 3745, 3742, 3081, 3080, 24, 3079, 3744])).
% 1.54/1.75 tff(3747,plain,(hskp0 | c0_1(a31) | c3_1(a31) | c2_1(a31) | (~c3_1(a7)) | c2_1(a7) | (~c0_1(a7)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~hskp20)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(3748,plain,
% 1.54/1.75 (c2_1(a31)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3747, 3733, 3643, 3732, 3615, 3614, 3616, 14, 13, 12, 3730])).
% 1.54/1.75 tff(3749,plain,
% 1.54/1.75 (c1_1(a31)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[393, 3731])).
% 1.54/1.75 tff(3750,plain,
% 1.54/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a31) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a31) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3751,plain,
% 1.54/1.75 (((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c3_1(a31) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(3752,plain,
% 1.54/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c3_1(a31) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3751])).
% 1.54/1.76 tff(3753,plain,
% 1.54/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a31) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3752, 3750])).
% 1.54/1.76 tff(3754,plain,
% 1.54/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3755,plain,
% 1.54/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c3_1(a31) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3754, 3753])).
% 1.54/1.76 tff(3756,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3755, 101, 3749, 3635, 3649, 3733, 14, 13, 12, 1264, 3748, 3709])).
% 1.54/1.76 tff(3757,plain,(c0_1(a2) | c2_1(a2) | c3_1(a2) | c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3758,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3757, 3707, 3706, 3705, 26])).
% 1.54/1.76 tff(3759,plain,(c1_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3760,plain,
% 1.54/1.76 (((~hskp24) | (~c1_1(a58))) <=> ((~hskp24) | (~c1_1(a58)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3761,plain,
% 1.54/1.76 (((~c1_1(a58)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a58)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3762,axiom,((~c1_1(a58)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.54/1.76 tff(3763,plain,
% 1.54/1.76 ((~hskp24) | (~c1_1(a58))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3762, 3761])).
% 1.54/1.76 tff(3764,plain,
% 1.54/1.76 ((~hskp24) | (~c1_1(a58))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3763, 3760])).
% 1.54/1.76 tff(3765,plain,
% 1.54/1.76 (~hskp24),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3764, 3759])).
% 1.54/1.76 tff(3766,plain,
% 1.54/1.76 ((~hskp21) | hskp6),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3054, 3765])).
% 1.54/1.76 tff(3767,plain,
% 1.54/1.76 (~hskp21),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3766, 25])).
% 1.54/1.76 tff(3768,plain,
% 1.54/1.76 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(3769,plain,
% 1.54/1.76 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[3768])).
% 1.54/1.76 tff(3770,plain,
% 1.54/1.76 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3771,plain,
% 1.54/1.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(3772,plain,
% 1.54/1.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[3771])).
% 1.54/1.76 tff(3773,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.54/1.76 tff(3774,plain,
% 1.54/1.76 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3773, 3772])).
% 1.54/1.76 tff(3775,plain,
% 1.54/1.76 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3774, 3770])).
% 1.54/1.76 tff(3776,plain,(
% 1.54/1.76 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.76 inference(skolemize,[status(sab)],[3775])).
% 1.54/1.76 tff(3777,plain,
% 1.54/1.76 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3776, 3769])).
% 1.54/1.76 tff(3778,plain,
% 1.54/1.76 (hskp21 | hskp13),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[768, 3765])).
% 1.54/1.76 tff(3779,plain,
% 1.54/1.76 (hskp13),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3778, 3767])).
% 1.54/1.76 tff(3780,plain,
% 1.54/1.76 (c2_1(a21)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[782, 3779])).
% 1.54/1.76 tff(3781,plain,
% 1.54/1.76 (c0_1(a21)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[790, 3779])).
% 1.54/1.76 tff(3782,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3783,plain,
% 1.54/1.76 ((hskp6 | (~ndr1_0) | (~c2_1(a21)) | (~c1_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58))) <=> (hskp6 | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3784,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a21)) | (~c1_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3783])).
% 1.54/1.76 tff(3785,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a21)) | (~c1_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3784, 3782])).
% 1.54/1.76 tff(3786,plain,
% 1.54/1.76 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a21)) | (~c1_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3787,plain,
% 1.54/1.76 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c1_1(a21)) | (~c0_1(a21)) | (~c2_1(a21))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3786, 3785])).
% 1.54/1.76 tff(3788,plain,
% 1.54/1.76 (~c1_1(a21)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3787, 101, 25, 726, 3781, 3780, 37, 3759, 3777])).
% 1.54/1.76 tff(3789,plain,
% 1.54/1.76 (~c3_1(a21)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[774, 3779])).
% 1.54/1.76 tff(3790,plain,
% 1.54/1.76 (hskp18),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2647, 101, 3781, 3780, 3789, 2641, 3788])).
% 1.54/1.76 tff(3791,plain,
% 1.54/1.76 (~c0_1(a31)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[423, 3790])).
% 1.54/1.76 tff(3792,plain,
% 1.54/1.76 (~c3_1(a31)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[385, 3790])).
% 1.54/1.76 tff(3793,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a58) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a58) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a58)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3794,plain,
% 1.54/1.76 ((hskp6 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp6 | c2_1(a58) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a58)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3795,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a58) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a58))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3794])).
% 1.54/1.76 tff(3796,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a58) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a58)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3795, 3793])).
% 1.54/1.76 tff(3797,plain,
% 1.54/1.76 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3798,plain,
% 1.54/1.76 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a58) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c3_1(a58))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3797, 3796])).
% 1.54/1.76 tff(3799,plain,
% 1.54/1.76 (hskp6 | c0_1(a2) | (~c3_1(a58))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3798, 101, 726, 3759, 13, 12, 1238])).
% 1.54/1.76 tff(3800,plain,
% 1.54/1.76 (~c3_1(a58)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3799, 25, 14])).
% 1.54/1.76 tff(3801,plain,
% 1.54/1.76 (c1_1(a31)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[393, 3790])).
% 1.54/1.76 tff(3802,plain,
% 1.54/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | c0_1(a58) | c3_1(a31) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c3_1(a31) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)) | c3_1(a58))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3803,plain,
% 1.54/1.76 (((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | c3_1(a58)) <=> (c2_1(a58) | c0_1(a58) | c3_1(a31) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)) | c3_1(a58))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3804,plain,
% 1.54/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | c0_1(a58) | c3_1(a31) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)) | c3_1(a58)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3803])).
% 1.54/1.76 tff(3805,plain,
% 1.54/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c3_1(a31) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)) | c3_1(a58))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3804, 3802])).
% 1.54/1.76 tff(3806,plain,
% 1.54/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a21) | (~c2_1(a21)) | (~c0_1(a21)) | c2_1(a58) | c0_1(a58) | c3_1(a58))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3807,plain,
% 1.54/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | c0_1(a58) | c3_1(a31) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a21)) | (~c1_1(a31)) | (~c2_1(a31)) | c3_1(a58)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3806, 3805])).
% 1.54/1.76 tff(3808,plain,
% 1.54/1.76 (~c2_1(a31)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3807, 101, 726, 3801, 3781, 3780, 37, 3792, 1264, 3800, 3788])).
% 1.54/1.76 tff(3809,plain,
% 1.54/1.76 (~hskp20),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3096, 3808, 11, 3792, 3791, 25])).
% 1.54/1.76 tff(3810,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c2_1(a58) | c0_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c2_1(a58) | c0_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3811,plain,
% 1.54/1.76 ((hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58) | c2_1(a58) | c0_1(a58)) <=> (hskp5 | c2_1(a58) | c0_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3812,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58) | c2_1(a58) | c0_1(a58))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | c2_1(a58) | c0_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3811])).
% 1.54/1.76 tff(3813,plain,
% 1.54/1.76 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58) | c2_1(a58) | c0_1(a58))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c2_1(a58) | c0_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3812, 3810])).
% 1.54/1.76 tff(3814,plain,
% 1.54/1.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a21) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58) | c2_1(a58) | c0_1(a58))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3815,plain,
% 1.54/1.76 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp5 | c2_1(a58) | c0_1(a58) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c2_1(a21)) | c3_1(a58)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3814, 3813])).
% 1.54/1.76 tff(3816,plain,
% 1.54/1.76 (hskp5),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3815, 101, 726, 3780, 37, 3789, 275, 3800, 3788])).
% 1.54/1.76 tff(3817,plain,
% 1.54/1.76 (~c1_1(a11)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[297, 3816])).
% 1.54/1.76 tff(3818,plain,
% 1.54/1.76 (c0_1(a11)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[305, 3816])).
% 1.54/1.76 tff(3819,plain,
% 1.54/1.76 (hskp20 | (~c3_1(a11))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3511, 101, 3781, 3780, 3818, 3789, 3817, 3048])).
% 1.54/1.76 tff(3820,plain,
% 1.54/1.76 (~c3_1(a11)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3819, 3809])).
% 1.54/1.76 tff(3821,plain,
% 1.54/1.76 (~c2_1(a11)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[291, 3816])).
% 1.54/1.76 tff(3822,plain,
% 1.54/1.76 (hskp20 | c3_1(a11)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3519, 101, 3767, 3817, 3821, 654])).
% 1.54/1.76 tff(3823,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3822, 3820, 3809])).
% 1.54/1.76 tff(3824,plain,(hskp6 | hskp0 | c2_1(a58) | c0_1(a58) | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(3825,plain,
% 1.54/1.76 (hskp6),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3824, 37, 726, 11, 14, 13, 12])).
% 1.54/1.76 tff(3826,plain,
% 1.54/1.76 (~c3_1(a13)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[177, 3825])).
% 1.54/1.76 tff(3827,plain,
% 1.54/1.76 (~c1_1(a13)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[183, 3825])).
% 1.54/1.76 tff(3828,plain,
% 1.54/1.76 (~c0_1(a13)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[189, 3825])).
% 1.54/1.76 tff(3829,plain,
% 1.54/1.76 (~c3_1(a38)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1001, 101, 596, 604, 3052, 3828, 3827, 3826, 36])).
% 1.54/1.76 tff(3830,plain,
% 1.54/1.76 (^[U: $i] : refl((hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(3831,plain,
% 1.54/1.76 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[3830])).
% 1.54/1.76 tff(3832,plain,
% 1.54/1.76 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3833,plain,
% 1.54/1.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp0) <=> ((hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0))), rewrite(((hskp22 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp0) <=> (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(3834,plain,
% 1.54/1.76 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp0) <=> ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[3833])).
% 1.54/1.76 tff(3835,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp22) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 1.54/1.76 tff(3836,plain,
% 1.54/1.76 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3835, 3834])).
% 1.54/1.76 tff(3837,plain,
% 1.54/1.76 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3836, 3832])).
% 1.54/1.76 tff(3838,plain,(
% 1.54/1.76 ![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(skolemize,[status(sab)],[3837])).
% 1.54/1.76 tff(3839,plain,
% 1.54/1.76 (![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3838, 3831])).
% 1.54/1.76 tff(3840,plain,
% 1.54/1.76 (hskp27),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[624, 3052, 588, 13, 12, 14])).
% 1.54/1.76 tff(3841,plain,
% 1.54/1.76 (c3_1(a12)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[560, 3840])).
% 1.54/1.76 tff(3842,plain,
% 1.54/1.76 (c1_1(a12)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[568, 3840])).
% 1.54/1.76 tff(3843,plain,
% 1.54/1.76 (c0_1(a12)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1114, 3840])).
% 1.54/1.76 tff(3844,plain,
% 1.54/1.76 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3845,plain,
% 1.54/1.76 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3846,plain,
% 1.54/1.76 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3845, 3844])).
% 1.54/1.76 tff(3847,plain,
% 1.54/1.76 (hskp22),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3846, 101, 11, 3843, 3842, 3841, 3839])).
% 1.54/1.76 tff(3848,plain,
% 1.54/1.76 (~c1_1(a42)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1391, 3847])).
% 1.54/1.76 tff(3849,plain,
% 1.54/1.76 (c2_1(a42)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1400, 3847])).
% 1.54/1.76 tff(3850,plain,
% 1.54/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | c1_1(a42) | c2_1(a38) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | c1_1(a42) | c2_1(a38) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3851,plain,
% 1.54/1.76 (((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58))) <=> (c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | c1_1(a42) | c2_1(a38) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3852,plain,
% 1.54/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | c1_1(a42) | c2_1(a38) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3851])).
% 1.54/1.76 tff(3853,plain,
% 1.54/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | c1_1(a42) | c2_1(a38) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[3852, 3850])).
% 1.54/1.76 tff(3854,plain,
% 1.54/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(3855,plain,
% 1.54/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a58) | c0_1(a58) | (~c1_1(a58)) | c1_1(a42) | c2_1(a38) | (~ndr1_0) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3854, 3853])).
% 1.54/1.76 tff(3856,plain,
% 1.54/1.76 (~c3_1(a42)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3855, 101, 726, 3849, 596, 37, 3759, 3848, 3052, 1965, 3829])).
% 1.54/1.76 tff(3857,plain,
% 1.54/1.76 (hskp8),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2198, 101, 3843, 3842, 3841, 596, 604, 2187, 3829])).
% 1.54/1.76 tff(3858,plain,
% 1.54/1.76 (~c3_1(a15)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1316, 3857])).
% 1.54/1.76 tff(3859,plain,
% 1.54/1.76 (~c2_1(a15)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1997, 3857])).
% 1.54/1.76 tff(3860,plain,
% 1.54/1.76 (~c1_1(a15)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2088, 3857])).
% 1.54/1.76 tff(3861,plain,
% 1.54/1.76 (c0_1(a42)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1408, 3847])).
% 1.54/1.76 tff(3862,plain,
% 1.54/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a42) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a42) | (~c0_1(a42)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(3863,plain,
% 1.54/1.76 (((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15)) <=> (c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a42) | (~c0_1(a42)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3864,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a42) | (~c0_1(a42))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3863])).
% 1.54/1.77 tff(3865,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a42) | (~c0_1(a42)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3864, 3862])).
% 1.54/1.77 tff(3866,plain,
% 1.54/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3867,plain,
% 1.54/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | c3_1(a42) | (~c0_1(a42))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3866, 3865])).
% 1.54/1.77 tff(3868,plain,
% 1.54/1.77 (~c2_1(a13)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3867, 101, 3861, 3848, 3860, 3859, 3858, 3828, 3826, 323, 3856])).
% 1.54/1.77 tff(3869,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c3_1(a42) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c3_1(a42) | (~c0_1(a42)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3870,plain,
% 1.54/1.77 ((hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42))) <=> (hskp18 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c3_1(a42) | (~c0_1(a42)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3871,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c3_1(a42) | (~c0_1(a42))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3870])).
% 1.54/1.77 tff(3872,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c3_1(a42) | (~c0_1(a42)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3871, 3869])).
% 1.54/1.77 tff(3873,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3874,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | c3_1(a42) | (~c0_1(a42))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3873, 3872])).
% 1.54/1.77 tff(3875,plain,
% 1.54/1.77 (hskp18),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3874, 101, 3861, 3849, 3848, 2641, 3856])).
% 1.54/1.77 tff(3876,plain,
% 1.54/1.77 (~c3_1(a31)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[385, 3875])).
% 1.54/1.77 tff(3877,plain,
% 1.54/1.77 (c1_1(a31)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[393, 3875])).
% 1.54/1.77 tff(3878,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c3_1(a31) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | (~c2_1(a31)) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a31) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | (~c2_1(a31)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3879,plain,
% 1.54/1.77 (((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c1_1(a42) | c3_1(a31) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | (~c2_1(a31)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3880,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c3_1(a31) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | (~c2_1(a31)) | (~c2_1(a42)) | (~c0_1(a42))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3879])).
% 1.54/1.77 tff(3881,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a31) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | (~c2_1(a31)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3880, 3878])).
% 1.54/1.77 tff(3882,plain,
% 1.54/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a31) | (~c2_1(a31)) | (~c1_1(a31)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c2_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3883,plain,
% 1.54/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c3_1(a31) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | (~c2_1(a31)) | (~c2_1(a42)) | (~c0_1(a42))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3882, 3881])).
% 1.54/1.77 tff(3884,plain,
% 1.54/1.77 (~c2_1(a31)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3883, 101, 3861, 3849, 3877, 3848, 3876, 3828, 3826, 1264, 3868])).
% 1.54/1.77 tff(3885,plain,
% 1.54/1.77 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.54/1.77 inference(bind,[status(th)],[])).
% 1.54/1.77 tff(3886,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.54/1.77 inference(quant_intro,[status(thm)],[3885])).
% 1.54/1.77 tff(3887,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3888,plain,
% 1.54/1.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_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))) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_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))) | (~c2_1(V))) | c1_1(V)) | hskp12) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_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))) | (~c2_1(V))) | c1_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.54/1.77 inference(bind,[status(th)],[])).
% 1.54/1.77 tff(3889,plain,
% 1.54/1.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.54/1.77 inference(quant_intro,[status(thm)],[3888])).
% 1.54/1.77 tff(3890,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.54/1.77 tff(3891,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3890, 3889])).
% 1.54/1.77 tff(3892,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3891, 3887])).
% 1.54/1.77 tff(3893,plain,(
% 1.54/1.77 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.54/1.77 inference(skolemize,[status(sab)],[3892])).
% 1.54/1.77 tff(3894,plain,
% 1.54/1.77 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3893, 3886])).
% 1.54/1.77 tff(3895,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3896,plain,
% 1.54/1.77 ((hskp12 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42))) <=> (hskp12 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3897,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3896])).
% 1.54/1.77 tff(3898,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3897, 3895])).
% 1.54/1.77 tff(3899,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3900,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp12 | c1_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c0_1(a42)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3899, 3898])).
% 1.54/1.77 tff(3901,plain,
% 1.54/1.77 (hskp12),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3900, 101, 3843, 3842, 3841, 3861, 3849, 3848, 3894])).
% 1.54/1.77 tff(3902,plain,
% 1.54/1.77 (~c3_1(a20)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[930, 3901])).
% 1.54/1.77 tff(3903,plain,
% 1.54/1.77 (~c1_1(a20)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[936, 3901])).
% 1.54/1.77 tff(3904,plain,
% 1.54/1.77 (c2_1(a20)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[944, 3901])).
% 1.54/1.77 tff(3905,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2560, 101, 3877, 3904, 3876, 3903, 3902, 3828, 3827, 362, 3868, 3884])).
% 1.54/1.77 tff(3906,plain,((~hskp21) | c2_1(a58) | c0_1(a58) | hskp0 | c2_1(a2) | c3_1(a2) | c0_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3907,plain,
% 1.54/1.77 (~hskp21),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3906, 37, 726, 11, 13, 12, 14])).
% 1.54/1.77 tff(3908,plain,
% 1.54/1.77 (c2_1(a13)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2321, 757, 3066])).
% 1.54/1.77 tff(3909,plain,
% 1.54/1.77 (hskp5 | (~c2_1(a13))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[284, 101, 225, 224, 14, 13, 12, 275])).
% 1.54/1.77 tff(3910,plain,
% 1.54/1.77 (hskp5),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3909, 3908])).
% 1.54/1.77 tff(3911,plain,
% 1.54/1.77 (~c2_1(a11)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[291, 3910])).
% 1.54/1.77 tff(3912,plain,
% 1.54/1.77 (~c1_1(a11)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[297, 3910])).
% 1.54/1.77 tff(3913,plain,
% 1.54/1.77 (c3_1(a11)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3519, 101, 757, 3066, 3912, 3911, 654])).
% 1.54/1.77 tff(3914,plain,
% 1.54/1.77 (hskp13),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3778, 757])).
% 1.54/1.77 tff(3915,plain,
% 1.54/1.77 (~c3_1(a21)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[774, 3914])).
% 1.54/1.77 tff(3916,plain,
% 1.54/1.77 (c0_1(a11)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[305, 3910])).
% 1.54/1.77 tff(3917,plain,
% 1.54/1.77 (c2_1(a21)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[782, 3914])).
% 1.54/1.77 tff(3918,plain,
% 1.54/1.77 (c0_1(a21)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[790, 3914])).
% 1.54/1.77 tff(3919,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3511, 101, 3066, 3918, 3917, 3916, 3915, 3912, 3048, 3913])).
% 1.54/1.77 tff(3920,plain,(hskp21 | hskp20 | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3921,plain,
% 1.54/1.77 (hskp20),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3920, 3907, 3827, 3826, 14, 13, 12])).
% 1.54/1.77 tff(3922,plain,
% 1.54/1.77 (~c0_1(a37)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[631, 3921])).
% 1.54/1.77 tff(3923,plain,
% 1.54/1.77 (c3_1(a37)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[516, 3921])).
% 1.54/1.77 tff(3924,plain,
% 1.54/1.77 (~c2_1(a37)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[639, 101, 11, 3923, 3922, 14, 13, 12, 24])).
% 1.54/1.77 tff(3925,plain,
% 1.54/1.77 ((~hskp20) | hskp0 | hskp3),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3033, 3765])).
% 1.54/1.77 tff(3926,plain,
% 1.54/1.77 (hskp3),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3925, 3921, 11])).
% 1.54/1.77 tff(3927,plain,
% 1.54/1.77 (~c2_1(a7)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2863, 3926])).
% 1.54/1.77 tff(3928,plain,
% 1.54/1.77 (c3_1(a7)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2873, 3926])).
% 1.54/1.77 tff(3929,plain,
% 1.54/1.77 (c0_1(a7)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2881, 3926])).
% 1.54/1.77 tff(3930,plain,
% 1.54/1.77 (~c1_1(a7)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2931, 101, 3929, 3928, 3828, 3827, 3826, 3927, 36])).
% 1.54/1.77 tff(3931,plain,
% 1.54/1.77 (c1_1(a37)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[524, 3921])).
% 1.54/1.77 tff(3932,plain,
% 1.54/1.77 (hskp28),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[643, 3921, 11, 12, 14, 13])).
% 1.54/1.77 tff(3933,plain,
% 1.54/1.77 (c3_1(a25)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[460, 3932])).
% 1.54/1.77 tff(3934,plain,
% 1.54/1.77 (c1_1(a25)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[468, 3932])).
% 1.54/1.77 tff(3935,plain,
% 1.54/1.77 (~c0_1(a25)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3152, 101, 3934, 3933, 3931, 3923, 3928, 3927, 1676, 3930, 3924])).
% 1.54/1.77 tff(3936,plain,
% 1.54/1.77 (c2_1(a25)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[476, 3932])).
% 1.54/1.77 tff(3937,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3000, 101, 11, 3936, 3933, 14, 13, 12, 24, 3935])).
% 1.54/1.77 tff(3938,plain,(c0_1(a58) | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | c2_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(3939,plain,
% 1.54/1.77 (c0_1(a58)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3938, 14, 11, 13, 12, 726])).
% 1.54/1.77 tff(3940,plain,
% 1.54/1.77 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3941,plain,
% 1.54/1.77 ((hskp24 | hskp6 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58))) <=> (hskp24 | hskp6 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3942,plain,
% 1.54/1.77 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3941])).
% 1.54/1.77 tff(3943,plain,
% 1.54/1.77 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3942, 3940])).
% 1.54/1.77 tff(3944,plain,
% 1.54/1.77 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3945,plain,
% 1.54/1.77 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3944, 3943])).
% 1.54/1.77 tff(3946,plain,
% 1.54/1.77 (hskp6 | c2_1(a58) | (~c0_1(a58))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3945, 101, 3765, 3759, 984])).
% 1.54/1.77 tff(3947,plain,
% 1.54/1.77 (hskp6),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3946, 3939, 726])).
% 1.54/1.77 tff(3948,plain,
% 1.54/1.77 (~c3_1(a13)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[177, 3947])).
% 1.54/1.77 tff(3949,plain,
% 1.54/1.77 (~c1_1(a13)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[183, 3947])).
% 1.54/1.77 tff(3950,plain,
% 1.54/1.77 (~c0_1(a13)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[189, 3947])).
% 1.54/1.77 tff(3951,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a58)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3952,plain,
% 1.54/1.77 (((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a58)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3953,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a58))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3952])).
% 1.54/1.77 tff(3954,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a58)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3953, 3951])).
% 1.54/1.77 tff(3955,plain,
% 1.54/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c1_1(a58)) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3956,plain,
% 1.54/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~ndr1_0) | (~c3_1(a58))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3955, 3954])).
% 1.54/1.77 tff(3957,plain,
% 1.54/1.77 (~c3_1(a58)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3956, 101, 726, 3939, 3759, 3950, 3949, 3948, 36])).
% 1.54/1.77 tff(3958,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3959,plain,
% 1.54/1.77 ((hskp27 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2)) <=> (hskp27 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3960,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3959])).
% 1.54/1.77 tff(3961,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3960, 3958])).
% 1.54/1.77 tff(3962,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c2_1(a58) | (~c1_1(a58)) | (~c0_1(a58)) | c3_1(a2) | c2_1(a2) | c0_1(a2))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3963,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp27 | c2_1(a58) | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3962, 3961])).
% 1.54/1.77 tff(3964,plain,
% 1.54/1.77 (hskp27 | (~c0_1(a58)) | c0_1(a2)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3963, 101, 726, 3759, 13, 12, 614])).
% 1.54/1.77 tff(3965,plain,
% 1.54/1.77 (hskp27),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3964, 3939, 14])).
% 1.54/1.77 tff(3966,plain,
% 1.54/1.77 (c3_1(a12)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[560, 3965])).
% 1.54/1.77 tff(3967,plain,
% 1.54/1.77 (c1_1(a12)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[568, 3965])).
% 1.54/1.77 tff(3968,plain,
% 1.54/1.77 (c0_1(a12)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1114, 3965])).
% 1.54/1.77 tff(3969,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | c3_1(a58) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | c3_1(a58) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3970,plain,
% 1.54/1.77 ((hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a58) | (~c0_1(a58)) | (~c1_1(a58))) <=> (hskp8 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | c3_1(a58) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3971,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a58) | (~c0_1(a58)) | (~c1_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | c3_1(a58) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3970])).
% 1.54/1.77 tff(3972,plain,
% 1.54/1.77 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a58) | (~c0_1(a58)) | (~c1_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | c3_1(a58) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[3971, 3969])).
% 1.54/1.77 tff(3973,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | c3_1(a58) | (~c0_1(a58)) | (~c1_1(a58)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(3974,plain,
% 1.54/1.77 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c1_1(V)))) | hskp8 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | c3_1(a58) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[3973, 3972])).
% 1.54/1.77 tff(3975,plain,
% 1.54/1.77 (hskp8),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3974, 101, 3968, 3967, 3966, 3939, 3759, 2187, 3957])).
% 1.54/1.77 tff(3976,plain,
% 1.54/1.77 (~c3_1(a15)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1316, 3975])).
% 1.54/1.77 tff(3977,plain,
% 1.54/1.77 (~c2_1(a15)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1997, 3975])).
% 1.54/1.77 tff(3978,plain,
% 1.54/1.77 (~c1_1(a15)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2088, 3975])).
% 1.54/1.77 tff(3979,plain,
% 1.54/1.77 (hskp22),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3846, 101, 11, 3968, 3967, 3966, 3839])).
% 1.54/1.77 tff(3980,plain,
% 1.54/1.77 (~c1_1(a42)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1391, 3979])).
% 1.54/1.77 tff(3981,plain,
% 1.54/1.77 (c2_1(a42)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1400, 3979])).
% 1.54/1.77 tff(3982,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3983,plain,
% 1.54/1.77 (((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(3984,plain,
% 1.54/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42))))),
% 1.61/1.78 inference(monotonicity,[status(thm)],[3983])).
% 1.61/1.78 tff(3985,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.61/1.78 inference(transitivity,[status(thm)],[3984, 3982])).
% 1.61/1.78 tff(3986,plain,
% 1.61/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c3_1(a15) | c2_1(a15) | c1_1(a15) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 1.61/1.78 inference(quant_inst,[status(thm)],[])).
% 1.61/1.78 tff(3987,plain,
% 1.61/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a42) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42))),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[3986, 3985])).
% 1.61/1.78 tff(3988,plain,
% 1.61/1.78 (~c3_1(a42)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3987, 101, 3981, 3980, 3978, 3977, 3976, 14, 13, 12, 344])).
% 1.61/1.78 tff(3989,plain,
% 1.61/1.78 (c0_1(a42)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[1408, 3979])).
% 1.61/1.78 tff(3990,plain,
% 1.61/1.78 (hskp12),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3900, 101, 3968, 3967, 3966, 3989, 3981, 3980, 3894])).
% 1.61/1.78 tff(3991,plain,
% 1.61/1.78 (~c3_1(a20)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[930, 3990])).
% 1.61/1.78 tff(3992,plain,
% 1.61/1.78 (~c1_1(a20)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[936, 3990])).
% 1.61/1.78 tff(3993,plain,
% 1.61/1.78 (c2_1(a20)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[944, 3990])).
% 1.61/1.78 tff(3994,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | (~c1_1(a58)) | c1_1(a20) | c3_1(a20) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a20)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | (~c1_1(a58)) | c1_1(a20) | c3_1(a20) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a20)) | c3_1(a58))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(3995,plain,
% 1.61/1.78 (((~ndr1_0) | c3_1(a58) | c2_1(a58) | (~c1_1(a58)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a15) | c1_1(a15) | c0_1(a15)) <=> (c2_1(a58) | (~c1_1(a58)) | c1_1(a20) | c3_1(a20) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a20)) | c3_1(a58))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(3996,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a58) | c2_1(a58) | (~c1_1(a58)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a58) | (~c1_1(a58)) | c1_1(a20) | c3_1(a20) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a20)) | c3_1(a58)))),
% 1.61/1.78 inference(monotonicity,[status(thm)],[3995])).
% 1.61/1.78 tff(3997,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a58) | c2_1(a58) | (~c1_1(a58)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a15) | c1_1(a15) | c0_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | (~c1_1(a58)) | c1_1(a20) | c3_1(a20) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a20)) | c3_1(a58))),
% 1.61/1.78 inference(transitivity,[status(thm)],[3996, 3994])).
% 1.61/1.78 tff(3998,plain,
% 1.61/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a58) | c2_1(a58) | (~c1_1(a58)) | c3_1(a20) | c1_1(a20) | (~c2_1(a20)) | c2_1(a15) | c1_1(a15) | c0_1(a15))),
% 1.61/1.78 inference(quant_inst,[status(thm)],[])).
% 1.61/1.78 tff(3999,plain,
% 1.61/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a58) | (~c1_1(a58)) | c1_1(a20) | c3_1(a20) | c1_1(a15) | c2_1(a15) | (~ndr1_0) | c0_1(a15) | (~c2_1(a20)) | c3_1(a58)),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[3998, 3997])).
% 1.61/1.78 tff(4000,plain,
% 1.61/1.78 (c0_1(a15)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3999, 101, 726, 3993, 3759, 3992, 3991, 3978, 3977, 362, 3957])).
% 1.61/1.78 tff(4001,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a42) | c1_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | c1_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4002,plain,
% 1.61/1.78 ((hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15))) <=> (hskp18 | c1_1(a42) | c1_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4003,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a42) | c1_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a42)) | (~c0_1(a42))))),
% 1.61/1.78 inference(monotonicity,[status(thm)],[4002])).
% 1.61/1.78 tff(4004,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | c1_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.61/1.78 inference(transitivity,[status(thm)],[4003, 4001])).
% 1.61/1.78 tff(4005,plain,
% 1.61/1.78 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)))),
% 1.61/1.78 inference(quant_inst,[status(thm)],[])).
% 1.61/1.78 tff(4006,plain,
% 1.61/1.78 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | c1_1(a15) | c3_1(a15) | (~ndr1_0) | (~c0_1(a15)) | (~c2_1(a42)) | (~c0_1(a42))),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[4005, 4004])).
% 1.61/1.78 tff(4007,plain,
% 1.61/1.78 (hskp18),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4006, 101, 3989, 3981, 3980, 3978, 3976, 2641, 4000])).
% 1.61/1.78 tff(4008,plain,
% 1.61/1.78 (~c3_1(a31)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[385, 4007])).
% 1.61/1.78 tff(4009,plain,
% 1.61/1.78 (~c0_1(a31)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[423, 4007])).
% 1.61/1.78 tff(4010,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a42) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a42) | (~c0_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a42) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a42) | (~c0_1(a42)))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4011,plain,
% 1.61/1.78 (((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15)) <=> (c1_1(a42) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a42) | (~c0_1(a42)))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4012,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a42) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a42) | (~c0_1(a42))))),
% 1.61/1.78 inference(monotonicity,[status(thm)],[4011])).
% 1.61/1.78 tff(4013,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a42) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a42) | (~c0_1(a42)))),
% 1.61/1.78 inference(transitivity,[status(thm)],[4012, 4010])).
% 1.61/1.78 tff(4014,plain,
% 1.61/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a42) | c1_1(a42) | (~c0_1(a42)) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a15) | c1_1(a15) | c3_1(a15))),
% 1.61/1.78 inference(quant_inst,[status(thm)],[])).
% 1.61/1.78 tff(4015,plain,
% 1.61/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a42) | c0_1(a31) | c3_1(a31) | c1_1(a15) | c2_1(a15) | c3_1(a15) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a42) | (~c0_1(a42))),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[4014, 4013])).
% 1.61/1.78 tff(4016,plain,
% 1.61/1.78 (~c2_1(a31)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4015, 101, 3989, 3980, 4009, 4008, 3978, 3977, 3976, 323, 3988])).
% 1.61/1.78 tff(4017,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | (~c0_1(a15)))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4018,plain,
% 1.61/1.78 (((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15)) <=> (c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | (~c0_1(a15)))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4019,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | (~c0_1(a15))))),
% 1.61/1.78 inference(monotonicity,[status(thm)],[4018])).
% 1.61/1.78 tff(4020,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | (~c0_1(a15)))),
% 1.61/1.78 inference(transitivity,[status(thm)],[4019, 4017])).
% 1.61/1.78 tff(4021,plain,
% 1.61/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a15) | c1_1(a15) | (~c0_1(a15)) | c3_1(a13) | c0_1(a13) | (~c2_1(a13)) | c2_1(a15) | c1_1(a15) | c3_1(a15))),
% 1.61/1.78 inference(quant_inst,[status(thm)],[])).
% 1.61/1.78 tff(4022,plain,
% 1.61/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a15) | c2_1(a15) | c3_1(a15) | c0_1(a13) | c3_1(a13) | (~ndr1_0) | (~c2_1(a13)) | (~c0_1(a15))),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[4021, 4020])).
% 1.61/1.78 tff(4023,plain,
% 1.61/1.78 ((~c2_1(a13)) | (~c0_1(a15))),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4022, 101, 3978, 3977, 3976, 3950, 3948, 323])).
% 1.61/1.78 tff(4024,plain,
% 1.61/1.78 (~c2_1(a13)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4023, 4000])).
% 1.61/1.78 tff(4025,plain,
% 1.61/1.78 (c1_1(a31)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[393, 4007])).
% 1.61/1.78 tff(4026,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a42) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a42)) | c3_1(a42))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a42) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a42)) | c3_1(a42))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4027,plain,
% 1.61/1.78 (((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)) | c2_1(a13) | c1_1(a13) | c0_1(a13)) <=> (c1_1(a42) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a42)) | c3_1(a42))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4028,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a42) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a42)) | c3_1(a42)))),
% 1.61/1.78 inference(monotonicity,[status(thm)],[4027])).
% 1.61/1.78 tff(4029,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)) | c2_1(a13) | c1_1(a13) | c0_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a42) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a42)) | c3_1(a42))),
% 1.61/1.78 inference(transitivity,[status(thm)],[4028, 4026])).
% 1.61/1.78 tff(4030,plain,
% 1.61/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a31) | c2_1(a31) | (~c1_1(a31)) | c3_1(a42) | c1_1(a42) | (~c2_1(a42)) | c2_1(a13) | c1_1(a13) | c0_1(a13))),
% 1.61/1.78 inference(quant_inst,[status(thm)],[])).
% 1.61/1.78 tff(4031,plain,
% 1.61/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a42) | c3_1(a31) | c0_1(a13) | c1_1(a13) | (~ndr1_0) | c2_1(a13) | (~c1_1(a31)) | c2_1(a31) | (~c2_1(a42)) | c3_1(a42)),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[4030, 4029])).
% 1.61/1.78 tff(4032,plain,
% 1.61/1.78 ($false),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4031, 101, 3981, 4025, 3980, 4008, 3950, 3949, 362, 4024, 4016, 3988])).
% 1.61/1.78 tff(4033,plain,(c0_1(a2) | c2_1(a2) | c3_1(a2) | c2_1(a58) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.61/1.78 tff(4034,plain,
% 1.61/1.78 (c0_1(a2)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4033, 726, 12, 13, 11])).
% 1.61/1.78 tff(4035,plain,
% 1.61/1.78 (~hskp1),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[253, 4034])).
% 1.61/1.78 tff(4036,plain,
% 1.61/1.78 (~hskp6),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3646, 4035, 11])).
% 1.61/1.78 tff(4037,plain,
% 1.61/1.78 (~hskp21),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3766, 4036])).
% 1.61/1.78 tff(4038,plain,
% 1.61/1.78 (hskp13),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3778, 4037])).
% 1.61/1.78 tff(4039,plain,
% 1.61/1.78 (c0_1(a21)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[790, 4038])).
% 1.61/1.78 tff(4040,plain,
% 1.61/1.78 (~c0_1(a58)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3946, 4036, 726])).
% 1.61/1.78 tff(4041,plain,
% 1.61/1.78 (c2_1(a21)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[782, 4038])).
% 1.61/1.78 tff(4042,plain,
% 1.61/1.78 (~c1_1(a21)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3787, 101, 4036, 726, 4039, 4041, 4040, 3759, 3777])).
% 1.61/1.78 tff(4043,plain,
% 1.61/1.78 (~c3_1(a21)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[774, 4038])).
% 1.61/1.78 tff(4044,plain,
% 1.61/1.78 (hskp18),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[2647, 101, 4039, 4041, 4043, 2641, 4042])).
% 1.61/1.78 tff(4045,plain,
% 1.61/1.78 (c1_1(a31)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[393, 4044])).
% 1.61/1.78 tff(4046,plain,
% 1.61/1.78 (hskp10),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3668, 101, 4035, 4041, 4043, 1786, 4042])).
% 1.61/1.78 tff(4047,plain,
% 1.61/1.78 (~c0_1(a18)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[874, 4046])).
% 1.61/1.78 tff(4048,plain,
% 1.61/1.78 (c3_1(a18)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[962, 4046])).
% 1.61/1.78 tff(4049,plain,
% 1.61/1.78 (~c1_1(a18)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[868, 4046])).
% 1.61/1.78 tff(4050,plain,
% 1.61/1.78 (~c0_1(a31)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[423, 4044])).
% 1.61/1.78 tff(4051,plain,
% 1.61/1.78 (~c3_1(a31)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[385, 4044])).
% 1.61/1.78 tff(4052,plain,
% 1.61/1.78 ($false),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3701, 4051, 4050, 4036, 4049, 4041, 4048, 4047, 4043, 11, 4045, 4039])).
% 1.61/1.78 tff(4053,plain,(c2_1(a58) | hskp0 | c3_1(a2) | c2_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.78 tff(4054,plain,
% 1.61/1.78 (c2_1(a58)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4053, 13, 12, 11])).
% 1.61/1.78 tff(4055,plain,
% 1.61/1.78 (~c3_1(a58)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[2963, 101, 11, 4054, 37, 14, 13, 12, 24])).
% 1.61/1.78 tff(4056,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4057,plain,
% 1.61/1.78 ((hskp6 | (~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58))) <=> (hskp6 | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4058,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)))),
% 1.61/1.78 inference(monotonicity,[status(thm)],[4057])).
% 1.61/1.78 tff(4059,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58))),
% 1.61/1.78 inference(transitivity,[status(thm)],[4058, 4056])).
% 1.61/1.78 tff(4060,plain,
% 1.61/1.78 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c3_1(a58) | c0_1(a58) | (~c2_1(a58)))),
% 1.61/1.78 inference(quant_inst,[status(thm)],[])).
% 1.61/1.78 tff(4061,plain,
% 1.61/1.78 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp6 | c0_1(a58) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | c3_1(a58)),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[4060, 4059])).
% 1.61/1.78 tff(4062,plain,
% 1.61/1.78 (hskp6),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4061, 101, 4054, 37, 3759, 162, 4055])).
% 1.61/1.78 tff(4063,plain,
% 1.61/1.78 (~c3_1(a13)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[177, 4062])).
% 1.61/1.78 tff(4064,plain,
% 1.61/1.78 (~c1_1(a13)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[183, 4062])).
% 1.61/1.78 tff(4065,plain,
% 1.61/1.78 (~c0_1(a13)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[189, 4062])).
% 1.61/1.78 tff(4066,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~c1_1(a58)) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c2_1(a58)) | c3_1(a58))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (~c1_1(a58)) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c2_1(a58)) | c3_1(a58))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4067,plain,
% 1.61/1.78 (((~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7))) <=> ((~c1_1(a58)) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c2_1(a58)) | c3_1(a58))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4068,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~c1_1(a58)) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c2_1(a58)) | c3_1(a58)))),
% 1.61/1.78 inference(monotonicity,[status(thm)],[4067])).
% 1.61/1.78 tff(4069,plain,
% 1.61/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (~c1_1(a58)) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c2_1(a58)) | c3_1(a58))),
% 1.61/1.78 inference(transitivity,[status(thm)],[4068, 4066])).
% 1.61/1.78 tff(4070,plain,
% 1.61/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a58) | (~c2_1(a58)) | (~c1_1(a58)) | c2_1(a7) | (~c3_1(a7)) | (~c0_1(a7)) | c2_1(a7) | c1_1(a7) | (~c3_1(a7)))),
% 1.61/1.78 inference(quant_inst,[status(thm)],[])).
% 1.61/1.78 tff(4071,plain,
% 1.61/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (~c1_1(a58)) | c2_1(a7) | (~ndr1_0) | (~c3_1(a7)) | (~c0_1(a7)) | c1_1(a7) | (~c2_1(a58)) | c3_1(a58)),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[4070, 4069])).
% 1.61/1.78 tff(4072,plain,
% 1.61/1.78 (c1_1(a7)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4071, 101, 59, 3191, 3190, 3759, 3189, 264, 2169])).
% 1.61/1.78 tff(4073,plain,
% 1.61/1.78 ($false),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[2931, 101, 3191, 3190, 226, 225, 224, 3189, 36, 4072])).
% 1.61/1.78 tff(4074,plain,((~hskp3) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~c2_1(a58)) | c3_1(a58)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.78 tff(4075,plain,
% 1.61/1.78 (~hskp3),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4074, 4065, 4064, 4063, 4054, 4055])).
% 1.61/1.78 tff(4076,plain,
% 1.61/1.78 (~hskp20),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3925, 4075, 11])).
% 1.61/1.78 tff(4077,plain,
% 1.61/1.78 (hskp21),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3920, 4076, 4064, 4063, 14, 13, 12])).
% 1.61/1.78 tff(4078,plain,
% 1.61/1.78 ((~hskp28) | hskp3),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[3028, 3765])).
% 1.61/1.78 tff(4079,plain,
% 1.61/1.78 (~hskp28),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4078, 4075])).
% 1.61/1.78 tff(4080,plain,
% 1.61/1.78 ((~hskp27) | hskp28 | hskp0 | hskp3),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[585, 3765])).
% 1.61/1.78 tff(4081,plain,
% 1.61/1.78 (~hskp27),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4080, 4079, 11, 4075])).
% 1.61/1.78 tff(4082,plain,
% 1.61/1.78 (c2_1(a38)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[624, 4081, 4077, 13, 12, 14])).
% 1.61/1.78 tff(4083,plain,
% 1.61/1.78 ($false),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[2399, 4082, 4077])).
% 1.61/1.78 tff(4084,plain,(c0_1(a58) | c2_1(a2) | c3_1(a2) | c0_1(a2) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.61/1.78 tff(4085,plain,
% 1.61/1.78 (c0_1(a58)),
% 1.61/1.78 inference(unit_resolution,[status(thm)],[4084, 14, 12, 13, 11])).
% 1.61/1.78 tff(4086,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a58)))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4087,plain,
% 1.61/1.78 ((hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | (~c1_1(a2))) <=> (hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a58)))),
% 1.61/1.78 inference(rewrite,[status(thm)],[])).
% 1.61/1.78 tff(4088,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | (~c1_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a58))))),
% 1.61/1.78 inference(monotonicity,[status(thm)],[4087])).
% 1.61/1.78 tff(4089,plain,
% 1.61/1.78 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | (~c1_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a58)))),
% 1.61/1.78 inference(transitivity,[status(thm)],[4088, 4086])).
% 1.61/1.78 tff(4090,plain,
% 1.61/1.78 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a2) | c0_1(a2) | (~c1_1(a2)))),
% 1.61/1.78 inference(quant_inst,[status(thm)],[])).
% 1.61/1.78 tff(4091,plain,
% 1.61/1.78 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a2) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c2_1(a58))),
% 1.61/1.78 inference(modus_ponens,[status(thm)],[4090, 4089])).
% 1.61/1.78 tff(4092,plain,
% 1.61/1.78 (hskp6 | (~c0_1(a58)) | c0_1(a2) | (~c1_1(a2))),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4091, 101, 4054, 3759, 13, 3777])).
% 1.61/1.79 tff(4093,plain,
% 1.61/1.79 (~c1_1(a2)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4092, 25, 14, 4085])).
% 1.61/1.79 tff(4094,plain,
% 1.61/1.79 (hskp20),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[661, 4093, 13, 3767])).
% 1.61/1.79 tff(4095,plain,
% 1.61/1.79 (~c0_1(a37)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[631, 4094])).
% 1.61/1.79 tff(4096,plain,
% 1.61/1.79 (c3_1(a37)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[516, 4094])).
% 1.61/1.79 tff(4097,plain,
% 1.61/1.79 (~c2_1(a37)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[639, 101, 11, 4096, 4095, 14, 13, 12, 24])).
% 1.61/1.79 tff(4098,plain,
% 1.61/1.79 (c1_1(a37)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[524, 4094])).
% 1.61/1.79 tff(4099,plain,
% 1.61/1.79 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a37) | (~ndr1_0) | c2_1(a37) | (~c1_1(a37)) | (~c2_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a37) | (~ndr1_0) | c2_1(a37) | (~c1_1(a37)) | (~c2_1(a58)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4100,plain,
% 1.61/1.79 ((hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a37) | c0_1(a37) | (~c1_1(a37))) <=> (hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a37) | (~ndr1_0) | c2_1(a37) | (~c1_1(a37)) | (~c2_1(a58)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4101,plain,
% 1.61/1.79 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a37) | c0_1(a37) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a37) | (~ndr1_0) | c2_1(a37) | (~c1_1(a37)) | (~c2_1(a58))))),
% 1.61/1.79 inference(monotonicity,[status(thm)],[4100])).
% 1.61/1.79 tff(4102,plain,
% 1.61/1.79 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a37) | c0_1(a37) | (~c1_1(a37)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a37) | (~ndr1_0) | c2_1(a37) | (~c1_1(a37)) | (~c2_1(a58)))),
% 1.61/1.79 inference(transitivity,[status(thm)],[4101, 4099])).
% 1.61/1.79 tff(4103,plain,
% 1.61/1.79 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)) | c2_1(a37) | c0_1(a37) | (~c1_1(a37)))),
% 1.61/1.79 inference(quant_inst,[status(thm)],[])).
% 1.61/1.79 tff(4104,plain,
% 1.61/1.79 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | (~c0_1(a58)) | (~c1_1(a58)) | c0_1(a37) | (~ndr1_0) | c2_1(a37) | (~c1_1(a37)) | (~c2_1(a58))),
% 1.61/1.79 inference(modus_ponens,[status(thm)],[4103, 4102])).
% 1.61/1.79 tff(4105,plain,
% 1.61/1.79 ($false),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4104, 101, 25, 4054, 4098, 4085, 3759, 4095, 3777, 4097])).
% 1.61/1.79 tff(4106,plain,(hskp6 | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.79 tff(4107,plain,
% 1.61/1.79 (hskp6),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4106, 14, 11, 13, 12])).
% 1.61/1.79 tff(4108,plain,
% 1.61/1.79 (~c3_1(a13)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[177, 4107])).
% 1.61/1.79 tff(4109,plain,
% 1.61/1.79 (~c1_1(a13)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[183, 4107])).
% 1.61/1.79 tff(4110,plain,
% 1.61/1.79 (hskp20),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3920, 3767, 225, 224, 14, 13, 12])).
% 1.61/1.79 tff(4111,plain,
% 1.61/1.79 (~c0_1(a37)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[631, 4110])).
% 1.61/1.79 tff(4112,plain,
% 1.61/1.79 (c3_1(a37)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[516, 4110])).
% 1.61/1.79 tff(4113,plain,
% 1.61/1.79 (~c2_1(a37)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[639, 101, 11, 4112, 4111, 14, 13, 12, 24])).
% 1.61/1.79 tff(4114,plain,
% 1.61/1.79 (c1_1(a37)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[524, 4110])).
% 1.61/1.79 tff(4115,plain,
% 1.61/1.79 ($false),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4104, 101, 25, 4054, 4114, 4085, 3759, 4111, 3777, 4113])).
% 1.61/1.79 tff(4116,plain,(hskp6 | hskp0 | c0_1(a2) | c2_1(a2) | c3_1(a2) | c1_1(a13) | c3_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.79 tff(4117,plain,
% 1.61/1.79 (hskp6),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4116, 225, 14, 13, 12, 11, 224])).
% 1.61/1.79 tff(4118,plain,
% 1.61/1.79 (~c0_1(a13)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[189, 4117])).
% 1.61/1.79 tff(4119,plain,
% 1.61/1.79 (hskp20),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3920, 757, 225, 224, 14, 13, 12])).
% 1.61/1.79 tff(4120,plain,
% 1.61/1.79 (hskp3),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3925, 4119, 11])).
% 1.61/1.79 tff(4121,plain,
% 1.61/1.79 (~c2_1(a7)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2863, 4120])).
% 1.61/1.79 tff(4122,plain,
% 1.61/1.79 (c3_1(a7)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2873, 4120])).
% 1.61/1.79 tff(4123,plain,
% 1.61/1.79 (c0_1(a7)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2881, 4120])).
% 1.61/1.79 tff(4124,plain,
% 1.61/1.79 (~c1_1(a21)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2898, 101, 3917, 4123, 4122, 3915, 4121, 264, 2866])).
% 1.61/1.79 tff(4125,plain,
% 1.61/1.79 (c3_1(a58)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4074, 4120, 225, 224, 4054, 4118])).
% 1.61/1.79 tff(4126,plain,
% 1.61/1.79 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp0 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c3_1(a58)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4127,plain,
% 1.61/1.79 ((hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a58)) | (~c1_1(a58)) | (~c0_1(a58))) <=> (hskp22 | hskp0 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c3_1(a58)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4128,plain,
% 1.61/1.79 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c3_1(a58))))),
% 1.61/1.79 inference(monotonicity,[status(thm)],[4127])).
% 1.61/1.79 tff(4129,plain,
% 1.61/1.79 (((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp0 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c3_1(a58)))),
% 1.61/1.79 inference(transitivity,[status(thm)],[4128, 4126])).
% 1.61/1.79 tff(4130,plain,
% 1.61/1.79 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(a58)) | (~c1_1(a58)) | (~c0_1(a58)))),
% 1.61/1.79 inference(quant_inst,[status(thm)],[])).
% 1.61/1.79 tff(4131,plain,
% 1.61/1.79 ((~![U: $i] : (hskp22 | hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | hskp0 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c3_1(a58))),
% 1.61/1.79 inference(modus_ponens,[status(thm)],[4130, 4129])).
% 1.61/1.79 tff(4132,plain,
% 1.61/1.79 (hskp22 | hskp0 | (~c0_1(a58)) | (~c3_1(a58))),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4131, 101, 3759, 3839])).
% 1.61/1.79 tff(4133,plain,
% 1.61/1.79 (hskp22),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4132, 4125, 11, 4085])).
% 1.61/1.79 tff(4134,plain,
% 1.61/1.79 (~c1_1(a42)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1391, 4133])).
% 1.61/1.79 tff(4135,plain,
% 1.61/1.79 (c2_1(a42)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1400, 4133])).
% 1.61/1.79 tff(4136,plain,
% 1.61/1.79 (c0_1(a42)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1408, 4133])).
% 1.61/1.79 tff(4137,plain,
% 1.61/1.79 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a42) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4138,plain,
% 1.61/1.79 ((hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21))) <=> (hskp18 | c1_1(a42) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4139,plain,
% 1.61/1.79 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a42) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a42)) | (~c0_1(a42))))),
% 1.61/1.79 inference(monotonicity,[status(thm)],[4138])).
% 1.61/1.79 tff(4140,plain,
% 1.61/1.79 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a42)) | (~c0_1(a42)))),
% 1.61/1.79 inference(transitivity,[status(thm)],[4139, 4137])).
% 1.61/1.79 tff(4141,plain,
% 1.61/1.79 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | c1_1(a42) | (~c2_1(a42)) | (~c0_1(a42)) | c3_1(a21) | c1_1(a21) | (~c0_1(a21)))),
% 1.61/1.79 inference(quant_inst,[status(thm)],[])).
% 1.61/1.79 tff(4142,plain,
% 1.61/1.79 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a42) | c3_1(a21) | (~ndr1_0) | c1_1(a21) | (~c0_1(a21)) | (~c2_1(a42)) | (~c0_1(a42))),
% 1.61/1.79 inference(modus_ponens,[status(thm)],[4141, 4140])).
% 1.61/1.79 tff(4143,plain,
% 1.61/1.79 (hskp18),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4142, 101, 4136, 4135, 3918, 4134, 3915, 2641, 4124])).
% 1.61/1.79 tff(4144,plain,
% 1.61/1.79 (~c0_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[423, 4143])).
% 1.61/1.79 tff(4145,plain,
% 1.61/1.79 (~c3_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[385, 4143])).
% 1.61/1.79 tff(4146,plain,
% 1.61/1.79 (c2_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3747, 4145, 11, 4119, 4122, 4121, 4123, 14, 13, 12, 4144])).
% 1.61/1.79 tff(4147,plain,
% 1.61/1.79 (c1_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[393, 4143])).
% 1.61/1.79 tff(4148,plain,
% 1.61/1.79 ($false),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3755, 101, 4147, 3918, 3917, 4145, 14, 13, 12, 1264, 4146, 4124])).
% 1.61/1.79 tff(4149,plain,(hskp21 | c0_1(a2) | c2_1(a2) | c3_1(a2) | hskp0 | c1_1(a7) | c1_1(a13) | c3_1(a13)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.79 tff(4150,plain,
% 1.61/1.79 (hskp21),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4149, 225, 13, 12, 11, 2866, 14, 224])).
% 1.61/1.79 tff(4151,plain,
% 1.61/1.79 (~c2_1(a38)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2399, 4150])).
% 1.61/1.79 tff(4152,plain,
% 1.61/1.79 (c1_1(a38)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[603, 4150])).
% 1.61/1.79 tff(4153,plain,
% 1.61/1.79 (c0_1(a38)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[595, 4150])).
% 1.61/1.79 tff(4154,plain,
% 1.61/1.79 (~c3_1(a38)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1001, 101, 4153, 4152, 4151, 4118, 225, 224, 36])).
% 1.61/1.79 tff(4155,plain,
% 1.61/1.79 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))))),
% 1.61/1.79 inference(bind,[status(th)],[])).
% 1.61/1.79 tff(4156,plain,
% 1.61/1.79 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 1.61/1.79 inference(quant_intro,[status(thm)],[4155])).
% 1.61/1.79 tff(4157,plain,
% 1.61/1.79 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4158,plain,
% 1.61/1.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp7) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))))),
% 1.61/1.79 inference(bind,[status(th)],[])).
% 1.61/1.79 tff(4159,plain,
% 1.61/1.79 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 1.61/1.79 inference(quant_intro,[status(thm)],[4158])).
% 1.61/1.79 tff(4160,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))) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.61/1.79 tff(4161,plain,
% 1.61/1.79 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 1.61/1.79 inference(modus_ponens,[status(thm)],[4160, 4159])).
% 1.61/1.79 tff(4162,plain,
% 1.61/1.79 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 1.61/1.79 inference(modus_ponens,[status(thm)],[4161, 4157])).
% 1.61/1.79 tff(4163,plain,(
% 1.61/1.79 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 1.61/1.79 inference(skolemize,[status(sab)],[4162])).
% 1.61/1.79 tff(4164,plain,
% 1.61/1.79 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))),
% 1.61/1.79 inference(modus_ponens,[status(thm)],[4163, 4156])).
% 1.61/1.79 tff(4165,plain,
% 1.61/1.79 (hskp27),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[624, 4151, 4150, 13, 12, 14])).
% 1.61/1.79 tff(4166,plain,
% 1.61/1.79 (c3_1(a12)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[560, 4165])).
% 1.61/1.79 tff(4167,plain,
% 1.61/1.79 (c1_1(a12)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[568, 4165])).
% 1.61/1.79 tff(4168,plain,
% 1.61/1.79 (c0_1(a12)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1114, 4165])).
% 1.61/1.79 tff(4169,plain,
% 1.61/1.79 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | (hskp7 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | hskp7 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4170,plain,
% 1.61/1.79 ((hskp7 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | (~c2_1(a58)) | (~c0_1(a58)) | (~c1_1(a58))) <=> (hskp7 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4171,plain,
% 1.61/1.79 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | (~c2_1(a58)) | (~c0_1(a58)) | (~c1_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | (hskp7 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))))),
% 1.61/1.79 inference(monotonicity,[status(thm)],[4170])).
% 1.61/1.79 tff(4172,plain,
% 1.61/1.79 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | (~c2_1(a58)) | (~c0_1(a58)) | (~c1_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | hskp7 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)))),
% 1.61/1.79 inference(transitivity,[status(thm)],[4171, 4169])).
% 1.61/1.79 tff(4173,plain,
% 1.61/1.79 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12)) | (~c2_1(a58)) | (~c0_1(a58)) | (~c1_1(a58)))),
% 1.61/1.79 inference(quant_inst,[status(thm)],[])).
% 1.61/1.79 tff(4174,plain,
% 1.61/1.79 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(V)))) | hskp7 | (~c0_1(a58)) | (~c1_1(a58)) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a12)) | (~c1_1(a12)) | (~c0_1(a12))),
% 1.61/1.79 inference(modus_ponens,[status(thm)],[4173, 4172])).
% 1.61/1.79 tff(4175,plain,
% 1.61/1.79 (hskp7),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4174, 101, 4168, 4167, 4166, 4054, 4085, 3759, 4164])).
% 1.61/1.79 tff(4176,plain,
% 1.61/1.79 (~c2_1(a14)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1330, 4175])).
% 1.61/1.79 tff(4177,plain,
% 1.61/1.79 (~c0_1(a14)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1352, 4175])).
% 1.61/1.79 tff(4178,plain,
% 1.61/1.79 (hskp22),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3846, 101, 11, 4168, 4167, 4166, 3839])).
% 1.61/1.79 tff(4179,plain,
% 1.61/1.79 (~c1_1(a42)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1391, 4178])).
% 1.61/1.79 tff(4180,plain,
% 1.61/1.79 (c1_1(a14)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1338, 4175])).
% 1.61/1.79 tff(4181,plain,
% 1.61/1.79 (c2_1(a42)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1400, 4178])).
% 1.61/1.79 tff(4182,plain,
% 1.61/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a42) | c2_1(a38) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a42) | c2_1(a38) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4183,plain,
% 1.61/1.79 (((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14))) <=> (c1_1(a42) | c2_1(a38) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4184,plain,
% 1.61/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a42) | c2_1(a38) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42))))),
% 1.61/1.79 inference(monotonicity,[status(thm)],[4183])).
% 1.61/1.79 tff(4185,plain,
% 1.61/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a42) | c2_1(a38) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 1.61/1.79 inference(transitivity,[status(thm)],[4184, 4182])).
% 1.61/1.79 tff(4186,plain,
% 1.61/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a38) | c2_1(a38) | (~c0_1(a38)) | c1_1(a42) | (~c2_1(a42)) | (~c3_1(a42)) | c2_1(a14) | c0_1(a14) | (~c1_1(a14)))),
% 1.61/1.79 inference(quant_inst,[status(thm)],[])).
% 1.61/1.79 tff(4187,plain,
% 1.61/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a42) | c2_1(a38) | c0_1(a14) | c2_1(a14) | (~ndr1_0) | (~c1_1(a14)) | c3_1(a38) | (~c0_1(a38)) | (~c2_1(a42)) | (~c3_1(a42))),
% 1.61/1.79 inference(modus_ponens,[status(thm)],[4186, 4185])).
% 1.61/1.79 tff(4188,plain,
% 1.61/1.79 (~c3_1(a42)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4187, 101, 4181, 4153, 4180, 4179, 4151, 4177, 4176, 1965, 4154])).
% 1.61/1.79 tff(4189,plain,
% 1.61/1.79 (hskp8),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2198, 101, 4168, 4167, 4166, 4153, 4152, 2187, 4154])).
% 1.61/1.79 tff(4190,plain,
% 1.61/1.79 (~c3_1(a15)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1316, 4189])).
% 1.61/1.79 tff(4191,plain,
% 1.61/1.79 (~c2_1(a15)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1997, 4189])).
% 1.61/1.79 tff(4192,plain,
% 1.61/1.79 (~c1_1(a15)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2088, 4189])).
% 1.61/1.79 tff(4193,plain,
% 1.61/1.79 (c0_1(a42)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1408, 4178])).
% 1.61/1.79 tff(4194,plain,
% 1.61/1.79 (~c2_1(a13)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3867, 101, 4193, 4179, 4192, 4191, 4190, 4118, 224, 323, 4188])).
% 1.61/1.79 tff(4195,plain,
% 1.61/1.79 (hskp18),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3874, 101, 4193, 4181, 4179, 2641, 4188])).
% 1.61/1.79 tff(4196,plain,
% 1.61/1.79 (~c3_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[385, 4195])).
% 1.61/1.79 tff(4197,plain,
% 1.61/1.79 (c1_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[393, 4195])).
% 1.61/1.79 tff(4198,plain,
% 1.61/1.79 (~c2_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3883, 101, 4193, 4181, 4197, 4179, 4196, 4118, 224, 1264, 4194])).
% 1.61/1.79 tff(4199,plain,
% 1.61/1.79 (hskp12),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3900, 101, 4168, 4167, 4166, 4193, 4181, 4179, 3894])).
% 1.61/1.79 tff(4200,plain,
% 1.61/1.79 (~c3_1(a20)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[930, 4199])).
% 1.61/1.79 tff(4201,plain,
% 1.61/1.79 (~c1_1(a20)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[936, 4199])).
% 1.61/1.79 tff(4202,plain,
% 1.61/1.79 (c2_1(a20)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[944, 4199])).
% 1.61/1.79 tff(4203,plain,
% 1.61/1.79 ($false),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2560, 101, 4197, 4202, 4196, 4201, 4200, 4118, 225, 362, 4194, 4198])).
% 1.61/1.79 tff(4204,plain,(c1_1(a13) | c3_1(a13) | hskp0 | c2_1(a2) | c3_1(a2) | c0_1(a2) | c1_1(a7)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.79 tff(4205,plain,
% 1.61/1.79 (c1_1(a7)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4204, 4108, 11, 13, 12, 14, 4109])).
% 1.61/1.79 tff(4206,plain,
% 1.61/1.79 (~c0_1(a13)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[189, 4107])).
% 1.61/1.79 tff(4207,assumption,(c1_1(a7)), introduced(assumption)).
% 1.61/1.79 tff(4208,plain,
% 1.61/1.79 ($false),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2931, 101, 3191, 3190, 226, 225, 224, 3189, 36, 4207])).
% 1.61/1.79 tff(4209,plain,((~hskp3) | c0_1(a13) | c1_1(a13) | c3_1(a13) | (~c1_1(a7))), inference(lemma,lemma(discharge,[]))).
% 1.61/1.79 tff(4210,plain,
% 1.61/1.79 (~hskp3),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4209, 4206, 4109, 4108, 4205])).
% 1.61/1.79 tff(4211,plain,
% 1.61/1.79 (~hskp20),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3925, 4210, 11])).
% 1.61/1.79 tff(4212,plain,
% 1.61/1.79 (hskp21),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3920, 4211, 4109, 4108, 14, 13, 12])).
% 1.61/1.79 tff(4213,plain,
% 1.61/1.79 (~hskp28),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4078, 4210])).
% 1.61/1.79 tff(4214,plain,
% 1.61/1.79 (~hskp27),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4080, 4213, 11, 4210])).
% 1.61/1.79 tff(4215,plain,
% 1.61/1.79 (c2_1(a38)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[624, 4214, 4212, 13, 12, 14])).
% 1.61/1.79 tff(4216,plain,
% 1.61/1.79 ($false),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2399, 4215, 4212])).
% 1.61/1.79 tff(4217,plain,(c0_1(a2) | c2_1(a2) | c3_1(a2) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.61/1.79 tff(4218,plain,
% 1.61/1.79 (c0_1(a2)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4217, 13, 12, 11])).
% 1.61/1.79 tff(4219,plain,
% 1.61/1.79 (~hskp1),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[253, 4218])).
% 1.61/1.79 tff(4220,plain,
% 1.61/1.79 (~hskp6),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3646, 4219, 11])).
% 1.61/1.79 tff(4221,plain,
% 1.61/1.79 (~hskp21),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3766, 4220])).
% 1.61/1.79 tff(4222,plain,
% 1.61/1.79 (hskp13),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3778, 4221])).
% 1.61/1.79 tff(4223,plain,
% 1.61/1.79 (c0_1(a21)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[790, 4222])).
% 1.61/1.79 tff(4224,plain,
% 1.61/1.79 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4225,plain,
% 1.61/1.79 ((hskp24 | hskp6 | (~ndr1_0) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2))) <=> (hskp24 | hskp6 | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4226,plain,
% 1.61/1.79 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2))))),
% 1.61/1.79 inference(monotonicity,[status(thm)],[4225])).
% 1.61/1.79 tff(4227,plain,
% 1.61/1.79 (((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)))),
% 1.61/1.79 inference(transitivity,[status(thm)],[4226, 4224])).
% 1.61/1.79 tff(4228,plain,
% 1.61/1.79 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp6 | (~ndr1_0) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)))),
% 1.61/1.79 inference(quant_inst,[status(thm)],[])).
% 1.61/1.79 tff(4229,plain,
% 1.61/1.79 ((~![U: $i] : (hskp24 | hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp6 | (~c0_1(a2)) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2))),
% 1.61/1.79 inference(modus_ponens,[status(thm)],[4228, 4227])).
% 1.61/1.79 tff(4230,plain,
% 1.61/1.79 (hskp6 | (~c0_1(a2)) | (~c1_1(a2))),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4229, 101, 3765, 13, 984])).
% 1.61/1.79 tff(4231,plain,
% 1.61/1.79 (~c1_1(a2)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4230, 4220, 4218])).
% 1.61/1.79 tff(4232,plain,
% 1.61/1.79 (hskp20),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[661, 4231, 13, 4221])).
% 1.61/1.79 tff(4233,plain,
% 1.61/1.79 (hskp3),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3925, 4232, 11])).
% 1.61/1.79 tff(4234,plain,
% 1.61/1.79 (~c2_1(a7)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2863, 4233])).
% 1.61/1.79 tff(4235,plain,
% 1.61/1.79 (c0_1(a7)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2881, 4233])).
% 1.61/1.79 tff(4236,plain,
% 1.61/1.79 (~c1_1(a7)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2919, 101, 3765, 4220, 4235, 4234, 984])).
% 1.61/1.79 tff(4237,plain,
% 1.61/1.79 (~c3_1(a21)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[774, 4222])).
% 1.61/1.79 tff(4238,plain,
% 1.61/1.79 (c3_1(a7)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2873, 4233])).
% 1.61/1.79 tff(4239,plain,
% 1.61/1.79 (c2_1(a21)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[782, 4222])).
% 1.61/1.79 tff(4240,plain,
% 1.61/1.79 (~c1_1(a21)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2898, 101, 4239, 4235, 4238, 4237, 4234, 264, 4236])).
% 1.61/1.79 tff(4241,plain,
% 1.61/1.79 (hskp18),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2647, 101, 4223, 4239, 4237, 2641, 4240])).
% 1.61/1.79 tff(4242,plain,
% 1.61/1.79 (c1_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[393, 4241])).
% 1.61/1.79 tff(4243,plain,
% 1.61/1.79 (hskp10 | c1_1(a21)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3668, 101, 4219, 4239, 4237, 1786])).
% 1.61/1.79 tff(4244,plain,
% 1.61/1.79 (hskp10),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4243, 4240])).
% 1.61/1.79 tff(4245,plain,
% 1.61/1.79 (~c0_1(a18)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[874, 4244])).
% 1.61/1.79 tff(4246,plain,
% 1.61/1.79 (c3_1(a18)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[962, 4244])).
% 1.61/1.79 tff(4247,plain,
% 1.61/1.79 (~c1_1(a18)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[868, 4244])).
% 1.61/1.79 tff(4248,plain,
% 1.61/1.79 (~c0_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[423, 4241])).
% 1.61/1.79 tff(4249,plain,
% 1.61/1.79 (~c3_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[385, 4241])).
% 1.61/1.79 tff(4250,plain,
% 1.61/1.79 ($false),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3701, 4249, 4248, 4220, 4247, 4239, 4246, 4245, 4237, 11, 4242, 4223])).
% 1.61/1.79 tff(4251,plain,(c2_1(a2) | hskp0 | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.79 tff(4252,plain,
% 1.61/1.79 (c2_1(a2)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4251, 11, 12])).
% 1.61/1.79 tff(4253,plain,
% 1.61/1.79 (~hskp1),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[247, 4252])).
% 1.61/1.79 tff(4254,plain,
% 1.61/1.79 (~hskp6),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3646, 4253, 11])).
% 1.61/1.79 tff(4255,plain,
% 1.61/1.79 (~hskp21),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3766, 4254])).
% 1.61/1.79 tff(4256,plain,
% 1.61/1.79 (hskp13),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3778, 4255])).
% 1.61/1.79 tff(4257,plain,
% 1.61/1.79 (c0_1(a21)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[790, 4256])).
% 1.61/1.79 tff(4258,plain,
% 1.61/1.79 (~c3_1(a21)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[774, 4256])).
% 1.61/1.79 tff(4259,plain,
% 1.61/1.79 (c2_1(a21)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[782, 4256])).
% 1.61/1.79 tff(4260,plain,
% 1.61/1.79 (~c1_1(a21)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2423, 101, 4254, 4257, 4259, 4258, 141])).
% 1.61/1.79 tff(4261,plain,
% 1.61/1.79 (hskp18),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2647, 101, 4257, 4259, 4258, 2641, 4260])).
% 1.61/1.79 tff(4262,plain,
% 1.61/1.79 (c1_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[393, 4261])).
% 1.61/1.79 tff(4263,plain,
% 1.61/1.79 (hskp10 | c1_1(a21)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3668, 101, 4253, 4259, 4258, 1786])).
% 1.61/1.79 tff(4264,plain,
% 1.61/1.79 (hskp10),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4263, 4260])).
% 1.61/1.79 tff(4265,plain,
% 1.61/1.79 (~c0_1(a18)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[874, 4264])).
% 1.61/1.79 tff(4266,plain,
% 1.61/1.79 (c3_1(a18)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[962, 4264])).
% 1.61/1.79 tff(4267,plain,
% 1.61/1.79 (~c1_1(a18)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[868, 4264])).
% 1.61/1.79 tff(4268,plain,
% 1.61/1.79 (~c0_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[423, 4261])).
% 1.61/1.79 tff(4269,plain,
% 1.61/1.79 (~c3_1(a31)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[385, 4261])).
% 1.61/1.79 tff(4270,plain,
% 1.61/1.79 ($false),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3701, 4269, 4268, 4254, 4267, 4259, 4266, 4265, 4258, 11, 4262, 4257])).
% 1.61/1.79 tff(4271,plain,(hskp0 | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.79 tff(4272,plain,
% 1.61/1.79 (hskp0),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4271, 12])).
% 1.61/1.79 tff(4273,plain,
% 1.61/1.79 ($false),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3642, 3190, 3191, 2457, 3189])).
% 1.61/1.79 tff(4274,plain,((~hskp3) | (~hskp0)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.79 tff(4275,plain,
% 1.61/1.79 (~hskp3),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4274, 4272])).
% 1.61/1.79 tff(4276,plain,
% 1.61/1.79 (~hskp28),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4078, 4275])).
% 1.61/1.79 tff(4277,plain,
% 1.61/1.79 (c1_1(a1)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[130, 4272])).
% 1.61/1.79 tff(4278,plain,
% 1.61/1.79 (~c3_1(a1)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[114, 4272])).
% 1.61/1.79 tff(4279,plain,
% 1.61/1.79 (c2_1(a1)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[122, 4272])).
% 1.61/1.79 tff(4280,plain,
% 1.61/1.79 (~c2_1(a13)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[332, 14, 4279, 4278, 4277, 13, 12])).
% 1.61/1.79 tff(4281,plain,
% 1.61/1.79 (hskp6),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[171, 4279, 4277, 4278])).
% 1.61/1.79 tff(4282,plain,
% 1.61/1.79 (~c3_1(a13)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[177, 4281])).
% 1.61/1.79 tff(4283,plain,
% 1.61/1.79 (~c1_1(a13)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[183, 4281])).
% 1.61/1.79 tff(4284,assumption,(~c2_1(a37)), introduced(assumption)).
% 1.61/1.79 tff(4285,plain,
% 1.61/1.79 (hskp20),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[3920, 757, 4283, 4282, 14, 13, 12])).
% 1.61/1.79 tff(4286,plain,
% 1.61/1.79 (c3_1(a37)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[516, 4285])).
% 1.61/1.79 tff(4287,plain,
% 1.61/1.79 (c1_1(a37)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[524, 4285])).
% 1.61/1.79 tff(4288,plain,
% 1.61/1.79 (hskp9),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[833, 101, 4287, 4286, 4277, 4279, 4278, 827, 4284])).
% 1.61/1.79 tff(4289,plain,
% 1.61/1.79 (~c3_1(a16)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[839, 4288])).
% 1.61/1.79 tff(4290,plain,
% 1.61/1.79 (c1_1(a16)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[847, 4288])).
% 1.61/1.79 tff(4291,plain,
% 1.61/1.79 (c0_1(a16)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[855, 4288])).
% 1.61/1.79 tff(4292,plain,
% 1.61/1.79 (hskp10),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[862, 101, 757, 4291, 4290, 4289, 813])).
% 1.61/1.79 tff(4293,plain,
% 1.61/1.79 (~c1_1(a18)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[868, 4292])).
% 1.61/1.79 tff(4294,plain,
% 1.61/1.79 (c3_1(a18)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[962, 4292])).
% 1.61/1.79 tff(4295,plain,
% 1.61/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a18) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a18) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4296,plain,
% 1.61/1.79 (((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2)) <=> (c1_1(a18) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)))),
% 1.61/1.79 inference(rewrite,[status(thm)],[])).
% 1.61/1.79 tff(4297,plain,
% 1.61/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a18) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18))))),
% 1.61/1.79 inference(monotonicity,[status(thm)],[4296])).
% 1.61/1.79 tff(4298,plain,
% 1.61/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a18) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18)))),
% 1.61/1.79 inference(transitivity,[status(thm)],[4297, 4295])).
% 1.61/1.79 tff(4299,plain,
% 1.61/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a18) | (~c2_1(a18)) | (~c3_1(a18)) | c3_1(a13) | c2_1(a13) | c1_1(a13) | c2_1(a2) | c0_1(a2) | c3_1(a2))),
% 1.61/1.79 inference(quant_inst,[status(thm)],[])).
% 1.61/1.79 tff(4300,plain,
% 1.61/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a18) | c1_1(a13) | c3_1(a13) | c0_1(a2) | c2_1(a2) | c3_1(a2) | (~ndr1_0) | c2_1(a13) | (~c2_1(a18)) | (~c3_1(a18))),
% 1.61/1.79 inference(modus_ponens,[status(thm)],[4299, 4298])).
% 1.61/1.79 tff(4301,plain,
% 1.61/1.79 (~c2_1(a18)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4300, 101, 4294, 4293, 4283, 4282, 14, 13, 12, 344, 4280])).
% 1.61/1.79 tff(4302,plain,
% 1.61/1.79 (~c0_1(a13)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[189, 4281])).
% 1.61/1.79 tff(4303,plain,
% 1.61/1.79 (~c0_1(a37)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[631, 4285])).
% 1.61/1.79 tff(4304,plain,
% 1.61/1.79 (hskp12),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[1079, 101, 4286, 4291, 4290, 4303, 4289, 918, 4284])).
% 1.61/1.79 tff(4305,plain,
% 1.61/1.79 (~c3_1(a20)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[930, 4304])).
% 1.61/1.79 tff(4306,plain,
% 1.61/1.79 (~c1_1(a20)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[936, 4304])).
% 1.61/1.79 tff(4307,plain,
% 1.61/1.79 (c2_1(a20)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[944, 4304])).
% 1.61/1.79 tff(4308,plain,
% 1.61/1.79 (hskp5),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[951, 101, 4307, 4306, 4305, 4302, 4282, 275, 4280])).
% 1.61/1.79 tff(4309,plain,
% 1.61/1.79 (~c2_1(a11)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[291, 4308])).
% 1.61/1.79 tff(4310,plain,
% 1.61/1.79 (~c1_1(a11)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[297, 4308])).
% 1.61/1.79 tff(4311,plain,
% 1.61/1.79 (~c0_1(a18)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[874, 4292])).
% 1.61/1.79 tff(4312,plain,
% 1.61/1.79 (c0_1(a11)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[305, 4308])).
% 1.61/1.79 tff(4313,plain,
% 1.61/1.79 ($false),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[969, 101, 4294, 4312, 4311, 4293, 4310, 4309, 697, 4301])).
% 1.61/1.79 tff(4314,plain,(c2_1(a37) | c0_1(a2) | c2_1(a2) | c3_1(a2) | hskp21), inference(lemma,lemma(discharge,[]))).
% 1.61/1.79 tff(4315,plain,
% 1.61/1.79 (c2_1(a37)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4314, 757, 13, 12, 14])).
% 1.61/1.79 tff(4316,plain,
% 1.61/1.79 ($false),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[529, 101, 3765, 4275, 4287, 4286, 10, 4315])).
% 1.61/1.79 tff(4317,plain,(hskp21 | c2_1(a2) | c3_1(a2) | c0_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.79 tff(4318,plain,
% 1.61/1.79 (hskp21),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[4317, 14, 12, 13])).
% 1.61/1.79 tff(4319,plain,
% 1.61/1.79 (~c2_1(a38)),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[2399, 4318])).
% 1.61/1.79 tff(4320,plain,
% 1.61/1.79 (hskp27),
% 1.61/1.79 inference(unit_resolution,[status(thm)],[624, 4319, 4318, 13, 12, 14])).
% 1.61/1.79 tff(4321,plain,
% 1.61/1.79 (c3_1(a12)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[560, 4320])).
% 1.61/1.80 tff(4322,plain,
% 1.61/1.80 (c1_1(a12)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[568, 4320])).
% 1.61/1.80 tff(4323,plain,
% 1.61/1.80 (~c2_1(a12)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[575, 101, 3765, 4275, 4322, 4321, 10])).
% 1.61/1.80 tff(4324,plain,
% 1.61/1.80 (c1_1(a38)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[603, 4318])).
% 1.61/1.80 tff(4325,plain,
% 1.61/1.80 (c0_1(a38)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[595, 4318])).
% 1.61/1.80 tff(4326,plain,
% 1.61/1.80 (~c3_1(a38)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1001, 101, 4325, 4324, 4319, 4302, 4283, 4282, 36])).
% 1.61/1.80 tff(4327,plain,
% 1.61/1.80 (c0_1(a12)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1114, 4320])).
% 1.61/1.80 tff(4328,plain,
% 1.61/1.80 ($false),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1121, 101, 4327, 4322, 4321, 4325, 4324, 901, 4326, 4323])).
% 1.61/1.80 tff(4329,plain,(c0_1(a2) | c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.80 tff(4330,plain,
% 1.61/1.80 (c0_1(a2)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[4329, 13, 12])).
% 1.61/1.80 tff(4331,plain,
% 1.61/1.80 (~hskp1),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[253, 4330])).
% 1.61/1.80 tff(4332,plain,
% 1.61/1.80 (hskp20),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[508, 4331, 4276])).
% 1.61/1.80 tff(4333,plain,
% 1.61/1.80 (c3_1(a37)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[516, 4332])).
% 1.61/1.80 tff(4334,plain,
% 1.61/1.80 (c1_1(a37)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[524, 4332])).
% 1.61/1.80 tff(4335,plain,
% 1.61/1.80 (~c2_1(a37)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[529, 101, 3765, 4275, 4334, 4333, 10])).
% 1.61/1.80 tff(4336,plain,
% 1.61/1.80 (hskp2 | hskp1),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[232, 101, 4302, 4283, 4282, 47])).
% 1.61/1.80 tff(4337,plain,
% 1.61/1.80 (hskp2),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[4336, 4331])).
% 1.61/1.80 tff(4338,plain,
% 1.61/1.80 (~c2_1(a3)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[197, 4337])).
% 1.61/1.80 tff(4339,plain,
% 1.61/1.80 (c3_1(a3)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[205, 4337])).
% 1.61/1.80 tff(4340,plain,
% 1.61/1.80 (c1_1(a3)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[213, 4337])).
% 1.61/1.80 tff(4341,plain,
% 1.61/1.80 (hskp9),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1218, 101, 4340, 4339, 4277, 4279, 4338, 4278, 827])).
% 1.61/1.80 tff(4342,plain,
% 1.61/1.80 (~c3_1(a16)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[839, 4341])).
% 1.61/1.80 tff(4343,plain,
% 1.61/1.80 (~c0_1(a37)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[631, 4332])).
% 1.61/1.80 tff(4344,plain,
% 1.61/1.80 (c1_1(a16)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[847, 4341])).
% 1.61/1.80 tff(4345,plain,
% 1.61/1.80 (c2_1(a16)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[3233, 101, 4333, 4344, 4277, 4279, 4343, 4342, 4278, 680, 4335])).
% 1.61/1.80 tff(4346,plain,
% 1.61/1.80 (~c2_1(a13)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1253, 101, 4331, 4340, 4339, 4302, 4283, 4338, 58])).
% 1.61/1.80 tff(4347,plain,
% 1.61/1.80 (~c1_1(a2)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1805, 101, 4340, 4339, 4302, 4283, 4282, 4338, 4330, 13, 36])).
% 1.61/1.80 tff(4348,plain,
% 1.61/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~c0_1(a2)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c1_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c1_1(a2))),
% 1.61/1.80 inference(rewrite,[status(thm)],[])).
% 1.61/1.80 tff(4349,plain,
% 1.61/1.80 (((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a2) | c1_1(a2) | c3_1(a2)) <=> ((~c0_1(a2)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c1_1(a2))),
% 1.61/1.80 inference(rewrite,[status(thm)],[])).
% 1.61/1.80 tff(4350,plain,
% 1.61/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a2) | c1_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~c0_1(a2)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c1_1(a2)))),
% 1.61/1.80 inference(monotonicity,[status(thm)],[4349])).
% 1.61/1.80 tff(4351,plain,
% 1.61/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a2) | c1_1(a2) | c3_1(a2))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c1_1(a2))),
% 1.61/1.80 inference(transitivity,[status(thm)],[4350, 4348])).
% 1.61/1.80 tff(4352,plain,
% 1.61/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)) | c2_1(a2) | c1_1(a2) | c3_1(a2))),
% 1.61/1.80 inference(quant_inst,[status(thm)],[])).
% 1.61/1.80 tff(4353,plain,
% 1.61/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (~c0_1(a2)) | c2_1(a2) | c3_1(a2) | c3_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c0_1(a1) | c1_1(a2)),
% 1.61/1.80 inference(modus_ponens,[status(thm)],[4352, 4351])).
% 1.61/1.80 tff(4354,plain,
% 1.61/1.80 ((~c0_1(a2)) | c0_1(a1) | c1_1(a2)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[4353, 101, 4279, 13, 12, 4278, 323])).
% 1.61/1.80 tff(4355,plain,
% 1.61/1.80 (c0_1(a1)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[4354, 4347, 4330])).
% 1.61/1.80 tff(4356,plain,
% 1.61/1.80 (~c0_1(a3)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1954, 101, 4340, 4339, 4302, 4283, 4282, 4338, 36])).
% 1.61/1.80 tff(4357,plain,
% 1.61/1.80 (hskp12 | (~c0_1(a1))),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[3254, 101, 4339, 4277, 4338, 4278, 918, 4356])).
% 1.61/1.80 tff(4358,plain,
% 1.61/1.80 (hskp12),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[4357, 4355])).
% 1.61/1.80 tff(4359,plain,
% 1.61/1.80 (~c1_1(a20)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[936, 4358])).
% 1.61/1.80 tff(4360,plain,
% 1.61/1.80 (c2_1(a20)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[944, 4358])).
% 1.61/1.80 tff(4361,plain,
% 1.61/1.80 (~c0_1(a20)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1281, 101, 4360, 4344, 4359, 4342, 4302, 4282, 1264, 4346, 4345])).
% 1.61/1.80 tff(4362,plain,
% 1.61/1.80 (~c3_1(a20)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[930, 4358])).
% 1.61/1.80 tff(4363,plain,
% 1.61/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a20) | c1_1(a13) | c3_1(a13) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c2_1(a13) | c0_1(a20) | (~c2_1(a20)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a20) | c1_1(a13) | c3_1(a13) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c2_1(a13) | c0_1(a20) | (~c2_1(a20)))),
% 1.61/1.80 inference(rewrite,[status(thm)],[])).
% 1.61/1.80 tff(4364,plain,
% 1.61/1.80 (((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c3_1(a13)) <=> (c3_1(a20) | c1_1(a13) | c3_1(a13) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c2_1(a13) | c0_1(a20) | (~c2_1(a20)))),
% 1.61/1.80 inference(rewrite,[status(thm)],[])).
% 1.61/1.80 tff(4365,plain,
% 1.61/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_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) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c3_1(a20) | c1_1(a13) | c3_1(a13) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c2_1(a13) | c0_1(a20) | (~c2_1(a20))))),
% 1.61/1.80 inference(monotonicity,[status(thm)],[4364])).
% 1.61/1.80 tff(4366,plain,
% 1.61/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_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) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a20) | c1_1(a13) | c3_1(a13) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c2_1(a13) | c0_1(a20) | (~c2_1(a20)))),
% 1.61/1.80 inference(transitivity,[status(thm)],[4365, 4363])).
% 1.61/1.80 tff(4367,plain,
% 1.61/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | c3_1(a2) | c1_1(a2) | (~c0_1(a2)) | c3_1(a20) | c0_1(a20) | (~c2_1(a20)) | c2_1(a13) | c1_1(a13) | c3_1(a13))),
% 1.61/1.80 inference(quant_inst,[status(thm)],[])).
% 1.61/1.80 tff(4368,plain,
% 1.61/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c3_1(a20) | c1_1(a13) | c3_1(a13) | (~c0_1(a2)) | c3_1(a2) | (~ndr1_0) | c1_1(a2) | c2_1(a13) | c0_1(a20) | (~c2_1(a20))),
% 1.61/1.80 inference(modus_ponens,[status(thm)],[4367, 4366])).
% 1.61/1.80 tff(4369,plain,
% 1.61/1.80 ($false),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[4368, 101, 4360, 4362, 4283, 4282, 4330, 12, 323, 4346, 4347, 4361])).
% 1.61/1.80 tff(4370,plain,(c2_1(a2) | c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.80 tff(4371,plain,
% 1.61/1.80 (c2_1(a2)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[4370, 12])).
% 1.61/1.80 tff(4372,plain,
% 1.61/1.80 (~hskp1),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[247, 4371])).
% 1.61/1.80 tff(4373,plain,
% 1.61/1.80 (hskp20),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[508, 4372, 4276])).
% 1.61/1.80 tff(4374,plain,
% 1.61/1.80 (c3_1(a37)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[516, 4373])).
% 1.61/1.80 tff(4375,plain,
% 1.61/1.80 (c1_1(a37)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[524, 4373])).
% 1.61/1.80 tff(4376,plain,
% 1.61/1.80 (~c2_1(a37)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[529, 101, 3765, 4275, 4375, 4374, 10])).
% 1.61/1.80 tff(4377,plain,
% 1.61/1.80 (hskp2),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[4336, 4372])).
% 1.61/1.80 tff(4378,plain,
% 1.61/1.80 (~c2_1(a3)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[197, 4377])).
% 1.61/1.80 tff(4379,plain,
% 1.61/1.80 (c3_1(a3)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[205, 4377])).
% 1.61/1.80 tff(4380,plain,
% 1.61/1.80 (c1_1(a3)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[213, 4377])).
% 1.61/1.80 tff(4381,plain,
% 1.61/1.80 (hskp9),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1218, 101, 4380, 4379, 4277, 4279, 4378, 4278, 827])).
% 1.61/1.80 tff(4382,plain,
% 1.61/1.80 (~c3_1(a16)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[839, 4381])).
% 1.61/1.80 tff(4383,plain,
% 1.61/1.80 (~c0_1(a37)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[631, 4373])).
% 1.61/1.80 tff(4384,plain,
% 1.61/1.80 (c1_1(a16)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[847, 4381])).
% 1.61/1.80 tff(4385,plain,
% 1.61/1.80 (c2_1(a16)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[3233, 101, 4374, 4384, 4277, 4279, 4383, 4382, 4278, 680, 4376])).
% 1.61/1.80 tff(4386,plain,
% 1.61/1.80 (~c2_1(a13)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1253, 101, 4372, 4380, 4379, 4302, 4283, 4378, 58])).
% 1.61/1.80 tff(4387,plain,
% 1.61/1.80 (c0_1(a16)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[855, 4381])).
% 1.61/1.80 tff(4388,plain,
% 1.61/1.80 (hskp12),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1079, 101, 4374, 4387, 4384, 4383, 4382, 918, 4376])).
% 1.61/1.80 tff(4389,plain,
% 1.61/1.80 (~c1_1(a20)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[936, 4388])).
% 1.61/1.80 tff(4390,plain,
% 1.61/1.80 (c2_1(a20)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[944, 4388])).
% 1.61/1.80 tff(4391,plain,
% 1.61/1.80 (~c0_1(a20)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1281, 101, 4390, 4384, 4389, 4382, 4302, 4282, 1264, 4386, 4385])).
% 1.61/1.80 tff(4392,plain,
% 1.61/1.80 ($false),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[1288, 101, 4372, 4390, 4380, 4379, 4389, 4378, 58, 4391])).
% 1.61/1.80 tff(4393,plain,(c3_1(a2)), inference(lemma,lemma(discharge,[]))).
% 1.61/1.80 tff(4394,plain,
% 1.61/1.80 (~hskp1),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[241, 4393])).
% 1.61/1.80 tff(4395,plain,
% 1.61/1.80 ((~hskp6) | hskp0),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[3646, 4394])).
% 1.61/1.80 tff(4396,plain,
% 1.61/1.80 (~hskp6),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[4395, 11])).
% 1.61/1.80 tff(4397,plain,
% 1.61/1.80 (~hskp21),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[3766, 4396])).
% 1.61/1.80 tff(4398,plain,
% 1.61/1.80 (hskp13),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[3778, 4397])).
% 1.61/1.80 tff(4399,plain,
% 1.61/1.80 (c0_1(a21)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[790, 4398])).
% 1.61/1.80 tff(4400,plain,
% 1.61/1.80 (~c3_1(a21)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[774, 4398])).
% 1.61/1.80 tff(4401,plain,
% 1.61/1.80 (c2_1(a21)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[782, 4398])).
% 1.61/1.80 tff(4402,plain,
% 1.61/1.80 (~c1_1(a21)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[2423, 101, 4396, 4399, 4401, 4400, 141])).
% 1.61/1.80 tff(4403,plain,
% 1.61/1.80 (hskp18),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[2647, 101, 4399, 4401, 4400, 2641, 4402])).
% 1.61/1.80 tff(4404,plain,
% 1.61/1.80 (c1_1(a31)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[393, 4403])).
% 1.61/1.80 tff(4405,plain,
% 1.61/1.80 (hskp10 | c1_1(a21)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[3668, 101, 4394, 4401, 4400, 1786])).
% 1.61/1.80 tff(4406,plain,
% 1.61/1.80 (hskp10),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[4405, 4402])).
% 1.61/1.80 tff(4407,plain,
% 1.61/1.80 (~c0_1(a18)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[874, 4406])).
% 1.61/1.80 tff(4408,plain,
% 1.61/1.80 (c3_1(a18)),
% 1.61/1.80 inference(unit_resolution,[status(thm)],[962, 4406])).
% 1.61/1.80 tff(4409,plain,
% 1.61/1.80 (~c1_1(a18)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[868, 4406])).
% 1.63/1.80 tff(4410,plain,
% 1.63/1.80 (~c0_1(a31)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[423, 4403])).
% 1.63/1.80 tff(4411,plain,
% 1.63/1.80 (~c3_1(a31)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[385, 4403])).
% 1.63/1.80 tff(4412,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[3701, 4411, 4410, 4396, 4409, 4401, 4408, 4407, 4400, 11, 4404, 4399])).
% 1.63/1.80 tff(4413,plain,(hskp0), inference(lemma,lemma(discharge,[]))).
% 1.63/1.80 tff(4414,plain,
% 1.63/1.80 (~hskp3),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[4274, 4413])).
% 1.63/1.80 tff(4415,plain,
% 1.63/1.80 (~hskp28),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[4078, 4414])).
% 1.63/1.80 tff(4416,plain,
% 1.63/1.80 (hskp28 | hskp20),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[508, 4394])).
% 1.63/1.80 tff(4417,plain,
% 1.63/1.80 (hskp20),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[4416, 4415])).
% 1.63/1.80 tff(4418,plain,
% 1.63/1.80 (c3_1(a37)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[516, 4417])).
% 1.63/1.80 tff(4419,plain,
% 1.63/1.80 (c1_1(a37)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[524, 4417])).
% 1.63/1.80 tff(4420,plain,
% 1.63/1.80 (~c2_1(a37)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[529, 101, 3765, 4414, 4419, 4418, 10])).
% 1.63/1.80 tff(4421,plain,
% 1.63/1.80 (~c3_1(a1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[114, 4413])).
% 1.63/1.80 tff(4422,plain,
% 1.63/1.80 (c1_1(a1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[130, 4413])).
% 1.63/1.80 tff(4423,plain,
% 1.63/1.80 (c2_1(a1)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[122, 4413])).
% 1.63/1.80 tff(4424,plain,
% 1.63/1.80 (hskp6),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[171, 4423, 4422, 4421])).
% 1.63/1.80 tff(4425,plain,
% 1.63/1.80 (~c3_1(a13)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[177, 4424])).
% 1.63/1.80 tff(4426,plain,
% 1.63/1.80 (~c1_1(a13)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[183, 4424])).
% 1.63/1.80 tff(4427,plain,
% 1.63/1.80 (~c0_1(a13)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[189, 4424])).
% 1.63/1.80 tff(4428,plain,
% 1.63/1.80 (hskp2),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[232, 101, 4394, 4427, 4426, 4425, 47])).
% 1.63/1.80 tff(4429,plain,
% 1.63/1.80 (~c2_1(a3)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[197, 4428])).
% 1.63/1.80 tff(4430,plain,
% 1.63/1.80 (c1_1(a3)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[213, 4428])).
% 1.63/1.80 tff(4431,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(4432,plain,
% 1.63/1.80 (((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13)) <=> (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.63/1.80 inference(rewrite,[status(thm)],[])).
% 1.63/1.80 tff(4433,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))))),
% 1.63/1.80 inference(monotonicity,[status(thm)],[4432])).
% 1.63/1.80 tff(4434,plain,
% 1.63/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)))),
% 1.63/1.80 inference(transitivity,[status(thm)],[4433, 4431])).
% 1.63/1.80 tff(4435,plain,
% 1.63/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37)) | c2_1(a3) | (~c0_1(a3)) | (~c1_1(a3)) | c1_1(a13) | c0_1(a13) | c3_1(a13))),
% 1.63/1.80 inference(quant_inst,[status(thm)],[])).
% 1.63/1.80 tff(4436,plain,
% 1.63/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a13) | c1_1(a13) | c3_1(a13) | c2_1(a3) | (~ndr1_0) | (~c0_1(a3)) | (~c1_1(a3)) | c2_1(a37) | (~c3_1(a37)) | (~c1_1(a37))),
% 1.63/1.80 inference(modus_ponens,[status(thm)],[4435, 4434])).
% 1.63/1.80 tff(4437,plain,
% 1.63/1.80 (~c0_1(a3)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[4436, 101, 4419, 4418, 4430, 4427, 4426, 4425, 4429, 36, 4420])).
% 1.63/1.80 tff(4438,plain,
% 1.63/1.80 (hskp9),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[833, 101, 4419, 4418, 4422, 4423, 4421, 827, 4420])).
% 1.63/1.80 tff(4439,plain,
% 1.63/1.80 (~c3_1(a16)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[839, 4438])).
% 1.63/1.80 tff(4440,plain,
% 1.63/1.80 (c3_1(a3)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[205, 4428])).
% 1.63/1.80 tff(4441,plain,
% 1.63/1.80 (c1_1(a16)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[847, 4438])).
% 1.63/1.80 tff(4442,plain,
% 1.63/1.80 (c2_1(a16)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[2848, 101, 4441, 4440, 4422, 4423, 4439, 4429, 4421, 680, 4437])).
% 1.63/1.80 tff(4443,plain,
% 1.63/1.80 (~c2_1(a13)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[890, 101, 4394, 4419, 4418, 4427, 4426, 58, 4420])).
% 1.63/1.80 tff(4444,plain,
% 1.63/1.80 (c0_1(a16)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[855, 4438])).
% 1.63/1.80 tff(4445,plain,
% 1.63/1.80 (hskp12),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[924, 101, 4444, 4441, 4440, 4439, 4429, 918, 4437])).
% 1.63/1.80 tff(4446,plain,
% 1.63/1.80 (~c1_1(a20)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[936, 4445])).
% 1.63/1.80 tff(4447,plain,
% 1.63/1.80 (c2_1(a20)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[944, 4445])).
% 1.63/1.80 tff(4448,plain,
% 1.63/1.80 (~c0_1(a20)),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1281, 101, 4447, 4441, 4446, 4439, 4427, 4425, 1264, 4443, 4442])).
% 1.63/1.80 tff(4449,plain,
% 1.63/1.80 ($false),
% 1.63/1.80 inference(unit_resolution,[status(thm)],[1288, 101, 4394, 4447, 4430, 4440, 4446, 4429, 58, 4448])).
% 1.63/1.80 % SZS output end Proof
% 1.63/1.81 % E exiting
%------------------------------------------------------------------------------