%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN443-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:39:07 AM UTC 2025
% Result : Unsatisfiable 0.70s 0.87s
% Output : Proof 0.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN443-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:35:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.70/0.87 % SZS status Unsatisfiable
% 0.70/0.87 % SZS output start Proof
% 0.70/0.87 tff(c1_1_type, type, (
% 0.70/0.87 c1_1: $i > $o)).
% 0.70/0.87 tff(a43_type, type, (
% 0.70/0.87 a43: $i)).
% 0.70/0.87 tff(hskp22_type, type, (
% 0.70/0.87 hskp22: $o)).
% 0.70/0.87 tff(c3_1_type, type, (
% 0.70/0.87 c3_1: $i > $o)).
% 0.70/0.87 tff(a31_type, type, (
% 0.70/0.87 a31: $i)).
% 0.70/0.87 tff(c2_1_type, type, (
% 0.70/0.87 c2_1: $i > $o)).
% 0.70/0.87 tff(a19_type, type, (
% 0.70/0.87 a19: $i)).
% 0.70/0.87 tff(c0_1_type, type, (
% 0.70/0.87 c0_1: $i > $o)).
% 0.70/0.87 tff(ndr1_0_type, type, (
% 0.70/0.87 ndr1_0: $o)).
% 0.70/0.87 tff(hskp11_type, type, (
% 0.70/0.87 hskp11: $o)).
% 0.70/0.87 tff(hskp2_type, type, (
% 0.70/0.87 hskp2: $o)).
% 0.70/0.87 tff(hskp30_type, type, (
% 0.70/0.87 hskp30: $o)).
% 0.70/0.87 tff(hskp18_type, type, (
% 0.70/0.87 hskp18: $o)).
% 0.70/0.87 tff(a3_type, type, (
% 0.70/0.87 a3: $i)).
% 0.70/0.87 tff(a36_type, type, (
% 0.70/0.87 a36: $i)).
% 0.70/0.87 tff(hskp4_type, type, (
% 0.70/0.87 hskp4: $o)).
% 0.70/0.87 tff(hskp19_type, type, (
% 0.70/0.87 hskp19: $o)).
% 0.70/0.87 tff(a58_type, type, (
% 0.70/0.87 a58: $i)).
% 0.70/0.87 tff(a34_type, type, (
% 0.70/0.87 a34: $i)).
% 0.70/0.87 tff(a1_type, type, (
% 0.70/0.87 a1: $i)).
% 0.70/0.87 tff(hskp0_type, type, (
% 0.70/0.87 hskp0: $o)).
% 0.70/0.87 tff(a33_type, type, (
% 0.70/0.87 a33: $i)).
% 0.70/0.87 tff(a4_type, type, (
% 0.70/0.87 a4: $i)).
% 0.70/0.87 tff(hskp3_type, type, (
% 0.70/0.87 hskp3: $o)).
% 0.70/0.87 tff(hskp24_type, type, (
% 0.70/0.87 hskp24: $o)).
% 0.70/0.87 tff(hskp27_type, type, (
% 0.70/0.87 hskp27: $o)).
% 0.70/0.87 tff(hskp28_type, type, (
% 0.70/0.87 hskp28: $o)).
% 0.70/0.87 tff(a9_type, type, (
% 0.70/0.87 a9: $i)).
% 0.70/0.87 tff(hskp7_type, type, (
% 0.70/0.87 hskp7: $o)).
% 0.70/0.87 tff(a25_type, type, (
% 0.70/0.87 a25: $i)).
% 0.70/0.87 tff(hskp29_type, type, (
% 0.70/0.87 hskp29: $o)).
% 0.70/0.87 tff(a5_type, type, (
% 0.70/0.87 a5: $i)).
% 0.70/0.87 tff(a8_type, type, (
% 0.70/0.87 a8: $i)).
% 0.70/0.87 tff(hskp6_type, type, (
% 0.70/0.87 hskp6: $o)).
% 0.70/0.87 tff(hskp5_type, type, (
% 0.70/0.87 hskp5: $o)).
% 0.70/0.87 tff(a6_type, type, (
% 0.70/0.87 a6: $i)).
% 0.70/0.87 tff(a12_type, type, (
% 0.70/0.87 a12: $i)).
% 0.70/0.87 tff(hskp9_type, type, (
% 0.70/0.87 hskp9: $o)).
% 0.70/0.87 tff(a26_type, type, (
% 0.70/0.87 a26: $i)).
% 0.70/0.87 tff(hskp14_type, type, (
% 0.70/0.87 hskp14: $o)).
% 0.70/0.87 tff(a64_type, type, (
% 0.70/0.87 a64: $i)).
% 0.70/0.87 tff(hskp25_type, type, (
% 0.70/0.87 hskp25: $o)).
% 0.70/0.87 tff(a10_type, type, (
% 0.70/0.87 a10: $i)).
% 0.70/0.87 tff(a2_type, type, (
% 0.70/0.87 a2: $i)).
% 0.70/0.87 tff(hskp1_type, type, (
% 0.70/0.87 hskp1: $o)).
% 0.70/0.87 tff(a42_type, type, (
% 0.70/0.87 a42: $i)).
% 0.70/0.87 tff(hskp21_type, type, (
% 0.70/0.87 hskp21: $o)).
% 0.70/0.87 tff(a15_type, type, (
% 0.70/0.87 a15: $i)).
% 0.70/0.87 tff(a27_type, type, (
% 0.70/0.87 a27: $i)).
% 0.70/0.87 tff(hskp15_type, type, (
% 0.70/0.87 hskp15: $o)).
% 0.70/0.87 tff(a32_type, type, (
% 0.70/0.87 a32: $i)).
% 0.70/0.87 tff(hskp17_type, type, (
% 0.70/0.87 hskp17: $o)).
% 0.70/0.87 tff(hskp16_type, type, (
% 0.70/0.87 hskp16: $o)).
% 0.70/0.87 tff(a52_type, type, (
% 0.70/0.87 a52: $i)).
% 0.70/0.87 tff(hskp23_type, type, (
% 0.70/0.87 hskp23: $o)).
% 0.70/0.87 tff(1,assumption,(~hskp22), introduced(assumption)).
% 0.70/0.87 tff(2,assumption,(~c2_1(a19)), introduced(assumption)).
% 0.70/0.87 tff(3,plain,
% 0.70/0.87 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(4,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[3])).
% 0.70/0.87 tff(5,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(6,plain,
% 0.70/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | 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)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(7,plain,
% 0.70/0.87 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[6])).
% 0.70/0.87 tff(8,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 0.70/0.87 tff(9,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.70/0.87 tff(10,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.70/0.87 tff(11,plain,(
% 0.70/0.87 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[10])).
% 0.70/0.87 tff(12,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.70/0.87 tff(13,plain,
% 0.70/0.87 ((hskp11 | hskp22) <=> (hskp11 | hskp22)),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(14,axiom,(hskp11 | hskp22), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.70/0.87 tff(15,plain,
% 0.70/0.87 (hskp11 | hskp22),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.70/0.87 tff(16,plain,
% 0.70/0.87 (hskp11),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[15, 1])).
% 0.70/0.87 tff(17,plain,
% 0.70/0.87 (((~hskp11) | (~c3_1(a19))) <=> ((~hskp11) | (~c3_1(a19)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(18,plain,
% 0.70/0.87 (((~c3_1(a19)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a19)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(19,axiom,((~c3_1(a19)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.70/0.87 tff(20,plain,
% 0.70/0.87 ((~hskp11) | (~c3_1(a19))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.70/0.87 tff(21,plain,
% 0.70/0.87 ((~hskp11) | (~c3_1(a19))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.70/0.87 tff(22,plain,
% 0.70/0.87 (~c3_1(a19)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[21, 16])).
% 0.70/0.87 tff(23,plain,
% 0.70/0.87 (((~hskp11) | c1_1(a19)) <=> ((~hskp11) | c1_1(a19))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(24,axiom,((~hskp11) | c1_1(a19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.70/0.87 tff(25,plain,
% 0.70/0.87 ((~hskp11) | c1_1(a19)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.70/0.87 tff(26,plain,
% 0.70/0.87 ((~hskp11) | c1_1(a19)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[25, 23])).
% 0.70/0.87 tff(27,plain,
% 0.70/0.87 ((~hskp11) | c1_1(a19)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.70/0.87 tff(28,plain,
% 0.70/0.87 ((~hskp11) | c1_1(a19)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.70/0.87 tff(29,plain,
% 0.70/0.87 ((~hskp11) | c1_1(a19)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.70/0.87 tff(30,plain,
% 0.70/0.87 (c1_1(a19)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[29, 16])).
% 0.70/0.87 tff(31,plain,
% 0.70/0.87 (((~hskp11) | c0_1(a19)) <=> ((~hskp11) | c0_1(a19))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(32,axiom,((~hskp11) | c0_1(a19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.70/0.87 tff(33,plain,
% 0.70/0.87 ((~hskp11) | c0_1(a19)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.70/0.87 tff(34,plain,
% 0.70/0.87 ((~hskp11) | c0_1(a19)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[33, 31])).
% 0.70/0.87 tff(35,plain,
% 0.70/0.87 ((~hskp11) | c0_1(a19)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.70/0.87 tff(36,plain,
% 0.70/0.87 ((~hskp11) | c0_1(a19)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.70/0.87 tff(37,plain,
% 0.70/0.87 ((~hskp11) | c0_1(a19)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.70/0.87 tff(38,plain,
% 0.70/0.87 (c0_1(a19)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[37, 16])).
% 0.70/0.87 tff(39,assumption,(~ndr1_0), introduced(assumption)).
% 0.70/0.87 tff(40,plain,
% 0.70/0.87 ((ndr1_0 | (~hskp2)) <=> (ndr1_0 | (~hskp2))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(41,plain,
% 0.70/0.87 (((~hskp2) | ndr1_0) <=> (ndr1_0 | (~hskp2))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(42,axiom,((~hskp2) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause30')).
% 0.70/0.87 tff(43,plain,
% 0.70/0.87 (ndr1_0 | (~hskp2)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.70/0.87 tff(44,plain,
% 0.70/0.87 (ndr1_0 | (~hskp2)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.70/0.87 tff(45,plain,
% 0.70/0.87 (~hskp2),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[44, 39])).
% 0.70/0.87 tff(46,plain,
% 0.70/0.87 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(47,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 0.70/0.87 tff(48,plain,
% 0.70/0.87 ((~hskp30) | ndr1_0),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.70/0.87 tff(49,plain,
% 0.70/0.87 ((~hskp30) | ndr1_0),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[48, 46])).
% 0.70/0.87 tff(50,plain,
% 0.70/0.87 ((~hskp30) | ndr1_0),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.70/0.87 tff(51,plain,
% 0.70/0.87 ((~hskp30) | ndr1_0),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.70/0.87 tff(52,plain,
% 0.70/0.87 ((~hskp30) | ndr1_0),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[51, 46])).
% 0.70/0.87 tff(53,plain,
% 0.70/0.87 (~hskp30),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[52, 39])).
% 0.70/0.87 tff(54,plain,
% 0.70/0.87 ((ndr1_0 | (~hskp18)) <=> (ndr1_0 | (~hskp18))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(55,plain,
% 0.70/0.87 (((~hskp18) | ndr1_0) <=> (ndr1_0 | (~hskp18))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(56,axiom,((~hskp18) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause14')).
% 0.70/0.87 tff(57,plain,
% 0.70/0.87 (ndr1_0 | (~hskp18)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.70/0.87 tff(58,plain,
% 0.70/0.87 (ndr1_0 | (~hskp18)),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.70/0.87 tff(59,plain,
% 0.70/0.87 (~hskp18),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[58, 39])).
% 0.70/0.87 tff(60,plain,
% 0.70/0.87 ((hskp30 | hskp18 | hskp2) <=> (hskp30 | hskp18 | hskp2)),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(61,plain,
% 0.70/0.87 (((hskp30 | hskp2) | hskp18) <=> (hskp30 | hskp18 | hskp2)),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(62,plain,
% 0.70/0.87 ((hskp30 | hskp2) <=> (hskp30 | hskp2)),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(63,plain,
% 0.70/0.87 (((hskp30 | hskp2) | hskp18) <=> ((hskp30 | hskp2) | hskp18)),
% 0.70/0.87 inference(monotonicity,[status(thm)],[62])).
% 0.70/0.87 tff(64,plain,
% 0.70/0.87 (((hskp30 | hskp2) | hskp18) <=> (hskp30 | hskp18 | hskp2)),
% 0.70/0.87 inference(transitivity,[status(thm)],[63, 61])).
% 0.70/0.87 tff(65,axiom,((hskp30 | hskp2) | hskp18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 0.70/0.87 tff(66,plain,
% 0.70/0.87 (hskp30 | hskp18 | hskp2),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.70/0.87 tff(67,plain,
% 0.70/0.87 (hskp30 | hskp18 | hskp2),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[66, 60])).
% 0.70/0.87 tff(68,plain,
% 0.70/0.87 (hskp30 | hskp18 | hskp2),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.70/0.87 tff(69,plain,
% 0.70/0.87 (hskp30 | hskp18 | hskp2),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[68, 60])).
% 0.70/0.87 tff(70,plain,
% 0.70/0.87 (hskp30 | hskp18 | hskp2),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[69, 60])).
% 0.70/0.87 tff(71,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[70, 59, 53, 45])).
% 0.70/0.87 tff(72,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(73,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c3_1(a19) | (~ndr1_0) | c2_1(a19) | (~c0_1(a19)) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c3_1(a19) | (~ndr1_0) | c2_1(a19) | (~c0_1(a19)) | (~c1_1(a19)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(74,plain,
% 0.70/0.87 ((hskp22 | (~ndr1_0) | c3_1(a19) | c2_1(a19) | (~c1_1(a19)) | c2_1(a19) | c3_1(a19) | (~c0_1(a19))) <=> (hskp22 | c3_1(a19) | (~ndr1_0) | c2_1(a19) | (~c0_1(a19)) | (~c1_1(a19)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(75,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a19) | c2_1(a19) | (~c1_1(a19)) | c2_1(a19) | c3_1(a19) | (~c0_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c3_1(a19) | (~ndr1_0) | c2_1(a19) | (~c0_1(a19)) | (~c1_1(a19))))),
% 0.70/0.87 inference(monotonicity,[status(thm)],[74])).
% 0.70/0.87 tff(76,plain,
% 0.70/0.87 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a19) | c2_1(a19) | (~c1_1(a19)) | c2_1(a19) | c3_1(a19) | (~c0_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c3_1(a19) | (~ndr1_0) | c2_1(a19) | (~c0_1(a19)) | (~c1_1(a19)))),
% 0.70/0.87 inference(transitivity,[status(thm)],[75, 73])).
% 0.70/0.87 tff(77,plain,
% 0.70/0.87 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a19) | c2_1(a19) | (~c1_1(a19)) | c2_1(a19) | c3_1(a19) | (~c0_1(a19)))),
% 0.70/0.87 inference(quant_inst,[status(thm)],[])).
% 0.70/0.87 tff(78,plain,
% 0.70/0.87 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c3_1(a19) | (~ndr1_0) | c2_1(a19) | (~c0_1(a19)) | (~c1_1(a19))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.70/0.87 tff(79,plain,
% 0.70/0.87 ($false),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[78, 1, 72, 38, 30, 22, 12, 2])).
% 0.70/0.87 tff(80,plain,(c2_1(a19) | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.70/0.87 tff(81,plain,
% 0.70/0.87 (c2_1(a19)),
% 0.70/0.87 inference(unit_resolution,[status(thm)],[80, 1])).
% 0.70/0.87 tff(82,plain,
% 0.70/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(83,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[82])).
% 0.70/0.87 tff(84,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(85,plain,
% 0.70/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | 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)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | 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)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(86,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[85])).
% 0.70/0.87 tff(87,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 0.70/0.87 tff(88,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.70/0.87 tff(89,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.70/0.87 tff(90,plain,(
% 0.70/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[89])).
% 0.70/0.87 tff(91,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.70/0.87 tff(92,plain,
% 0.70/0.87 (^[U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(93,plain,
% 0.70/0.87 (![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[92])).
% 0.70/0.87 tff(94,plain,
% 0.70/0.87 (![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(95,plain,
% 0.70/0.87 (^[U: $i] : 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)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(96,plain,
% 0.70/0.87 (![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> ![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[95])).
% 0.70/0.87 tff(97,axiom,(![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.70/0.87 tff(98,plain,
% 0.70/0.87 (![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.70/0.87 tff(99,plain,
% 0.70/0.87 (![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.70/0.87 tff(100,plain,(
% 0.70/0.87 ![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.87 inference(skolemize,[status(sab)],[99])).
% 0.70/0.87 tff(101,plain,
% 0.70/0.87 (![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.70/0.87 tff(102,plain,
% 0.70/0.87 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(103,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[102])).
% 0.70/0.87 tff(104,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(105,plain,
% 0.70/0.87 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp22))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(106,plain,
% 0.70/0.87 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[105])).
% 0.70/0.87 tff(107,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 0.70/0.87 tff(108,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.70/0.87 tff(109,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.70/0.87 tff(110,plain,(
% 0.70/0.87 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[109])).
% 0.70/0.87 tff(111,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.70/0.87 tff(112,plain,
% 0.70/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(113,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[112])).
% 0.70/0.87 tff(114,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(115,plain,
% 0.70/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(116,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[115])).
% 0.70/0.87 tff(117,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 0.70/0.87 tff(118,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.70/0.87 tff(119,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.70/0.87 tff(120,plain,(
% 0.70/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[119])).
% 0.70/0.87 tff(121,plain,
% 0.70/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.70/0.87 tff(122,assumption,(~hskp18), introduced(assumption)).
% 0.70/0.87 tff(123,assumption,(~hskp30), introduced(assumption)).
% 0.70/0.87 tff(124,plain,
% 0.70/0.87 (^[U: $i] : refl((hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(125,plain,
% 0.70/0.87 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[124])).
% 0.70/0.87 tff(126,plain,
% 0.70/0.87 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(127,plain,
% 0.70/0.87 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp27) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp27))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp27) <=> (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp27) <=> (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(128,plain,
% 0.70/0.87 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp27) <=> ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[127])).
% 0.70/0.87 tff(129,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 0.70/0.87 tff(130,plain,
% 0.70/0.87 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.70/0.87 tff(131,plain,
% 0.70/0.87 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.70/0.87 tff(132,plain,(
% 0.70/0.87 ![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(skolemize,[status(sab)],[131])).
% 0.70/0.87 tff(133,plain,
% 0.70/0.87 (![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.70/0.87 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.70/0.87 tff(134,plain,
% 0.70/0.87 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.70/0.87 inference(bind,[status(th)],[])).
% 0.70/0.87 tff(135,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.87 inference(quant_intro,[status(thm)],[134])).
% 0.70/0.87 tff(136,plain,
% 0.70/0.87 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.87 inference(rewrite,[status(thm)],[])).
% 0.70/0.87 tff(137,plain,
% 0.70/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp19) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp19))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(138,plain,
% 0.70/0.88 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[137])).
% 0.70/0.88 tff(139,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.70/0.88 tff(140,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.70/0.88 tff(141,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.70/0.88 tff(142,plain,(
% 0.70/0.88 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.88 inference(skolemize,[status(sab)],[141])).
% 0.70/0.88 tff(143,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.70/0.88 tff(144,assumption,(hskp4), introduced(assumption)).
% 0.70/0.88 tff(145,plain,
% 0.70/0.88 (((~hskp4) | (~c1_1(a5))) <=> ((~hskp4) | (~c1_1(a5)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(146,plain,
% 0.70/0.88 (((~c1_1(a5)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a5)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(147,axiom,((~c1_1(a5)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.70/0.88 tff(148,plain,
% 0.70/0.88 ((~hskp4) | (~c1_1(a5))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.70/0.88 tff(149,plain,
% 0.70/0.88 ((~hskp4) | (~c1_1(a5))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[148, 145])).
% 0.70/0.88 tff(150,plain,
% 0.70/0.88 (~c1_1(a5)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[149, 144])).
% 0.70/0.88 tff(151,plain,
% 0.70/0.88 (hskp2),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[70, 123, 122])).
% 0.70/0.88 tff(152,plain,
% 0.70/0.88 (((~hskp2) | (~c1_1(a3))) <=> ((~hskp2) | (~c1_1(a3)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(153,plain,
% 0.70/0.88 (((~c1_1(a3)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a3)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(154,axiom,((~c1_1(a3)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.70/0.88 tff(155,plain,
% 0.70/0.88 ((~hskp2) | (~c1_1(a3))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.70/0.88 tff(156,plain,
% 0.70/0.88 ((~hskp2) | (~c1_1(a3))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[155, 152])).
% 0.70/0.88 tff(157,plain,
% 0.70/0.88 (~c1_1(a3)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[156, 151])).
% 0.70/0.88 tff(158,plain,
% 0.70/0.88 (((~hskp2) | c2_1(a3)) <=> ((~hskp2) | c2_1(a3))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(159,axiom,((~hskp2) | c2_1(a3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.70/0.88 tff(160,plain,
% 0.70/0.88 ((~hskp2) | c2_1(a3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.70/0.88 tff(161,plain,
% 0.70/0.88 ((~hskp2) | c2_1(a3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[160, 158])).
% 0.70/0.88 tff(162,plain,
% 0.70/0.88 ((~hskp2) | c2_1(a3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[161, 158])).
% 0.70/0.88 tff(163,plain,
% 0.70/0.88 ((~hskp2) | c2_1(a3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.70/0.88 tff(164,plain,
% 0.70/0.88 ((~hskp2) | c2_1(a3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[163, 158])).
% 0.70/0.88 tff(165,plain,
% 0.70/0.88 (c2_1(a3)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[164, 151])).
% 0.70/0.88 tff(166,plain,
% 0.70/0.88 (((~hskp2) | c0_1(a3)) <=> ((~hskp2) | c0_1(a3))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(167,axiom,((~hskp2) | c0_1(a3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.70/0.88 tff(168,plain,
% 0.70/0.88 ((~hskp2) | c0_1(a3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.70/0.88 tff(169,plain,
% 0.70/0.88 ((~hskp2) | c0_1(a3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[168, 166])).
% 0.70/0.88 tff(170,plain,
% 0.70/0.88 ((~hskp2) | c0_1(a3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[169, 166])).
% 0.70/0.88 tff(171,plain,
% 0.70/0.88 ((~hskp2) | c0_1(a3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.70/0.88 tff(172,plain,
% 0.70/0.88 ((~hskp2) | c0_1(a3)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[171, 166])).
% 0.70/0.88 tff(173,plain,
% 0.70/0.88 (c0_1(a3)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[172, 151])).
% 0.70/0.88 tff(174,plain,
% 0.70/0.88 (((~hskp4) | c3_1(a5)) <=> ((~hskp4) | c3_1(a5))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(175,axiom,((~hskp4) | c3_1(a5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.70/0.88 tff(176,plain,
% 0.70/0.88 ((~hskp4) | c3_1(a5)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.70/0.88 tff(177,plain,
% 0.70/0.88 ((~hskp4) | c3_1(a5)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[176, 174])).
% 0.70/0.88 tff(178,plain,
% 0.70/0.88 ((~hskp4) | c3_1(a5)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[177, 174])).
% 0.70/0.88 tff(179,plain,
% 0.70/0.88 ((~hskp4) | c3_1(a5)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.70/0.88 tff(180,plain,
% 0.70/0.88 ((~hskp4) | c3_1(a5)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[179, 174])).
% 0.70/0.88 tff(181,plain,
% 0.70/0.88 (c3_1(a5)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[180, 144])).
% 0.70/0.88 tff(182,plain,
% 0.70/0.88 (((~hskp4) | c2_1(a5)) <=> ((~hskp4) | c2_1(a5))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(183,axiom,((~hskp4) | c2_1(a5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.70/0.88 tff(184,plain,
% 0.70/0.88 ((~hskp4) | c2_1(a5)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.70/0.88 tff(185,plain,
% 0.70/0.88 ((~hskp4) | c2_1(a5)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[184, 182])).
% 0.70/0.88 tff(186,plain,
% 0.70/0.88 ((~hskp4) | c2_1(a5)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[185, 182])).
% 0.70/0.88 tff(187,plain,
% 0.70/0.88 ((~hskp4) | c2_1(a5)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.70/0.88 tff(188,plain,
% 0.70/0.88 ((~hskp4) | c2_1(a5)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[187, 182])).
% 0.70/0.88 tff(189,plain,
% 0.70/0.88 (c2_1(a5)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[188, 144])).
% 0.70/0.88 tff(190,assumption,(~c1_1(a5)), introduced(assumption)).
% 0.70/0.88 tff(191,assumption,(hskp3), introduced(assumption)).
% 0.70/0.88 tff(192,plain,
% 0.70/0.88 (((~hskp3) | (~c0_1(a4))) <=> ((~hskp3) | (~c0_1(a4)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(193,plain,
% 0.70/0.88 (((~c0_1(a4)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a4)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(194,axiom,((~c0_1(a4)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.70/0.88 tff(195,plain,
% 0.70/0.88 ((~hskp3) | (~c0_1(a4))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.70/0.88 tff(196,plain,
% 0.70/0.88 ((~hskp3) | (~c0_1(a4))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[195, 192])).
% 0.70/0.88 tff(197,plain,
% 0.70/0.88 (~c0_1(a4)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[196, 191])).
% 0.70/0.88 tff(198,plain,
% 0.70/0.88 (((~hskp3) | (~c1_1(a4))) <=> ((~hskp3) | (~c1_1(a4)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(199,plain,
% 0.70/0.88 (((~c1_1(a4)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a4)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(200,axiom,((~c1_1(a4)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.70/0.88 tff(201,plain,
% 0.70/0.88 ((~hskp3) | (~c1_1(a4))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.70/0.88 tff(202,plain,
% 0.70/0.88 ((~hskp3) | (~c1_1(a4))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[201, 198])).
% 0.70/0.88 tff(203,plain,
% 0.70/0.88 (~c1_1(a4)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[202, 191])).
% 0.70/0.88 tff(204,assumption,(~c1_1(a4)), introduced(assumption)).
% 0.70/0.88 tff(205,assumption,(~c0_1(a4)), introduced(assumption)).
% 0.70/0.88 tff(206,assumption,(~c3_1(a6)), introduced(assumption)).
% 0.70/0.88 tff(207,assumption,(~c3_1(a4)), introduced(assumption)).
% 0.70/0.88 tff(208,plain,
% 0.70/0.88 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c3_1(a4) | c0_1(a4) | c1_1(a4) | (~ndr1_0))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c3_1(a4) | c0_1(a4) | c1_1(a4) | (~ndr1_0))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(209,plain,
% 0.70/0.88 ((hskp4 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c0_1(a4)) <=> (hskp4 | c3_1(a4) | c0_1(a4) | c1_1(a4) | (~ndr1_0))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(210,plain,
% 0.70/0.88 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c3_1(a4) | c0_1(a4) | c1_1(a4) | (~ndr1_0)))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[209])).
% 0.70/0.88 tff(211,plain,
% 0.70/0.88 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c3_1(a4) | c0_1(a4) | c1_1(a4) | (~ndr1_0))),
% 0.70/0.88 inference(transitivity,[status(thm)],[210, 208])).
% 0.70/0.88 tff(212,plain,
% 0.70/0.88 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c0_1(a4))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(213,plain,
% 0.70/0.88 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c3_1(a4) | c0_1(a4) | c1_1(a4) | (~ndr1_0)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.70/0.88 tff(214,plain,
% 0.70/0.88 (hskp4 | c3_1(a4) | c0_1(a4)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[213, 72, 204, 101])).
% 0.70/0.88 tff(215,plain,
% 0.70/0.88 (hskp4),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[214, 207, 205])).
% 0.70/0.88 tff(216,plain,
% 0.70/0.88 (c3_1(a5)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[180, 215])).
% 0.70/0.88 tff(217,plain,
% 0.70/0.88 (c2_1(a5)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[188, 215])).
% 0.70/0.88 tff(218,assumption,(~c0_1(a5)), introduced(assumption)).
% 0.70/0.88 tff(219,plain,
% 0.70/0.88 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(220,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[219])).
% 0.70/0.88 tff(221,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(222,plain,
% 0.70/0.88 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(223,plain,
% 0.70/0.88 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[222])).
% 0.70/0.88 tff(224,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.70/0.88 tff(225,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.70/0.88 tff(226,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.70/0.88 tff(227,plain,(
% 0.70/0.88 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.88 inference(skolemize,[status(sab)],[226])).
% 0.70/0.88 tff(228,plain,
% 0.70/0.88 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.70/0.88 tff(229,assumption,(~c1_1(a3)), introduced(assumption)).
% 0.70/0.88 tff(230,assumption,(c2_1(a3)), introduced(assumption)).
% 0.70/0.88 tff(231,assumption,(c0_1(a3)), introduced(assumption)).
% 0.70/0.88 tff(232,assumption,(c3_1(a5)), introduced(assumption)).
% 0.70/0.88 tff(233,assumption,(c2_1(a5)), introduced(assumption)).
% 0.70/0.88 tff(234,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(235,plain,
% 0.70/0.88 ((hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5))) <=> (hskp5 | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(236,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5))))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[235])).
% 0.70/0.88 tff(237,plain,
% 0.70/0.88 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[236, 234])).
% 0.70/0.88 tff(238,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(239,plain,
% 0.70/0.88 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.70/0.88 tff(240,plain,
% 0.70/0.88 (hskp5),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[239, 72, 233, 232, 231, 230, 229, 228, 218])).
% 0.70/0.88 tff(241,plain,
% 0.70/0.88 (((~hskp5) | c0_1(a6)) <=> ((~hskp5) | c0_1(a6))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(242,axiom,((~hskp5) | c0_1(a6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.70/0.88 tff(243,plain,
% 0.70/0.88 ((~hskp5) | c0_1(a6)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.70/0.88 tff(244,plain,
% 0.70/0.88 ((~hskp5) | c0_1(a6)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[243, 241])).
% 0.70/0.88 tff(245,plain,
% 0.70/0.88 ((~hskp5) | c0_1(a6)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[244, 241])).
% 0.70/0.88 tff(246,plain,
% 0.70/0.88 ((~hskp5) | c0_1(a6)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[245, 241])).
% 0.70/0.88 tff(247,plain,
% 0.70/0.88 ((~hskp5) | c0_1(a6)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[246, 241])).
% 0.70/0.88 tff(248,plain,
% 0.70/0.88 (c0_1(a6)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[247, 240])).
% 0.70/0.88 tff(249,plain,
% 0.70/0.88 (((~hskp5) | c2_1(a6)) <=> ((~hskp5) | c2_1(a6))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(250,axiom,((~hskp5) | c2_1(a6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.70/0.88 tff(251,plain,
% 0.70/0.88 ((~hskp5) | c2_1(a6)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.70/0.88 tff(252,plain,
% 0.70/0.88 ((~hskp5) | c2_1(a6)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[251, 249])).
% 0.70/0.88 tff(253,plain,
% 0.70/0.88 ((~hskp5) | c2_1(a6)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[252, 249])).
% 0.70/0.88 tff(254,plain,
% 0.70/0.88 ((~hskp5) | c2_1(a6)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.70/0.88 tff(255,plain,
% 0.70/0.88 ((~hskp5) | c2_1(a6)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[254, 249])).
% 0.70/0.88 tff(256,plain,
% 0.70/0.88 (c2_1(a6)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[255, 240])).
% 0.70/0.88 tff(257,plain,
% 0.70/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a6) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a6)) | (~c0_1(a6)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a6) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a6)) | (~c0_1(a6)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(258,plain,
% 0.70/0.88 (((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5))) <=> (c3_1(a6) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a6)) | (~c0_1(a6)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(259,plain,
% 0.70/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a6) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a6)) | (~c0_1(a6))))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[258])).
% 0.70/0.88 tff(260,plain,
% 0.70/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a6) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a6)) | (~c0_1(a6)))),
% 0.70/0.88 inference(transitivity,[status(thm)],[259, 257])).
% 0.70/0.88 tff(261,plain,
% 0.70/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(262,plain,
% 0.70/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a6) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a5)) | c0_1(a5) | (~c3_1(a5)) | (~c2_1(a6)) | (~c0_1(a6))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.70/0.88 tff(263,plain,
% 0.70/0.88 ((~c2_1(a6)) | (~c0_1(a6))),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[262, 72, 233, 232, 231, 230, 206, 229, 91, 218])).
% 0.70/0.88 tff(264,plain,
% 0.70/0.88 ($false),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[263, 256, 248])).
% 0.70/0.88 tff(265,plain,(c0_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | (~c0_1(a3)) | (~c2_1(a3)) | c3_1(a6) | c1_1(a3)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.88 tff(266,plain,
% 0.70/0.88 (c0_1(a5)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[265, 217, 216, 173, 165, 206, 157])).
% 0.70/0.88 tff(267,plain,
% 0.70/0.88 (^[U: $i] : refl((hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(268,plain,
% 0.70/0.88 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[267])).
% 0.70/0.88 tff(269,plain,
% 0.70/0.88 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(270,plain,
% 0.70/0.88 (^[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)) | hskp30) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp30))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp30) | hskp18) <=> ((hskp30 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp18))), rewrite(((hskp30 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp18) <=> (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp30) | hskp18) <=> (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(271,plain,
% 0.70/0.88 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp30) | hskp18) <=> ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[270])).
% 0.70/0.88 tff(272,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp30) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.70/0.88 tff(273,plain,
% 0.70/0.88 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.70/0.88 tff(274,plain,
% 0.70/0.88 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[273, 269])).
% 0.70/0.88 tff(275,plain,(
% 0.70/0.88 ![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.70/0.88 inference(skolemize,[status(sab)],[274])).
% 0.70/0.88 tff(276,plain,
% 0.70/0.88 (![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[275, 268])).
% 0.70/0.88 tff(277,assumption,(~hskp14), introduced(assumption)).
% 0.70/0.88 tff(278,plain,
% 0.70/0.88 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c3_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c3_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(279,plain,
% 0.70/0.88 ((hskp30 | hskp18 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c2_1(a4)) <=> (hskp30 | hskp18 | c3_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(280,plain,
% 0.70/0.88 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c2_1(a4))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c3_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4)))),
% 0.70/0.88 inference(monotonicity,[status(thm)],[279])).
% 0.70/0.88 tff(281,plain,
% 0.70/0.88 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c2_1(a4))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c3_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4))),
% 0.70/0.88 inference(transitivity,[status(thm)],[280, 278])).
% 0.70/0.88 tff(282,plain,
% 0.70/0.88 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a4) | c1_1(a4) | c2_1(a4))),
% 0.70/0.88 inference(quant_inst,[status(thm)],[])).
% 0.70/0.88 tff(283,plain,
% 0.70/0.88 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c3_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4)),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.70/0.88 tff(284,plain,
% 0.70/0.88 (c3_1(a4) | c2_1(a4)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[283, 123, 72, 122, 204, 276])).
% 0.70/0.88 tff(285,plain,
% 0.70/0.88 (c2_1(a4)),
% 0.70/0.88 inference(unit_resolution,[status(thm)],[284, 207])).
% 0.70/0.88 tff(286,plain,
% 0.70/0.88 (^[U: $i] : refl((hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(287,plain,
% 0.70/0.88 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[286])).
% 0.70/0.88 tff(288,plain,
% 0.70/0.88 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.70/0.88 inference(rewrite,[status(thm)],[])).
% 0.70/0.88 tff(289,plain,
% 0.70/0.88 (^[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)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) | hskp14) <=> ((hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14))), rewrite(((hskp18 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) | hskp14) <=> (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.70/0.88 inference(bind,[status(th)],[])).
% 0.70/0.88 tff(290,plain,
% 0.70/0.88 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) | hskp14) <=> ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.70/0.88 inference(quant_intro,[status(thm)],[289])).
% 0.70/0.88 tff(291,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp18) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.70/0.88 tff(292,plain,
% 0.70/0.88 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.70/0.88 tff(293,plain,
% 0.70/0.88 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[292, 288])).
% 0.70/0.88 tff(294,plain,(
% 0.70/0.88 ![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.70/0.88 inference(skolemize,[status(sab)],[293])).
% 0.70/0.88 tff(295,plain,
% 0.70/0.88 (![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.70/0.88 inference(modus_ponens,[status(thm)],[294, 287])).
% 0.70/0.88 tff(296,assumption,(c2_1(a4)), introduced(assumption)).
% 0.70/0.88 tff(297,plain,
% 0.70/0.88 (^[U: $i] : refl((hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.70/0.89 inference(bind,[status(th)],[])).
% 0.70/0.89 tff(298,plain,
% 0.70/0.89 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.70/0.89 inference(quant_intro,[status(thm)],[297])).
% 0.70/0.89 tff(299,plain,
% 0.70/0.89 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(300,plain,
% 0.70/0.89 (^[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)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp14) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp14))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp14) <=> (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp14) <=> (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.70/0.89 inference(bind,[status(th)],[])).
% 0.70/0.89 tff(301,plain,
% 0.70/0.89 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp14) <=> ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.70/0.89 inference(quant_intro,[status(thm)],[300])).
% 0.70/0.89 tff(302,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 0.70/0.89 tff(303,plain,
% 0.70/0.89 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.70/0.89 tff(304,plain,
% 0.70/0.89 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[303, 299])).
% 0.70/0.89 tff(305,plain,(
% 0.70/0.89 ![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.70/0.89 inference(skolemize,[status(sab)],[304])).
% 0.70/0.89 tff(306,plain,
% 0.70/0.89 (![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[305, 298])).
% 0.70/0.89 tff(307,plain,
% 0.70/0.89 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | c3_1(a4) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c3_1(a4) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(308,plain,
% 0.70/0.89 ((hskp29 | hskp14 | (~ndr1_0) | c3_1(a4) | c0_1(a4) | (~c2_1(a4))) <=> (hskp29 | hskp14 | c3_1(a4) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(309,plain,
% 0.70/0.89 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a4) | c0_1(a4) | (~c2_1(a4)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | c3_1(a4) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4))))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[308])).
% 0.70/0.89 tff(310,plain,
% 0.70/0.89 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a4) | c0_1(a4) | (~c2_1(a4)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c3_1(a4) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)))),
% 0.70/0.89 inference(transitivity,[status(thm)],[309, 307])).
% 0.70/0.89 tff(311,plain,
% 0.70/0.89 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a4) | c0_1(a4) | (~c2_1(a4)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(312,plain,
% 0.70/0.89 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c3_1(a4) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.70/0.89 tff(313,plain,
% 0.70/0.89 (hskp29 | hskp14 | c3_1(a4) | (~c2_1(a4))),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[312, 72, 205, 306])).
% 0.70/0.89 tff(314,plain,
% 0.70/0.89 (hskp29),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[313, 277, 207, 296])).
% 0.70/0.89 tff(315,plain,
% 0.70/0.89 (((~hskp29) | c0_1(a25)) <=> ((~hskp29) | c0_1(a25))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(316,axiom,((~hskp29) | c0_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.70/0.89 tff(317,plain,
% 0.70/0.89 ((~hskp29) | c0_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.70/0.89 tff(318,plain,
% 0.70/0.89 ((~hskp29) | c0_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[317, 315])).
% 0.70/0.89 tff(319,plain,
% 0.70/0.89 ((~hskp29) | c0_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[318, 315])).
% 0.70/0.89 tff(320,plain,
% 0.70/0.89 ((~hskp29) | c0_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[319, 315])).
% 0.70/0.89 tff(321,plain,
% 0.70/0.89 ((~hskp29) | c0_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[320, 315])).
% 0.70/0.89 tff(322,plain,
% 0.70/0.89 (c0_1(a25)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[321, 314])).
% 0.70/0.89 tff(323,plain,
% 0.70/0.89 (((~hskp29) | c2_1(a25)) <=> ((~hskp29) | c2_1(a25))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(324,axiom,((~hskp29) | c2_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.70/0.89 tff(325,plain,
% 0.70/0.89 ((~hskp29) | c2_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.70/0.89 tff(326,plain,
% 0.70/0.89 ((~hskp29) | c2_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[325, 323])).
% 0.70/0.89 tff(327,plain,
% 0.70/0.89 ((~hskp29) | c2_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[326, 323])).
% 0.70/0.89 tff(328,plain,
% 0.70/0.89 ((~hskp29) | c2_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[327, 323])).
% 0.70/0.89 tff(329,plain,
% 0.70/0.89 ((~hskp29) | c2_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[328, 323])).
% 0.70/0.89 tff(330,plain,
% 0.70/0.89 (c2_1(a25)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[329, 314])).
% 0.70/0.89 tff(331,plain,
% 0.70/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W))))),
% 0.70/0.89 inference(bind,[status(th)],[])).
% 0.70/0.89 tff(332,plain,
% 0.70/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 0.70/0.89 inference(quant_intro,[status(thm)],[331])).
% 0.70/0.89 tff(333,plain,
% 0.70/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(334,plain,
% 0.70/0.89 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~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)) | (~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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))))),
% 0.70/0.89 inference(bind,[status(th)],[])).
% 0.70/0.89 tff(335,plain,
% 0.70/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 0.70/0.89 inference(quant_intro,[status(thm)],[334])).
% 0.70/0.89 tff(336,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | (~c2_1(W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 0.70/0.89 tff(337,plain,
% 0.70/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.70/0.89 tff(338,plain,
% 0.70/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[337, 333])).
% 0.70/0.89 tff(339,plain,(
% 0.70/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 0.70/0.89 inference(skolemize,[status(sab)],[338])).
% 0.70/0.89 tff(340,plain,
% 0.70/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[339, 332])).
% 0.70/0.89 tff(341,plain,
% 0.70/0.89 (((~hskp29) | c1_1(a25)) <=> ((~hskp29) | c1_1(a25))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(342,axiom,((~hskp29) | c1_1(a25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 0.70/0.89 tff(343,plain,
% 0.70/0.89 ((~hskp29) | c1_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.70/0.89 tff(344,plain,
% 0.70/0.89 ((~hskp29) | c1_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[343, 341])).
% 0.70/0.89 tff(345,plain,
% 0.70/0.89 ((~hskp29) | c1_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[344, 341])).
% 0.70/0.89 tff(346,plain,
% 0.70/0.89 ((~hskp29) | c1_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[345, 341])).
% 0.70/0.89 tff(347,plain,
% 0.70/0.89 ((~hskp29) | c1_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[346, 341])).
% 0.70/0.89 tff(348,plain,
% 0.70/0.89 (c1_1(a25)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[347, 314])).
% 0.70/0.89 tff(349,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c2_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(350,plain,
% 0.70/0.89 (((~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)) | (~c0_1(a25))) <=> ((~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(351,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c2_1(a25))))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[350])).
% 0.70/0.89 tff(352,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)) | (~c0_1(a25)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c2_1(a25)))),
% 0.70/0.89 inference(transitivity,[status(thm)],[351, 349])).
% 0.70/0.89 tff(353,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a25)) | (~c3_1(a25)) | (~c1_1(a25)) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c1_1(a25)) | (~c2_1(a25)) | (~c0_1(a25)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(354,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c1_1(a25)) | (~c3_1(a25)) | (~c0_1(a25)) | (~c2_1(a25))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.70/0.89 tff(355,plain,
% 0.70/0.89 (~c3_1(a25)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[354, 72, 322, 348, 330, 340])).
% 0.70/0.89 tff(356,assumption,(hskp27), introduced(assumption)).
% 0.70/0.89 tff(357,plain,
% 0.70/0.89 (((~hskp27) | c3_1(a10)) <=> ((~hskp27) | c3_1(a10))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(358,axiom,((~hskp27) | c3_1(a10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.70/0.89 tff(359,plain,
% 0.70/0.89 ((~hskp27) | c3_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.70/0.89 tff(360,plain,
% 0.70/0.89 ((~hskp27) | c3_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[359, 357])).
% 0.70/0.89 tff(361,plain,
% 0.70/0.89 ((~hskp27) | c3_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[360, 357])).
% 0.70/0.89 tff(362,plain,
% 0.70/0.89 ((~hskp27) | c3_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[361, 357])).
% 0.70/0.89 tff(363,plain,
% 0.70/0.89 ((~hskp27) | c3_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[362, 357])).
% 0.70/0.89 tff(364,plain,
% 0.70/0.89 (c3_1(a10)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[363, 356])).
% 0.70/0.89 tff(365,plain,
% 0.70/0.89 (((~hskp27) | c2_1(a10)) <=> ((~hskp27) | c2_1(a10))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(366,axiom,((~hskp27) | c2_1(a10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.70/0.89 tff(367,plain,
% 0.70/0.89 ((~hskp27) | c2_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.70/0.89 tff(368,plain,
% 0.70/0.89 ((~hskp27) | c2_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[367, 365])).
% 0.70/0.89 tff(369,plain,
% 0.70/0.89 ((~hskp27) | c2_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[368, 365])).
% 0.70/0.89 tff(370,plain,
% 0.70/0.89 ((~hskp27) | c2_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[369, 365])).
% 0.70/0.89 tff(371,plain,
% 0.70/0.89 ((~hskp27) | c2_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[370, 365])).
% 0.70/0.89 tff(372,plain,
% 0.70/0.89 (c2_1(a10)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[371, 356])).
% 0.70/0.89 tff(373,plain,
% 0.70/0.89 (((~hskp27) | c1_1(a10)) <=> ((~hskp27) | c1_1(a10))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(374,axiom,((~hskp27) | c1_1(a10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.70/0.89 tff(375,plain,
% 0.70/0.89 ((~hskp27) | c1_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.70/0.89 tff(376,plain,
% 0.70/0.89 ((~hskp27) | c1_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[375, 373])).
% 0.70/0.89 tff(377,plain,
% 0.70/0.89 ((~hskp27) | c1_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[376, 373])).
% 0.70/0.89 tff(378,plain,
% 0.70/0.89 ((~hskp27) | c1_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[377, 373])).
% 0.70/0.89 tff(379,plain,
% 0.70/0.89 ((~hskp27) | c1_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[378, 373])).
% 0.70/0.89 tff(380,plain,
% 0.70/0.89 (c1_1(a10)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[379, 356])).
% 0.70/0.89 tff(381,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(382,plain,
% 0.70/0.89 (((~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c0_1(a10))) <=> ((~ndr1_0) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(383,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c0_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c0_1(a10))))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[382])).
% 0.70/0.89 tff(384,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c0_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)))),
% 0.70/0.89 inference(transitivity,[status(thm)],[383, 381])).
% 0.70/0.89 tff(385,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | (~c1_1(a10)) | (~c3_1(a10)) | (~c0_1(a10)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c0_1(a10)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(386,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)) | (~c0_1(a10))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.70/0.89 tff(387,plain,
% 0.70/0.89 (~c0_1(a10)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[386, 72, 380, 372, 364, 340])).
% 0.70/0.89 tff(388,assumption,(~c3_1(a25)), introduced(assumption)).
% 0.70/0.89 tff(389,assumption,(c2_1(a25)), introduced(assumption)).
% 0.70/0.89 tff(390,assumption,(c0_1(a25)), introduced(assumption)).
% 0.70/0.89 tff(391,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25) | (~c2_1(a10)) | (~c3_1(a10)) | c0_1(a10))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25) | (~c2_1(a10)) | (~c3_1(a10)) | c0_1(a10))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(392,plain,
% 0.70/0.89 (((~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a10) | (~c2_1(a10)) | (~c3_1(a10))) <=> (c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25) | (~c2_1(a10)) | (~c3_1(a10)) | c0_1(a10))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(393,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a10) | (~c2_1(a10)) | (~c3_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25) | (~c2_1(a10)) | (~c3_1(a10)) | c0_1(a10)))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[392])).
% 0.70/0.89 tff(394,plain,
% 0.70/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a10) | (~c2_1(a10)) | (~c3_1(a10)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25) | (~c2_1(a10)) | (~c3_1(a10)) | c0_1(a10))),
% 0.70/0.89 inference(transitivity,[status(thm)],[393, 391])).
% 0.70/0.89 tff(395,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a10) | (~c2_1(a10)) | (~c3_1(a10)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(396,plain,
% 0.70/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25) | (~c2_1(a10)) | (~c3_1(a10)) | c0_1(a10)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.70/0.89 tff(397,plain,
% 0.70/0.89 ($false),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[396, 72, 390, 389, 372, 364, 231, 230, 229, 91, 388, 387])).
% 0.70/0.89 tff(398,plain,((~hskp27) | (~c0_1(a25)) | (~c2_1(a25)) | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3) | c3_1(a25)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.89 tff(399,plain,
% 0.70/0.89 (~hskp27),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[398, 355, 330, 231, 230, 229, 322])).
% 0.70/0.89 tff(400,plain,
% 0.70/0.89 (^[U: $i] : refl((hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.70/0.89 inference(bind,[status(th)],[])).
% 0.70/0.89 tff(401,plain,
% 0.70/0.89 (![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.89 inference(quant_intro,[status(thm)],[400])).
% 0.70/0.89 tff(402,plain,
% 0.70/0.89 (![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(403,plain,
% 0.70/0.89 (^[U: $i] : 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)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp25) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp25))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp25) <=> (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp25) <=> (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.70/0.89 inference(bind,[status(th)],[])).
% 0.70/0.89 tff(404,plain,
% 0.70/0.89 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp25) <=> ![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.89 inference(quant_intro,[status(thm)],[403])).
% 0.70/0.89 tff(405,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp27) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 0.70/0.89 tff(406,plain,
% 0.70/0.89 (![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.70/0.89 tff(407,plain,
% 0.70/0.89 (![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[406, 402])).
% 0.70/0.89 tff(408,plain,(
% 0.70/0.89 ![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.89 inference(skolemize,[status(sab)],[407])).
% 0.70/0.89 tff(409,plain,
% 0.70/0.89 (![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[408, 401])).
% 0.70/0.89 tff(410,plain,
% 0.70/0.89 (((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | c3_1(a25))) <=> ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp25 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | c3_1(a25))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(411,plain,
% 0.70/0.89 ((hskp27 | hskp25 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25))) <=> (hskp27 | hskp25 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | c3_1(a25))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(412,plain,
% 0.70/0.89 (((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)))) <=> ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | c3_1(a25)))),
% 0.70/0.89 inference(monotonicity,[status(thm)],[411])).
% 0.70/0.89 tff(413,plain,
% 0.70/0.89 (((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)))) <=> ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp25 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | c3_1(a25))),
% 0.70/0.89 inference(transitivity,[status(thm)],[412, 410])).
% 0.70/0.89 tff(414,plain,
% 0.70/0.89 ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c1_1(a25)))),
% 0.70/0.89 inference(quant_inst,[status(thm)],[])).
% 0.70/0.89 tff(415,plain,
% 0.70/0.89 ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp25 | (~ndr1_0) | (~c1_1(a25)) | (~c2_1(a25)) | c3_1(a25)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.70/0.89 tff(416,plain,
% 0.70/0.89 (hskp27 | hskp25),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[415, 72, 348, 330, 409, 355])).
% 0.70/0.89 tff(417,plain,
% 0.70/0.89 (hskp25),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[416, 399])).
% 0.70/0.89 tff(418,plain,
% 0.70/0.89 (((~hskp25) | (~c2_1(a64))) <=> ((~hskp25) | (~c2_1(a64)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(419,plain,
% 0.70/0.89 (((~c2_1(a64)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a64)))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(420,axiom,((~c2_1(a64)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 0.70/0.89 tff(421,plain,
% 0.70/0.89 ((~hskp25) | (~c2_1(a64))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.70/0.89 tff(422,plain,
% 0.70/0.89 ((~hskp25) | (~c2_1(a64))),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[421, 418])).
% 0.70/0.89 tff(423,plain,
% 0.70/0.89 (~c2_1(a64)),
% 0.70/0.89 inference(unit_resolution,[status(thm)],[422, 417])).
% 0.70/0.89 tff(424,plain,
% 0.70/0.89 (((~hskp25) | c3_1(a64)) <=> ((~hskp25) | c3_1(a64))),
% 0.70/0.89 inference(rewrite,[status(thm)],[])).
% 0.70/0.89 tff(425,axiom,((~hskp25) | c3_1(a64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.70/0.89 tff(426,plain,
% 0.70/0.89 ((~hskp25) | c3_1(a64)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.70/0.89 tff(427,plain,
% 0.70/0.89 ((~hskp25) | c3_1(a64)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[426, 424])).
% 0.70/0.89 tff(428,plain,
% 0.70/0.89 ((~hskp25) | c3_1(a64)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[427, 424])).
% 0.70/0.89 tff(429,plain,
% 0.70/0.89 ((~hskp25) | c3_1(a64)),
% 0.70/0.89 inference(modus_ponens,[status(thm)],[428, 424])).
% 0.70/0.90 tff(430,plain,
% 0.70/0.90 ((~hskp25) | c3_1(a64)),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[429, 424])).
% 0.70/0.90 tff(431,plain,
% 0.70/0.90 (c3_1(a64)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[430, 417])).
% 0.70/0.90 tff(432,plain,
% 0.70/0.90 (((~hskp25) | c1_1(a64)) <=> ((~hskp25) | c1_1(a64))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(433,axiom,((~hskp25) | c1_1(a64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.70/0.90 tff(434,plain,
% 0.70/0.90 ((~hskp25) | c1_1(a64)),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.70/0.90 tff(435,plain,
% 0.70/0.90 ((~hskp25) | c1_1(a64)),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[434, 432])).
% 0.70/0.90 tff(436,plain,
% 0.70/0.90 ((~hskp25) | c1_1(a64)),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[435, 432])).
% 0.70/0.90 tff(437,plain,
% 0.70/0.90 ((~hskp25) | c1_1(a64)),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[436, 432])).
% 0.70/0.90 tff(438,plain,
% 0.70/0.90 ((~hskp25) | c1_1(a64)),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[437, 432])).
% 0.70/0.90 tff(439,plain,
% 0.70/0.90 (c1_1(a64)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[438, 417])).
% 0.70/0.90 tff(440,plain,
% 0.70/0.90 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | c2_1(a64) | (~ndr1_0) | (~c3_1(a64)) | (~c1_1(a64)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c2_1(a64) | (~ndr1_0) | (~c3_1(a64)) | (~c1_1(a64)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(441,plain,
% 0.70/0.90 ((hskp18 | hskp14 | (~ndr1_0) | c2_1(a64) | (~c3_1(a64)) | (~c1_1(a64))) <=> (hskp18 | hskp14 | c2_1(a64) | (~ndr1_0) | (~c3_1(a64)) | (~c1_1(a64)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(442,plain,
% 0.70/0.90 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a64) | (~c3_1(a64)) | (~c1_1(a64)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | c2_1(a64) | (~ndr1_0) | (~c3_1(a64)) | (~c1_1(a64))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[441])).
% 0.70/0.90 tff(443,plain,
% 0.70/0.90 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a64) | (~c3_1(a64)) | (~c1_1(a64)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c2_1(a64) | (~ndr1_0) | (~c3_1(a64)) | (~c1_1(a64)))),
% 0.70/0.90 inference(transitivity,[status(thm)],[442, 440])).
% 0.70/0.90 tff(444,plain,
% 0.70/0.90 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a64) | (~c3_1(a64)) | (~c1_1(a64)))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(445,plain,
% 0.70/0.90 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c2_1(a64) | (~ndr1_0) | (~c3_1(a64)) | (~c1_1(a64))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.70/0.90 tff(446,plain,
% 0.70/0.90 ($false),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[445, 72, 122, 277, 439, 431, 423, 295])).
% 0.70/0.90 tff(447,plain,(hskp14 | hskp18 | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3) | c3_1(a4) | (~c2_1(a4)) | c0_1(a4)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.90 tff(448,plain,
% 0.70/0.90 ($false),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[447, 285, 207, 173, 165, 157, 122, 277, 205])).
% 0.70/0.90 tff(449,plain,(c3_1(a4) | hskp18 | hskp14 | c0_1(a4) | hskp30 | c1_1(a4)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.90 tff(450,plain,
% 0.70/0.90 (hskp14),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[449, 207, 122, 205, 123, 204])).
% 0.70/0.90 tff(451,plain,
% 0.70/0.90 (((~hskp14) | (~c2_1(a26))) <=> ((~hskp14) | (~c2_1(a26)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(452,plain,
% 0.70/0.90 (((~c2_1(a26)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a26)))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(453,axiom,((~c2_1(a26)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.70/0.90 tff(454,plain,
% 0.70/0.90 ((~hskp14) | (~c2_1(a26))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.70/0.90 tff(455,plain,
% 0.70/0.90 ((~hskp14) | (~c2_1(a26))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[454, 451])).
% 0.70/0.90 tff(456,plain,
% 0.70/0.90 (~c2_1(a26)),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[455, 450])).
% 0.70/0.90 tff(457,plain,
% 0.73/0.90 (((~hskp14) | (~c1_1(a26))) <=> ((~hskp14) | (~c1_1(a26)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(458,plain,
% 0.73/0.90 (((~c1_1(a26)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a26)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(459,axiom,((~c1_1(a26)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.73/0.90 tff(460,plain,
% 0.73/0.90 ((~hskp14) | (~c1_1(a26))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.73/0.90 tff(461,plain,
% 0.73/0.90 ((~hskp14) | (~c1_1(a26))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[460, 457])).
% 0.73/0.90 tff(462,plain,
% 0.73/0.90 (~c1_1(a26)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[461, 450])).
% 0.73/0.90 tff(463,plain,
% 0.73/0.90 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c3_1(a26))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c3_1(a26))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(464,plain,
% 0.73/0.90 ((hskp30 | hskp18 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c2_1(a26)) <=> (hskp30 | hskp18 | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c3_1(a26))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(465,plain,
% 0.73/0.90 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c2_1(a26))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c3_1(a26)))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[464])).
% 0.73/0.90 tff(466,plain,
% 0.73/0.90 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c2_1(a26))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c3_1(a26))),
% 0.73/0.90 inference(transitivity,[status(thm)],[465, 463])).
% 0.73/0.90 tff(467,plain,
% 0.73/0.90 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c2_1(a26))),
% 0.73/0.90 inference(quant_inst,[status(thm)],[])).
% 0.73/0.90 tff(468,plain,
% 0.73/0.90 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c3_1(a26)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.73/0.90 tff(469,plain,
% 0.73/0.90 (c3_1(a26)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[468, 123, 72, 122, 462, 456, 276])).
% 0.73/0.90 tff(470,plain,
% 0.73/0.90 (^[U: $i] : refl((hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.73/0.90 inference(bind,[status(th)],[])).
% 0.73/0.90 tff(471,plain,
% 0.73/0.90 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.90 inference(quant_intro,[status(thm)],[470])).
% 0.73/0.90 tff(472,plain,
% 0.73/0.90 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(473,plain,
% 0.73/0.90 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp3) <=> ((hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp3))), rewrite(((hskp9 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp3) <=> (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp3) <=> (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.73/0.90 inference(bind,[status(th)],[])).
% 0.73/0.90 tff(474,plain,
% 0.73/0.90 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp3) <=> ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.90 inference(quant_intro,[status(thm)],[473])).
% 0.73/0.90 tff(475,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp9) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 0.73/0.90 tff(476,plain,
% 0.73/0.90 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.73/0.90 tff(477,plain,
% 0.73/0.90 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[476, 472])).
% 0.73/0.90 tff(478,plain,(
% 0.73/0.90 ![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.90 inference(skolemize,[status(sab)],[477])).
% 0.73/0.90 tff(479,plain,
% 0.73/0.90 (![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[478, 471])).
% 0.73/0.90 tff(480,plain,
% 0.73/0.90 (((~hskp14) | (~c0_1(a26))) <=> ((~hskp14) | (~c0_1(a26)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(481,plain,
% 0.73/0.90 (((~c0_1(a26)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a26)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(482,axiom,((~c0_1(a26)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.73/0.90 tff(483,plain,
% 0.73/0.90 ((~hskp14) | (~c0_1(a26))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.73/0.90 tff(484,plain,
% 0.73/0.90 ((~hskp14) | (~c0_1(a26))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[483, 480])).
% 0.73/0.90 tff(485,plain,
% 0.73/0.90 (~c0_1(a26)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[484, 450])).
% 0.73/0.90 tff(486,plain,
% 0.73/0.90 (((~hskp3) | c3_1(a4)) <=> ((~hskp3) | c3_1(a4))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(487,axiom,((~hskp3) | c3_1(a4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.73/0.90 tff(488,plain,
% 0.73/0.90 ((~hskp3) | c3_1(a4)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.73/0.90 tff(489,plain,
% 0.73/0.90 ((~hskp3) | c3_1(a4)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[488, 486])).
% 0.73/0.90 tff(490,plain,
% 0.73/0.90 ((~hskp3) | c3_1(a4)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[489, 486])).
% 0.73/0.90 tff(491,plain,
% 0.73/0.90 ((~hskp3) | c3_1(a4)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[490, 486])).
% 0.73/0.90 tff(492,plain,
% 0.73/0.90 ((~hskp3) | c3_1(a4)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[491, 486])).
% 0.73/0.90 tff(493,plain,
% 0.73/0.90 (~hskp3),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[492, 207])).
% 0.73/0.90 tff(494,assumption,(~hskp9), introduced(assumption)).
% 0.73/0.90 tff(495,plain,
% 0.73/0.90 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp3 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp9 | hskp3 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(496,plain,
% 0.73/0.90 ((hskp9 | hskp3 | (~ndr1_0) | c1_1(a26) | c0_1(a26) | (~c3_1(a26))) <=> (hskp9 | hskp3 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(497,plain,
% 0.73/0.90 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp3 | (~ndr1_0) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp3 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26))))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[496])).
% 0.73/0.90 tff(498,plain,
% 0.73/0.90 (((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp3 | (~ndr1_0) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp9 | hskp3 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26)))),
% 0.73/0.90 inference(transitivity,[status(thm)],[497, 495])).
% 0.73/0.90 tff(499,plain,
% 0.73/0.90 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp9 | hskp3 | (~ndr1_0) | c1_1(a26) | c0_1(a26) | (~c3_1(a26)))),
% 0.73/0.90 inference(quant_inst,[status(thm)],[])).
% 0.73/0.90 tff(500,plain,
% 0.73/0.90 ((~![U: $i] : (hskp9 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp9 | hskp3 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | (~c3_1(a26))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.73/0.90 tff(501,plain,
% 0.73/0.90 ($false),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[500, 72, 494, 493, 485, 462, 479, 469])).
% 0.73/0.90 tff(502,plain,(c3_1(a4) | hskp9 | hskp30 | hskp18 | c0_1(a4) | c1_1(a4)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.90 tff(503,plain,
% 0.73/0.90 (hskp9),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[502, 207, 123, 122, 205, 204])).
% 0.73/0.90 tff(504,plain,
% 0.73/0.90 (((~hskp9) | c1_1(a12)) <=> ((~hskp9) | c1_1(a12))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(505,axiom,((~hskp9) | c1_1(a12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.73/0.90 tff(506,plain,
% 0.73/0.90 ((~hskp9) | c1_1(a12)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.73/0.90 tff(507,plain,
% 0.73/0.90 ((~hskp9) | c1_1(a12)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[506, 504])).
% 0.73/0.90 tff(508,plain,
% 0.73/0.90 ((~hskp9) | c1_1(a12)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[507, 504])).
% 0.73/0.90 tff(509,plain,
% 0.73/0.90 ((~hskp9) | c1_1(a12)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[508, 504])).
% 0.73/0.90 tff(510,plain,
% 0.73/0.90 ((~hskp9) | c1_1(a12)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[509, 504])).
% 0.73/0.90 tff(511,plain,
% 0.73/0.90 (c1_1(a12)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[510, 503])).
% 0.73/0.90 tff(512,plain,
% 0.73/0.90 (((~hskp9) | (~c3_1(a12))) <=> ((~hskp9) | (~c3_1(a12)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(513,plain,
% 0.73/0.90 (((~c3_1(a12)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a12)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(514,axiom,((~c3_1(a12)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.73/0.90 tff(515,plain,
% 0.73/0.90 ((~hskp9) | (~c3_1(a12))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.73/0.90 tff(516,plain,
% 0.73/0.90 ((~hskp9) | (~c3_1(a12))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[515, 512])).
% 0.73/0.90 tff(517,plain,
% 0.73/0.90 (~c3_1(a12)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[516, 503])).
% 0.73/0.90 tff(518,plain,
% 0.73/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))))),
% 0.73/0.90 inference(bind,[status(th)],[])).
% 0.73/0.90 tff(519,plain,
% 0.73/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_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) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.73/0.90 inference(quant_intro,[status(thm)],[518])).
% 0.73/0.90 tff(520,plain,
% 0.73/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_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) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(521,plain,
% 0.73/0.90 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))))),
% 0.73/0.90 inference(bind,[status(th)],[])).
% 0.73/0.90 tff(522,plain,
% 0.73/0.90 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.73/0.90 inference(quant_intro,[status(thm)],[521])).
% 0.73/0.90 tff(523,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 0.73/0.90 tff(524,plain,
% 0.73/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.73/0.90 tff(525,plain,
% 0.73/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[524, 520])).
% 0.73/0.90 tff(526,plain,(
% 0.73/0.90 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.73/0.90 inference(skolemize,[status(sab)],[525])).
% 0.73/0.90 tff(527,plain,
% 0.73/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[526, 519])).
% 0.73/0.90 tff(528,assumption,(~hskp0), introduced(assumption)).
% 0.73/0.90 tff(529,plain,
% 0.73/0.90 (^[U: $i] : refl((hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.73/0.90 inference(bind,[status(th)],[])).
% 0.73/0.90 tff(530,plain,
% 0.73/0.90 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.90 inference(quant_intro,[status(thm)],[529])).
% 0.73/0.90 tff(531,plain,
% 0.73/0.90 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(532,plain,
% 0.73/0.90 (^[U: $i] : 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)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp0) <=> ((hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp0))), rewrite(((hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp0) <=> (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp0) <=> (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.73/0.90 inference(bind,[status(th)],[])).
% 0.73/0.90 tff(533,plain,
% 0.73/0.90 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp0) <=> ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.90 inference(quant_intro,[status(thm)],[532])).
% 0.73/0.90 tff(534,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp1) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.73/0.90 tff(535,plain,
% 0.73/0.90 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[534, 533])).
% 0.73/0.90 tff(536,plain,
% 0.73/0.90 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[535, 531])).
% 0.73/0.90 tff(537,plain,(
% 0.73/0.90 ![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.90 inference(skolemize,[status(sab)],[536])).
% 0.73/0.90 tff(538,plain,
% 0.73/0.90 (![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[537, 530])).
% 0.73/0.90 tff(539,plain,
% 0.73/0.90 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(540,plain,
% 0.73/0.90 ((hskp1 | hskp0 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5))) <=> (hskp1 | hskp0 | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(541,plain,
% 0.73/0.90 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))))),
% 0.73/0.90 inference(monotonicity,[status(thm)],[540])).
% 0.73/0.90 tff(542,plain,
% 0.73/0.90 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.73/0.90 inference(transitivity,[status(thm)],[541, 539])).
% 0.73/0.90 tff(543,plain,
% 0.73/0.90 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.73/0.90 inference(quant_inst,[status(thm)],[])).
% 0.73/0.90 tff(544,plain,
% 0.73/0.90 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.73/0.90 tff(545,plain,
% 0.73/0.90 (hskp1 | hskp0 | (~c2_1(a5)) | (~c3_1(a5))),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[544, 72, 190, 538])).
% 0.73/0.90 tff(546,plain,
% 0.73/0.90 (hskp1),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[545, 528, 233, 232])).
% 0.73/0.90 tff(547,plain,
% 0.73/0.90 (((~hskp1) | (~c2_1(a2))) <=> ((~hskp1) | (~c2_1(a2)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(548,plain,
% 0.73/0.90 (((~c2_1(a2)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a2)))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(549,axiom,((~c2_1(a2)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.73/0.90 tff(550,plain,
% 0.73/0.90 ((~hskp1) | (~c2_1(a2))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[549, 548])).
% 0.73/0.90 tff(551,plain,
% 0.73/0.90 ((~hskp1) | (~c2_1(a2))),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[550, 547])).
% 0.73/0.90 tff(552,plain,
% 0.73/0.90 (~c2_1(a2)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[551, 546])).
% 0.73/0.90 tff(553,plain,
% 0.73/0.90 (((~hskp1) | c3_1(a2)) <=> ((~hskp1) | c3_1(a2))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(554,axiom,((~hskp1) | c3_1(a2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.73/0.90 tff(555,plain,
% 0.73/0.90 ((~hskp1) | c3_1(a2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.73/0.90 tff(556,plain,
% 0.73/0.90 ((~hskp1) | c3_1(a2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[555, 553])).
% 0.73/0.90 tff(557,plain,
% 0.73/0.90 ((~hskp1) | c3_1(a2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[556, 553])).
% 0.73/0.90 tff(558,plain,
% 0.73/0.90 ((~hskp1) | c3_1(a2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[557, 553])).
% 0.73/0.90 tff(559,plain,
% 0.73/0.90 ((~hskp1) | c3_1(a2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[558, 553])).
% 0.73/0.90 tff(560,plain,
% 0.73/0.90 (c3_1(a2)),
% 0.73/0.90 inference(unit_resolution,[status(thm)],[559, 546])).
% 0.73/0.90 tff(561,plain,
% 0.73/0.90 (((~hskp1) | c0_1(a2)) <=> ((~hskp1) | c0_1(a2))),
% 0.73/0.90 inference(rewrite,[status(thm)],[])).
% 0.73/0.90 tff(562,axiom,((~hskp1) | c0_1(a2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.73/0.90 tff(563,plain,
% 0.73/0.90 ((~hskp1) | c0_1(a2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.73/0.90 tff(564,plain,
% 0.73/0.90 ((~hskp1) | c0_1(a2)),
% 0.73/0.90 inference(modus_ponens,[status(thm)],[563, 561])).
% 0.73/0.91 tff(565,plain,
% 0.73/0.91 ((~hskp1) | c0_1(a2)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[564, 561])).
% 0.73/0.91 tff(566,plain,
% 0.73/0.91 ((~hskp1) | c0_1(a2)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[565, 561])).
% 0.73/0.91 tff(567,plain,
% 0.73/0.91 ((~hskp1) | c0_1(a2)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[566, 561])).
% 0.73/0.91 tff(568,plain,
% 0.73/0.91 (c0_1(a2)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[567, 546])).
% 0.73/0.91 tff(569,plain,
% 0.73/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a3) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_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) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a3) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a3)) | (~c0_1(a3)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(570,plain,
% 0.73/0.91 (((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3))) <=> (c1_1(a3) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a3)) | (~c0_1(a3)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(571,plain,
% 0.73/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a3) | (~c2_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) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a3) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a3)) | (~c0_1(a3))))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[570])).
% 0.73/0.91 tff(572,plain,
% 0.73/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a3) | (~c2_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) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a3) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a3)) | (~c0_1(a3)))),
% 0.73/0.91 inference(transitivity,[status(thm)],[571, 569])).
% 0.73/0.91 tff(573,plain,
% 0.73/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)))),
% 0.73/0.91 inference(quant_inst,[status(thm)],[])).
% 0.73/0.91 tff(574,plain,
% 0.73/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a3) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a3)) | (~c0_1(a3))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.73/0.91 tff(575,plain,
% 0.73/0.91 (~c1_1(a2)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[574, 72, 231, 230, 568, 560, 229, 552, 527])).
% 0.73/0.91 tff(576,plain,
% 0.73/0.91 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.73/0.91 inference(bind,[status(th)],[])).
% 0.73/0.91 tff(577,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.73/0.91 inference(quant_intro,[status(thm)],[576])).
% 0.73/0.91 tff(578,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(579,plain,
% 0.73/0.91 (^[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)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.73/0.91 inference(bind,[status(th)],[])).
% 0.73/0.91 tff(580,plain,
% 0.73/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.73/0.91 inference(quant_intro,[status(thm)],[579])).
% 0.73/0.91 tff(581,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 0.73/0.91 tff(582,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.73/0.91 tff(583,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[582, 578])).
% 0.73/0.91 tff(584,plain,(
% 0.73/0.91 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.73/0.91 inference(skolemize,[status(sab)],[583])).
% 0.73/0.91 tff(585,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[584, 577])).
% 0.73/0.91 tff(586,assumption,(~c3_1(a12)), introduced(assumption)).
% 0.73/0.91 tff(587,assumption,(c1_1(a12)), introduced(assumption)).
% 0.73/0.91 tff(588,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c3_1(a12) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a12)) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a12) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a12)) | (~c1_1(a12)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(589,plain,
% 0.73/0.91 ((hskp0 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2))) <=> (hskp0 | c3_1(a12) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a12)) | (~c1_1(a12)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(590,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c3_1(a12) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a12)) | (~c1_1(a12))))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[589])).
% 0.73/0.91 tff(591,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a12) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a12)) | (~c1_1(a12)))),
% 0.73/0.91 inference(transitivity,[status(thm)],[590, 588])).
% 0.73/0.91 tff(592,plain,
% 0.73/0.91 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))),
% 0.73/0.91 inference(quant_inst,[status(thm)],[])).
% 0.73/0.91 tff(593,plain,
% 0.73/0.91 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a12) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a12)) | (~c1_1(a12))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[592, 591])).
% 0.73/0.91 tff(594,plain,
% 0.73/0.91 (~c0_1(a12)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[593, 72, 528, 587, 560, 586, 552, 585, 575])).
% 0.73/0.91 tff(595,plain,
% 0.73/0.91 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.73/0.91 inference(bind,[status(th)],[])).
% 0.73/0.91 tff(596,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.73/0.91 inference(quant_intro,[status(thm)],[595])).
% 0.73/0.91 tff(597,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(598,plain,
% 0.73/0.91 (^[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(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.73/0.91 inference(bind,[status(th)],[])).
% 0.73/0.91 tff(599,plain,
% 0.73/0.91 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.73/0.91 inference(quant_intro,[status(thm)],[598])).
% 0.73/0.91 tff(600,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 0.73/0.91 tff(601,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.73/0.91 tff(602,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[601, 597])).
% 0.73/0.91 tff(603,plain,(
% 0.73/0.91 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.73/0.91 inference(skolemize,[status(sab)],[602])).
% 0.73/0.91 tff(604,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[603, 596])).
% 0.73/0.91 tff(605,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(606,plain,
% 0.73/0.91 ((hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2))) <=> (hskp22 | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(607,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a5))))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[606])).
% 0.73/0.91 tff(608,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.73/0.91 inference(transitivity,[status(thm)],[607, 605])).
% 0.73/0.91 tff(609,plain,
% 0.73/0.91 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))),
% 0.73/0.91 inference(quant_inst,[status(thm)],[])).
% 0.73/0.91 tff(610,plain,
% 0.73/0.91 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c2_1(a5)) | (~c3_1(a5))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.73/0.91 tff(611,plain,
% 0.73/0.91 (hskp22),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[610, 72, 233, 232, 560, 190, 552, 111, 575])).
% 0.73/0.91 tff(612,plain,
% 0.73/0.91 (((~hskp22) | (~c3_1(a43))) <=> ((~hskp22) | (~c3_1(a43)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(613,plain,
% 0.73/0.91 (((~c3_1(a43)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a43)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(614,axiom,((~c3_1(a43)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.73/0.91 tff(615,plain,
% 0.73/0.91 ((~hskp22) | (~c3_1(a43))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[614, 613])).
% 0.73/0.91 tff(616,plain,
% 0.73/0.91 ((~hskp22) | (~c3_1(a43))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[615, 612])).
% 0.73/0.91 tff(617,plain,
% 0.73/0.91 (~c3_1(a43)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[616, 611])).
% 0.73/0.91 tff(618,plain,
% 0.73/0.91 (((~hskp22) | (~c1_1(a43))) <=> ((~hskp22) | (~c1_1(a43)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(619,plain,
% 0.73/0.91 (((~c1_1(a43)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a43)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(620,axiom,((~c1_1(a43)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.73/0.91 tff(621,plain,
% 0.73/0.91 ((~hskp22) | (~c1_1(a43))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[620, 619])).
% 0.73/0.91 tff(622,plain,
% 0.73/0.91 ((~hskp22) | (~c1_1(a43))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[621, 618])).
% 0.73/0.91 tff(623,plain,
% 0.73/0.91 (~c1_1(a43)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[622, 611])).
% 0.73/0.91 tff(624,plain,
% 0.73/0.91 (((~hskp22) | c2_1(a43)) <=> ((~hskp22) | c2_1(a43))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(625,axiom,((~hskp22) | c2_1(a43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.73/0.91 tff(626,plain,
% 0.73/0.91 ((~hskp22) | c2_1(a43)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[625, 624])).
% 0.73/0.91 tff(627,plain,
% 0.73/0.91 ((~hskp22) | c2_1(a43)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[626, 624])).
% 0.73/0.91 tff(628,plain,
% 0.73/0.91 ((~hskp22) | c2_1(a43)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[627, 624])).
% 0.73/0.91 tff(629,plain,
% 0.73/0.91 ((~hskp22) | c2_1(a43)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[628, 624])).
% 0.73/0.91 tff(630,plain,
% 0.73/0.91 ((~hskp22) | c2_1(a43)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[629, 624])).
% 0.73/0.91 tff(631,plain,
% 0.73/0.91 (c2_1(a43)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[630, 611])).
% 0.73/0.91 tff(632,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp0 | c1_1(a43) | c3_1(a43) | c3_1(a12) | (~ndr1_0) | c0_1(a12) | (~c1_1(a12)) | (~c2_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp0 | c1_1(a43) | c3_1(a43) | c3_1(a12) | (~ndr1_0) | c0_1(a12) | (~c1_1(a12)) | (~c2_1(a43)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(633,plain,
% 0.73/0.91 ((hskp0 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c2_1(a43)) | c0_1(a12) | c3_1(a12) | (~c1_1(a12))) <=> (hskp0 | c1_1(a43) | c3_1(a43) | c3_1(a12) | (~ndr1_0) | c0_1(a12) | (~c1_1(a12)) | (~c2_1(a43)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(634,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c2_1(a43)) | c0_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp0 | c1_1(a43) | c3_1(a43) | c3_1(a12) | (~ndr1_0) | c0_1(a12) | (~c1_1(a12)) | (~c2_1(a43))))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[633])).
% 0.73/0.91 tff(635,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c2_1(a43)) | c0_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp0 | c1_1(a43) | c3_1(a43) | c3_1(a12) | (~ndr1_0) | c0_1(a12) | (~c1_1(a12)) | (~c2_1(a43)))),
% 0.73/0.91 inference(transitivity,[status(thm)],[634, 632])).
% 0.73/0.91 tff(636,plain,
% 0.73/0.91 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c2_1(a43)) | c0_1(a12) | c3_1(a12) | (~c1_1(a12)))),
% 0.73/0.91 inference(quant_inst,[status(thm)],[])).
% 0.73/0.91 tff(637,plain,
% 0.73/0.91 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp0 | c1_1(a43) | c3_1(a43) | c3_1(a12) | (~ndr1_0) | c0_1(a12) | (~c1_1(a12)) | (~c2_1(a43))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[636, 635])).
% 0.73/0.91 tff(638,plain,
% 0.73/0.91 ($false),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[637, 72, 528, 631, 587, 623, 617, 586, 604, 594])).
% 0.73/0.91 tff(639,plain,(hskp0 | (~c1_1(a12)) | c3_1(a12) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.91 tff(640,plain,
% 0.73/0.91 (hskp0),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[639, 217, 517, 511, 216, 190, 173, 165, 157])).
% 0.73/0.91 tff(641,plain,
% 0.73/0.91 (((~hskp0) | (~c0_1(a1))) <=> ((~hskp0) | (~c0_1(a1)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(642,plain,
% 0.73/0.91 (((~c0_1(a1)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a1)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(643,axiom,((~c0_1(a1)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 0.73/0.91 tff(644,plain,
% 0.73/0.91 ((~hskp0) | (~c0_1(a1))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.73/0.91 tff(645,plain,
% 0.73/0.91 ((~hskp0) | (~c0_1(a1))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[644, 641])).
% 0.73/0.91 tff(646,plain,
% 0.73/0.91 (~c0_1(a1)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[645, 640])).
% 0.73/0.91 tff(647,plain,
% 0.73/0.91 (((~hskp0) | c1_1(a1)) <=> ((~hskp0) | c1_1(a1))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(648,axiom,((~hskp0) | c1_1(a1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.73/0.91 tff(649,plain,
% 0.73/0.91 ((~hskp0) | c1_1(a1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[648, 647])).
% 0.73/0.91 tff(650,plain,
% 0.73/0.91 ((~hskp0) | c1_1(a1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[649, 647])).
% 0.73/0.91 tff(651,plain,
% 0.73/0.91 ((~hskp0) | c1_1(a1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[650, 647])).
% 0.73/0.91 tff(652,plain,
% 0.73/0.91 ((~hskp0) | c1_1(a1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[651, 647])).
% 0.73/0.91 tff(653,plain,
% 0.73/0.91 ((~hskp0) | c1_1(a1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[652, 647])).
% 0.73/0.91 tff(654,plain,
% 0.73/0.91 (c1_1(a1)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[653, 640])).
% 0.73/0.91 tff(655,plain,
% 0.73/0.91 (((~hskp0) | c2_1(a1)) <=> ((~hskp0) | c2_1(a1))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(656,axiom,((~hskp0) | c2_1(a1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.73/0.91 tff(657,plain,
% 0.73/0.91 ((~hskp0) | c2_1(a1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[656, 655])).
% 0.73/0.91 tff(658,plain,
% 0.73/0.91 ((~hskp0) | c2_1(a1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[657, 655])).
% 0.73/0.91 tff(659,plain,
% 0.73/0.91 ((~hskp0) | c2_1(a1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[658, 655])).
% 0.73/0.91 tff(660,plain,
% 0.73/0.91 ((~hskp0) | c2_1(a1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[659, 655])).
% 0.73/0.91 tff(661,plain,
% 0.73/0.91 ((~hskp0) | c2_1(a1)),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[660, 655])).
% 0.73/0.91 tff(662,plain,
% 0.73/0.91 (c2_1(a1)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[661, 640])).
% 0.73/0.91 tff(663,assumption,(~c0_1(a1)), introduced(assumption)).
% 0.73/0.91 tff(664,assumption,(c0_1(a5)), introduced(assumption)).
% 0.73/0.91 tff(665,plain,
% 0.73/0.91 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.73/0.91 inference(bind,[status(th)],[])).
% 0.73/0.91 tff(666,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.91 inference(quant_intro,[status(thm)],[665])).
% 0.73/0.91 tff(667,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(668,plain,
% 0.73/0.91 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | 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)) | c1_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)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.73/0.91 inference(bind,[status(th)],[])).
% 0.73/0.91 tff(669,plain,
% 0.73/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.91 inference(quant_intro,[status(thm)],[668])).
% 0.73/0.91 tff(670,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 0.73/0.91 tff(671,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.73/0.91 tff(672,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[671, 667])).
% 0.73/0.91 tff(673,plain,(
% 0.73/0.91 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.91 inference(skolemize,[status(sab)],[672])).
% 0.73/0.91 tff(674,plain,
% 0.73/0.91 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[673, 666])).
% 0.73/0.91 tff(675,assumption,(hskp14), introduced(assumption)).
% 0.73/0.91 tff(676,plain,
% 0.73/0.91 (~c2_1(a26)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[455, 675])).
% 0.73/0.91 tff(677,plain,
% 0.73/0.91 (~c1_1(a26)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[461, 675])).
% 0.73/0.91 tff(678,plain,
% 0.73/0.91 (~c0_1(a26)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[484, 675])).
% 0.73/0.91 tff(679,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(680,plain,
% 0.73/0.91 ((hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a26) | c1_1(a26) | c0_1(a26)) <=> (hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.73/0.91 inference(rewrite,[status(thm)],[])).
% 0.73/0.91 tff(681,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a26) | c1_1(a26) | c0_1(a26))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5))))),
% 0.73/0.91 inference(monotonicity,[status(thm)],[680])).
% 0.73/0.91 tff(682,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a26) | c1_1(a26) | c0_1(a26))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.73/0.91 inference(transitivity,[status(thm)],[681, 679])).
% 0.73/0.91 tff(683,plain,
% 0.73/0.91 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a26) | c1_1(a26) | c0_1(a26))),
% 0.73/0.91 inference(quant_inst,[status(thm)],[])).
% 0.73/0.91 tff(684,plain,
% 0.73/0.91 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5))),
% 0.73/0.91 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.73/0.91 tff(685,plain,
% 0.73/0.91 (hskp1),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[684, 72, 233, 678, 677, 676, 190, 674, 664])).
% 0.73/0.91 tff(686,plain,
% 0.73/0.91 (~c2_1(a2)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[551, 685])).
% 0.73/0.91 tff(687,plain,
% 0.73/0.91 (c3_1(a26)),
% 0.73/0.91 inference(unit_resolution,[status(thm)],[468, 123, 72, 122, 677, 676, 276])).
% 0.73/0.91 tff(688,plain,
% 0.73/0.91 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a26)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(689,plain,
% 0.73/0.92 ((hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26))) <=> (hskp22 | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a26)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(690,plain,
% 0.73/0.92 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a26))))),
% 0.73/0.92 inference(monotonicity,[status(thm)],[689])).
% 0.73/0.92 tff(691,plain,
% 0.73/0.92 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a26)))),
% 0.73/0.92 inference(transitivity,[status(thm)],[690, 688])).
% 0.73/0.92 tff(692,plain,
% 0.73/0.92 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26)))),
% 0.73/0.92 inference(quant_inst,[status(thm)],[])).
% 0.73/0.92 tff(693,plain,
% 0.73/0.92 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a26) | c2_1(a26) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a26))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.73/0.92 tff(694,plain,
% 0.73/0.92 (hskp22 | (~c3_1(a26))),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[693, 72, 233, 232, 677, 676, 190, 111])).
% 0.73/0.92 tff(695,plain,
% 0.73/0.92 (hskp22),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[694, 687])).
% 0.73/0.92 tff(696,plain,
% 0.73/0.92 (~c3_1(a43)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[616, 695])).
% 0.73/0.92 tff(697,plain,
% 0.73/0.92 (~c1_1(a43)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[622, 695])).
% 0.73/0.92 tff(698,assumption,(c2_1(a1)), introduced(assumption)).
% 0.73/0.92 tff(699,assumption,(c1_1(a1)), introduced(assumption)).
% 0.73/0.92 tff(700,plain,
% 0.73/0.92 (c3_1(a2)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[559, 685])).
% 0.73/0.92 tff(701,plain,
% 0.73/0.92 (c0_1(a2)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[567, 685])).
% 0.73/0.92 tff(702,plain,
% 0.73/0.92 (c2_1(a43)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[630, 695])).
% 0.73/0.92 tff(703,plain,
% 0.73/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c2_1(a2) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a2) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(704,plain,
% 0.73/0.92 (((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1))) <=> (c1_1(a43) | c3_1(a43) | c2_1(a2) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(705,plain,
% 0.73/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c2_1(a2) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43))))),
% 0.73/0.92 inference(monotonicity,[status(thm)],[704])).
% 0.73/0.92 tff(706,plain,
% 0.73/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a2) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)))),
% 0.73/0.92 inference(transitivity,[status(thm)],[705, 703])).
% 0.73/0.92 tff(707,plain,
% 0.73/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))),
% 0.73/0.92 inference(quant_inst,[status(thm)],[])).
% 0.73/0.92 tff(708,plain,
% 0.73/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a2) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[707, 706])).
% 0.73/0.92 tff(709,plain,
% 0.73/0.92 ($false),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[708, 72, 702, 701, 700, 699, 698, 697, 696, 686, 663, 121])).
% 0.73/0.92 tff(710,plain,((~hskp14) | (~c1_1(a1)) | (~c2_1(a1)) | c0_1(a1) | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | hskp30 | hskp18 | (~c0_1(a5))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.92 tff(711,plain,
% 0.73/0.92 ($false),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[710, 662, 654, 450, 646, 217, 216, 190, 123, 122, 266])).
% 0.73/0.92 tff(712,plain,(c3_1(a4) | c1_1(a5) | hskp30 | hskp18 | c3_1(a6) | c0_1(a4) | c1_1(a4)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.92 tff(713,plain,
% 0.73/0.92 (c3_1(a4)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[712, 206, 123, 122, 190, 205, 204])).
% 0.73/0.92 tff(714,plain,
% 0.73/0.92 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.73/0.92 inference(bind,[status(th)],[])).
% 0.73/0.92 tff(715,plain,
% 0.73/0.92 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.73/0.92 inference(quant_intro,[status(thm)],[714])).
% 0.73/0.92 tff(716,plain,
% 0.73/0.92 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(717,plain,
% 0.73/0.92 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_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) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.73/0.92 inference(bind,[status(th)],[])).
% 0.73/0.92 tff(718,plain,
% 0.73/0.92 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.73/0.92 inference(quant_intro,[status(thm)],[717])).
% 0.73/0.92 tff(719,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 0.73/0.92 tff(720,plain,
% 0.73/0.92 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[719, 718])).
% 0.73/0.92 tff(721,plain,
% 0.73/0.92 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[720, 716])).
% 0.73/0.92 tff(722,plain,(
% 0.73/0.92 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.73/0.92 inference(skolemize,[status(sab)],[721])).
% 0.73/0.92 tff(723,plain,
% 0.73/0.92 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[722, 715])).
% 0.73/0.92 tff(724,assumption,(~hskp6), introduced(assumption)).
% 0.73/0.92 tff(725,assumption,(c3_1(a4)), introduced(assumption)).
% 0.73/0.92 tff(726,plain,
% 0.73/0.92 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.73/0.92 inference(bind,[status(th)],[])).
% 0.73/0.92 tff(727,plain,
% 0.73/0.92 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.92 inference(quant_intro,[status(thm)],[726])).
% 0.73/0.92 tff(728,plain,
% 0.73/0.92 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(729,plain,
% 0.73/0.92 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.73/0.92 inference(bind,[status(th)],[])).
% 0.73/0.92 tff(730,plain,
% 0.73/0.92 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.92 inference(quant_intro,[status(thm)],[729])).
% 0.73/0.92 tff(731,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.73/0.92 tff(732,plain,
% 0.73/0.92 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[731, 730])).
% 0.73/0.92 tff(733,plain,
% 0.73/0.92 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[732, 728])).
% 0.73/0.92 tff(734,plain,(
% 0.73/0.92 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.92 inference(skolemize,[status(sab)],[733])).
% 0.73/0.92 tff(735,plain,
% 0.73/0.92 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[734, 727])).
% 0.73/0.92 tff(736,plain,
% 0.73/0.92 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c3_1(a4)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c3_1(a4)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(737,plain,
% 0.73/0.92 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c3_1(a4))) <=> (hskp7 | hskp6 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c3_1(a4)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(738,plain,
% 0.73/0.92 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c3_1(a4)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c3_1(a4))))),
% 0.73/0.92 inference(monotonicity,[status(thm)],[737])).
% 0.73/0.92 tff(739,plain,
% 0.73/0.92 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c3_1(a4)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c3_1(a4)))),
% 0.73/0.92 inference(transitivity,[status(thm)],[738, 736])).
% 0.73/0.92 tff(740,plain,
% 0.73/0.92 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c3_1(a4)))),
% 0.73/0.92 inference(quant_inst,[status(thm)],[])).
% 0.73/0.92 tff(741,plain,
% 0.73/0.92 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp7 | hskp6 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c3_1(a4))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.73/0.92 tff(742,plain,
% 0.73/0.92 (hskp7 | hskp6 | c0_1(a4) | (~c3_1(a4))),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[741, 72, 204, 735])).
% 0.73/0.92 tff(743,plain,
% 0.73/0.92 (hskp7),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[742, 725, 724, 205])).
% 0.73/0.92 tff(744,plain,
% 0.73/0.92 (((~hskp7) | (~c2_1(a9))) <=> ((~hskp7) | (~c2_1(a9)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(745,plain,
% 0.73/0.92 (((~c2_1(a9)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a9)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(746,axiom,((~c2_1(a9)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.73/0.92 tff(747,plain,
% 0.73/0.92 ((~hskp7) | (~c2_1(a9))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[746, 745])).
% 0.73/0.92 tff(748,plain,
% 0.73/0.92 ((~hskp7) | (~c2_1(a9))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[747, 744])).
% 0.73/0.92 tff(749,plain,
% 0.73/0.92 (~c2_1(a9)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[748, 743])).
% 0.73/0.92 tff(750,plain,
% 0.73/0.92 (((~hskp7) | (~c0_1(a9))) <=> ((~hskp7) | (~c0_1(a9)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(751,plain,
% 0.73/0.92 (((~c0_1(a9)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a9)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(752,axiom,((~c0_1(a9)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.73/0.92 tff(753,plain,
% 0.73/0.92 ((~hskp7) | (~c0_1(a9))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[752, 751])).
% 0.73/0.92 tff(754,plain,
% 0.73/0.92 ((~hskp7) | (~c0_1(a9))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[753, 750])).
% 0.73/0.92 tff(755,plain,
% 0.73/0.92 (~c0_1(a9)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[754, 743])).
% 0.73/0.92 tff(756,plain,
% 0.73/0.92 (((~hskp7) | c1_1(a9)) <=> ((~hskp7) | c1_1(a9))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(757,axiom,((~hskp7) | c1_1(a9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.73/0.92 tff(758,plain,
% 0.73/0.92 ((~hskp7) | c1_1(a9)),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[757, 756])).
% 0.73/0.92 tff(759,plain,
% 0.73/0.92 ((~hskp7) | c1_1(a9)),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[758, 756])).
% 0.73/0.92 tff(760,plain,
% 0.73/0.92 ((~hskp7) | c1_1(a9)),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[759, 756])).
% 0.73/0.92 tff(761,plain,
% 0.73/0.92 ((~hskp7) | c1_1(a9)),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[760, 756])).
% 0.73/0.92 tff(762,plain,
% 0.73/0.92 ((~hskp7) | c1_1(a9)),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[761, 756])).
% 0.73/0.92 tff(763,plain,
% 0.73/0.92 (c1_1(a9)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[762, 743])).
% 0.73/0.92 tff(764,plain,
% 0.73/0.92 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a9) | c2_1(a9) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a9)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a9) | c2_1(a9) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a9)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(765,plain,
% 0.73/0.92 ((hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a9) | c0_1(a9) | (~c1_1(a9))) <=> (hskp6 | c0_1(a9) | c2_1(a9) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a9)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(766,plain,
% 0.73/0.92 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a9) | c0_1(a9) | (~c1_1(a9)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a9) | c2_1(a9) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a9))))),
% 0.73/0.92 inference(monotonicity,[status(thm)],[765])).
% 0.73/0.92 tff(767,plain,
% 0.73/0.92 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a9) | c0_1(a9) | (~c1_1(a9)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a9) | c2_1(a9) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a9)))),
% 0.73/0.92 inference(transitivity,[status(thm)],[766, 764])).
% 0.73/0.92 tff(768,plain,
% 0.73/0.92 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a9) | c0_1(a9) | (~c1_1(a9)))),
% 0.73/0.92 inference(quant_inst,[status(thm)],[])).
% 0.73/0.92 tff(769,plain,
% 0.73/0.92 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a9) | c2_1(a9) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a9))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[768, 767])).
% 0.73/0.92 tff(770,plain,
% 0.73/0.92 (c2_1(a4)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[769, 72, 724, 763, 725, 755, 749, 205, 723])).
% 0.73/0.92 tff(771,plain,
% 0.73/0.92 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(772,plain,
% 0.73/0.92 ((hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c3_1(a4)) | (~c2_1(a4))) <=> (hskp5 | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(773,plain,
% 0.73/0.92 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c3_1(a4)) | (~c2_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4))))),
% 0.73/0.92 inference(monotonicity,[status(thm)],[772])).
% 0.73/0.92 tff(774,plain,
% 0.73/0.92 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c3_1(a4)) | (~c2_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)))),
% 0.73/0.92 inference(transitivity,[status(thm)],[773, 771])).
% 0.73/0.92 tff(775,plain,
% 0.73/0.92 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c3_1(a4)) | (~c2_1(a4)))),
% 0.73/0.92 inference(quant_inst,[status(thm)],[])).
% 0.73/0.92 tff(776,plain,
% 0.73/0.92 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp5 | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.73/0.92 tff(777,plain,
% 0.73/0.92 (hskp5 | (~c2_1(a4)) | (~c3_1(a4))),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[776, 72, 231, 230, 205, 229, 228])).
% 0.73/0.92 tff(778,plain,
% 0.73/0.92 (hskp5),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[777, 770, 725])).
% 0.73/0.92 tff(779,plain,
% 0.73/0.92 (c0_1(a6)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[247, 778])).
% 0.73/0.92 tff(780,plain,
% 0.73/0.92 (c2_1(a6)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[255, 778])).
% 0.73/0.92 tff(781,plain,
% 0.73/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a6) | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a6) | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(782,plain,
% 0.73/0.92 (((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4))) <=> (c3_1(a6) | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(783,plain,
% 0.73/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a6) | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6))))),
% 0.73/0.92 inference(monotonicity,[status(thm)],[782])).
% 0.73/0.92 tff(784,plain,
% 0.73/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a6) | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6)))),
% 0.73/0.92 inference(transitivity,[status(thm)],[783, 781])).
% 0.73/0.92 tff(785,plain,
% 0.73/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4)))),
% 0.73/0.92 inference(quant_inst,[status(thm)],[])).
% 0.73/0.92 tff(786,plain,
% 0.73/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a6) | c0_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[785, 784])).
% 0.73/0.92 tff(787,plain,
% 0.73/0.92 ((~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6))),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[786, 72, 231, 230, 206, 205, 229, 91])).
% 0.73/0.92 tff(788,plain,
% 0.73/0.92 ($false),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[787, 780, 779, 725, 770])).
% 0.73/0.92 tff(789,plain,((~c3_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | c3_1(a6) | c0_1(a4) | c1_1(a3) | hskp6 | c1_1(a4)), inference(lemma,lemma(discharge,[]))).
% 0.73/0.92 tff(790,plain,
% 0.73/0.92 (hskp6),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[789, 713, 165, 206, 205, 157, 173, 204])).
% 0.73/0.92 tff(791,plain,
% 0.73/0.92 (((~hskp6) | (~c2_1(a8))) <=> ((~hskp6) | (~c2_1(a8)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(792,plain,
% 0.73/0.92 (((~c2_1(a8)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a8)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(793,axiom,((~c2_1(a8)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.73/0.92 tff(794,plain,
% 0.73/0.92 ((~hskp6) | (~c2_1(a8))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[793, 792])).
% 0.73/0.92 tff(795,plain,
% 0.73/0.92 ((~hskp6) | (~c2_1(a8))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[794, 791])).
% 0.73/0.92 tff(796,plain,
% 0.73/0.92 (~c2_1(a8)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[795, 790])).
% 0.73/0.92 tff(797,plain,
% 0.73/0.92 (((~hskp6) | (~c3_1(a8))) <=> ((~hskp6) | (~c3_1(a8)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(798,plain,
% 0.73/0.92 (((~c3_1(a8)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a8)))),
% 0.73/0.92 inference(rewrite,[status(thm)],[])).
% 0.73/0.92 tff(799,axiom,((~c3_1(a8)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.73/0.92 tff(800,plain,
% 0.73/0.92 ((~hskp6) | (~c3_1(a8))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.73/0.92 tff(801,plain,
% 0.73/0.92 ((~hskp6) | (~c3_1(a8))),
% 0.73/0.92 inference(modus_ponens,[status(thm)],[800, 797])).
% 0.73/0.92 tff(802,plain,
% 0.73/0.92 (~c3_1(a8)),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[801, 790])).
% 0.73/0.92 tff(803,assumption,(~c3_1(a8)), introduced(assumption)).
% 0.73/0.92 tff(804,assumption,(~c2_1(a8)), introduced(assumption)).
% 0.73/0.92 tff(805,assumption,(~c3_1(a5)), introduced(assumption)).
% 0.73/0.92 tff(806,plain,
% 0.73/0.92 (~hskp4),
% 0.73/0.92 inference(unit_resolution,[status(thm)],[180, 805])).
% 0.73/0.93 tff(807,plain,
% 0.73/0.93 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c3_1(a5) | c1_1(a5) | (~ndr1_0) | c0_1(a5))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c3_1(a5) | c1_1(a5) | (~ndr1_0) | c0_1(a5))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(808,plain,
% 0.73/0.93 ((hskp4 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c0_1(a5)) <=> (hskp4 | c3_1(a5) | c1_1(a5) | (~ndr1_0) | c0_1(a5))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(809,plain,
% 0.73/0.93 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c3_1(a5) | c1_1(a5) | (~ndr1_0) | c0_1(a5)))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[808])).
% 0.73/0.93 tff(810,plain,
% 0.73/0.93 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c3_1(a5) | c1_1(a5) | (~ndr1_0) | c0_1(a5))),
% 0.73/0.93 inference(transitivity,[status(thm)],[809, 807])).
% 0.73/0.93 tff(811,plain,
% 0.73/0.93 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c0_1(a5))),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(812,plain,
% 0.73/0.93 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c3_1(a5) | c1_1(a5) | (~ndr1_0) | c0_1(a5)),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[811, 810])).
% 0.73/0.93 tff(813,plain,
% 0.73/0.93 (hskp4 | c3_1(a5) | c0_1(a5)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[812, 72, 190, 101])).
% 0.73/0.93 tff(814,plain,
% 0.73/0.93 (c0_1(a5)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[813, 805, 806])).
% 0.73/0.93 tff(815,plain,
% 0.73/0.93 (c3_1(a4)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[214, 806, 205])).
% 0.73/0.93 tff(816,plain,
% 0.73/0.93 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c2_1(a5) | c3_1(a5) | c1_1(a5) | (~ndr1_0))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c2_1(a5) | c3_1(a5) | c1_1(a5) | (~ndr1_0))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(817,plain,
% 0.73/0.93 ((hskp30 | hskp18 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c2_1(a5)) <=> (hskp30 | hskp18 | c2_1(a5) | c3_1(a5) | c1_1(a5) | (~ndr1_0))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(818,plain,
% 0.73/0.93 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c2_1(a5))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c2_1(a5) | c3_1(a5) | c1_1(a5) | (~ndr1_0)))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[817])).
% 0.73/0.93 tff(819,plain,
% 0.73/0.93 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c2_1(a5))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c2_1(a5) | c3_1(a5) | c1_1(a5) | (~ndr1_0))),
% 0.73/0.93 inference(transitivity,[status(thm)],[818, 816])).
% 0.73/0.93 tff(820,plain,
% 0.73/0.93 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | c2_1(a5))),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(821,plain,
% 0.73/0.93 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c2_1(a5) | c3_1(a5) | c1_1(a5) | (~ndr1_0)),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[820, 819])).
% 0.73/0.93 tff(822,plain,
% 0.73/0.93 (c2_1(a5) | c3_1(a5)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[821, 123, 72, 122, 190, 276])).
% 0.73/0.93 tff(823,plain,
% 0.73/0.93 (c2_1(a5)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[822, 805])).
% 0.73/0.93 tff(824,plain,
% 0.73/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(825,plain,
% 0.73/0.93 (((~ndr1_0) | c3_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4))) <=> (c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(826,plain,
% 0.73/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a5)) | (~c0_1(a5))))),
% 0.73/0.93 inference(monotonicity,[status(thm)],[825])).
% 0.73/0.93 tff(827,plain,
% 0.73/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.73/0.93 inference(transitivity,[status(thm)],[826, 824])).
% 0.73/0.93 tff(828,plain,
% 0.73/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a4) | (~c2_1(a4)) | (~c3_1(a4)))),
% 0.73/0.93 inference(quant_inst,[status(thm)],[])).
% 0.73/0.93 tff(829,plain,
% 0.73/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | (~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a5)) | (~c0_1(a5))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[828, 827])).
% 0.73/0.93 tff(830,plain,
% 0.73/0.93 (~c2_1(a4)),
% 0.73/0.93 inference(unit_resolution,[status(thm)],[829, 72, 823, 805, 815, 190, 205, 91, 814])).
% 0.73/0.93 tff(831,plain,
% 0.73/0.93 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.73/0.93 inference(bind,[status(th)],[])).
% 0.73/0.93 tff(832,plain,
% 0.73/0.93 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.73/0.93 inference(quant_intro,[status(thm)],[831])).
% 0.73/0.93 tff(833,plain,
% 0.73/0.93 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(834,plain,
% 0.73/0.93 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.73/0.93 inference(bind,[status(th)],[])).
% 0.73/0.93 tff(835,plain,
% 0.73/0.93 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.73/0.93 inference(quant_intro,[status(thm)],[834])).
% 0.73/0.93 tff(836,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.73/0.93 tff(837,plain,
% 0.73/0.93 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[836, 835])).
% 0.73/0.93 tff(838,plain,
% 0.73/0.93 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[837, 833])).
% 0.73/0.93 tff(839,plain,(
% 0.73/0.93 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.73/0.93 inference(skolemize,[status(sab)],[838])).
% 0.73/0.93 tff(840,plain,
% 0.73/0.93 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.73/0.93 inference(modus_ponens,[status(thm)],[839, 832])).
% 0.73/0.93 tff(841,plain,
% 0.73/0.93 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a5)))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(842,plain,
% 0.73/0.93 ((hskp9 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c0_1(a4) | (~c3_1(a4))) <=> (hskp9 | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a5)))),
% 0.73/0.93 inference(rewrite,[status(thm)],[])).
% 0.73/0.93 tff(843,plain,
% 0.73/0.93 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c0_1(a4) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a5))))),
% 0.76/0.93 inference(monotonicity,[status(thm)],[842])).
% 0.76/0.93 tff(844,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c0_1(a4) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a5)))),
% 0.76/0.93 inference(transitivity,[status(thm)],[843, 841])).
% 0.76/0.93 tff(845,plain,
% 0.76/0.93 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c0_1(a4) | (~c3_1(a4)))),
% 0.76/0.93 inference(quant_inst,[status(thm)],[])).
% 0.76/0.93 tff(846,plain,
% 0.76/0.93 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp9 | c3_1(a5) | c1_1(a5) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a5))),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[845, 844])).
% 0.76/0.93 tff(847,plain,
% 0.76/0.93 ($false),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[846, 72, 494, 805, 815, 190, 205, 840, 830, 814])).
% 0.76/0.93 tff(848,plain,(c3_1(a5) | hskp9 | c1_1(a5) | c0_1(a4) | c1_1(a4) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/0.93 tff(849,plain,
% 0.76/0.93 (c3_1(a5)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[848, 494, 190, 205, 204, 123, 122])).
% 0.76/0.93 tff(850,plain,
% 0.76/0.93 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | c1_1(a8))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | c1_1(a8))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(851,plain,
% 0.76/0.93 ((hskp30 | hskp18 | (~ndr1_0) | c3_1(a8) | c1_1(a8) | c2_1(a8)) <=> (hskp30 | hskp18 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | c1_1(a8))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(852,plain,
% 0.76/0.93 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a8) | c1_1(a8) | c2_1(a8))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | c1_1(a8)))),
% 0.76/0.93 inference(monotonicity,[status(thm)],[851])).
% 0.76/0.93 tff(853,plain,
% 0.76/0.93 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a8) | c1_1(a8) | c2_1(a8))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | c1_1(a8))),
% 0.76/0.93 inference(transitivity,[status(thm)],[852, 850])).
% 0.76/0.93 tff(854,plain,
% 0.76/0.93 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a8) | c1_1(a8) | c2_1(a8))),
% 0.76/0.93 inference(quant_inst,[status(thm)],[])).
% 0.76/0.93 tff(855,plain,
% 0.76/0.93 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | c1_1(a8)),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.76/0.93 tff(856,plain,
% 0.76/0.93 (c2_1(a8) | c1_1(a8)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[855, 123, 72, 122, 803, 276])).
% 0.76/0.93 tff(857,plain,
% 0.76/0.93 (c1_1(a8)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[856, 804])).
% 0.76/0.93 tff(858,assumption,(c1_1(a8)), introduced(assumption)).
% 0.76/0.93 tff(859,assumption,(~c2_1(a5)), introduced(assumption)).
% 0.76/0.93 tff(860,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c2_1(a5) | c1_1(a5) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a5) | c1_1(a5) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(861,plain,
% 0.76/0.93 ((hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a5) | c1_1(a5) | c0_1(a5)) <=> (hskp1 | c2_1(a5) | c1_1(a5) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(862,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c2_1(a5) | c1_1(a5) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5)))),
% 0.76/0.93 inference(monotonicity,[status(thm)],[861])).
% 0.76/0.93 tff(863,plain,
% 0.76/0.93 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a5) | c1_1(a5) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5))),
% 0.76/0.93 inference(transitivity,[status(thm)],[862, 860])).
% 0.76/0.93 tff(864,plain,
% 0.76/0.93 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a5) | c1_1(a5) | c0_1(a5))),
% 0.76/0.93 inference(quant_inst,[status(thm)],[])).
% 0.76/0.93 tff(865,plain,
% 0.76/0.93 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c2_1(a5) | c1_1(a5) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a5)),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[864, 863])).
% 0.76/0.93 tff(866,plain,
% 0.76/0.93 (hskp1 | c0_1(a5)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[865, 72, 859, 231, 230, 190, 229, 674])).
% 0.76/0.93 tff(867,plain,
% 0.76/0.93 (hskp1),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[866, 218])).
% 0.76/0.93 tff(868,plain,
% 0.76/0.93 (~c2_1(a2)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[551, 867])).
% 0.76/0.93 tff(869,plain,
% 0.76/0.93 (c3_1(a2)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[559, 867])).
% 0.76/0.93 tff(870,plain,
% 0.76/0.93 (c0_1(a2)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[567, 867])).
% 0.76/0.93 tff(871,plain,
% 0.76/0.93 (~c1_1(a2)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[574, 72, 231, 230, 870, 869, 229, 868, 527])).
% 0.76/0.93 tff(872,plain,
% 0.76/0.93 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.76/0.93 inference(bind,[status(th)],[])).
% 0.76/0.93 tff(873,plain,
% 0.76/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_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) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/0.93 inference(quant_intro,[status(thm)],[872])).
% 0.76/0.93 tff(874,plain,
% 0.76/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_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) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(875,plain,
% 0.76/0.93 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.76/0.93 inference(bind,[status(th)],[])).
% 0.76/0.93 tff(876,plain,
% 0.76/0.93 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_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) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/0.93 inference(quant_intro,[status(thm)],[875])).
% 0.76/0.93 tff(877,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.76/0.93 tff(878,plain,
% 0.76/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[877, 876])).
% 0.76/0.93 tff(879,plain,
% 0.76/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[878, 874])).
% 0.76/0.93 tff(880,plain,(
% 0.76/0.93 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/0.93 inference(skolemize,[status(sab)],[879])).
% 0.76/0.93 tff(881,plain,
% 0.76/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[880, 873])).
% 0.76/0.93 tff(882,plain,
% 0.76/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c0_1(a5) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c0_1(a5) | (~c0_1(a8)))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(883,plain,
% 0.76/0.93 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a5) | c1_1(a5) | c0_1(a5)) <=> (c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c0_1(a5) | (~c0_1(a8)))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(884,plain,
% 0.76/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c0_1(a5) | (~c0_1(a8))))),
% 0.76/0.93 inference(monotonicity,[status(thm)],[883])).
% 0.76/0.93 tff(885,plain,
% 0.76/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a5) | c1_1(a5) | c0_1(a5))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c0_1(a5) | (~c0_1(a8)))),
% 0.76/0.93 inference(transitivity,[status(thm)],[884, 882])).
% 0.76/0.93 tff(886,plain,
% 0.76/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a5) | c1_1(a5) | c0_1(a5))),
% 0.76/0.93 inference(quant_inst,[status(thm)],[])).
% 0.76/0.93 tff(887,plain,
% 0.76/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c0_1(a5) | (~c0_1(a8))),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[886, 885])).
% 0.76/0.93 tff(888,plain,
% 0.76/0.93 (~c0_1(a8)),
% 0.76/0.93 inference(unit_resolution,[status(thm)],[887, 72, 859, 870, 804, 803, 190, 868, 881, 218, 871])).
% 0.76/0.93 tff(889,plain,
% 0.76/0.93 (((~hskp6) | c0_1(a8)) <=> ((~hskp6) | c0_1(a8))),
% 0.76/0.93 inference(rewrite,[status(thm)],[])).
% 0.76/0.93 tff(890,axiom,((~hskp6) | c0_1(a8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.76/0.93 tff(891,plain,
% 0.76/0.93 ((~hskp6) | c0_1(a8)),
% 0.76/0.93 inference(modus_ponens,[status(thm)],[890, 889])).
% 0.76/0.93 tff(892,plain,
% 0.76/0.94 ((~hskp6) | c0_1(a8)),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[891, 889])).
% 0.76/0.94 tff(893,plain,
% 0.76/0.94 ((~hskp6) | c0_1(a8)),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[892, 889])).
% 0.76/0.94 tff(894,plain,
% 0.76/0.94 ((~hskp6) | c0_1(a8)),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[893, 889])).
% 0.76/0.94 tff(895,plain,
% 0.76/0.94 ((~hskp6) | c0_1(a8)),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[894, 889])).
% 0.76/0.94 tff(896,plain,
% 0.76/0.94 (~hskp6),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[895, 888])).
% 0.76/0.94 tff(897,plain,
% 0.76/0.94 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a8) | c2_1(a5) | c2_1(a8) | (~ndr1_0) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a8) | c2_1(a5) | c2_1(a8) | (~ndr1_0) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a8)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(898,plain,
% 0.76/0.94 ((hskp6 | (~ndr1_0) | c0_1(a5) | c2_1(a5) | (~c3_1(a5)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8))) <=> (hskp6 | c0_1(a8) | c2_1(a5) | c2_1(a8) | (~ndr1_0) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a8)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(899,plain,
% 0.76/0.94 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a5) | c2_1(a5) | (~c3_1(a5)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a8) | c2_1(a5) | c2_1(a8) | (~ndr1_0) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a8))))),
% 0.76/0.94 inference(monotonicity,[status(thm)],[898])).
% 0.76/0.94 tff(900,plain,
% 0.76/0.94 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a5) | c2_1(a5) | (~c3_1(a5)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a8) | c2_1(a5) | c2_1(a8) | (~ndr1_0) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a8)))),
% 0.76/0.94 inference(transitivity,[status(thm)],[899, 897])).
% 0.76/0.94 tff(901,plain,
% 0.76/0.94 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a5) | c2_1(a5) | (~c3_1(a5)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))),
% 0.76/0.94 inference(quant_inst,[status(thm)],[])).
% 0.76/0.94 tff(902,plain,
% 0.76/0.94 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a8) | c2_1(a5) | c2_1(a8) | (~ndr1_0) | c0_1(a5) | (~c3_1(a5)) | (~c1_1(a8))),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[901, 900])).
% 0.76/0.94 tff(903,plain,
% 0.76/0.94 (hskp6 | c0_1(a8)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[902, 72, 859, 232, 804, 723, 218, 858])).
% 0.76/0.94 tff(904,plain,
% 0.76/0.94 ($false),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[903, 896, 888])).
% 0.76/0.94 tff(905,plain,(c0_1(a5) | c2_1(a5) | (~c3_1(a5)) | c2_1(a8) | (~c1_1(a8)) | c3_1(a8) | c1_1(a5) | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.94 tff(906,plain,
% 0.76/0.94 (c0_1(a5)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[905, 859, 232, 804, 858, 803, 190, 231, 230, 229])).
% 0.76/0.94 tff(907,assumption,(~c2_1(a4)), introduced(assumption)).
% 0.76/0.94 tff(908,plain,
% 0.76/0.94 (~hskp4),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[188, 859])).
% 0.76/0.94 tff(909,plain,
% 0.76/0.94 (c3_1(a4)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[214, 908, 205])).
% 0.76/0.94 tff(910,plain,
% 0.76/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a5)) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a5)) | (~c0_1(a8)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(911,plain,
% 0.76/0.94 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4)) <=> (c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a5)) | (~c0_1(a8)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(912,plain,
% 0.76/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a5)) | (~c0_1(a8))))),
% 0.76/0.94 inference(monotonicity,[status(thm)],[911])).
% 0.76/0.94 tff(913,plain,
% 0.76/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a5)) | (~c0_1(a8)))),
% 0.76/0.94 inference(transitivity,[status(thm)],[912, 910])).
% 0.76/0.94 tff(914,plain,
% 0.76/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a5) | c1_1(a5) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4))),
% 0.76/0.94 inference(quant_inst,[status(thm)],[])).
% 0.76/0.94 tff(915,plain,
% 0.76/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a5) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a5)) | (~c0_1(a8))),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[914, 913])).
% 0.76/0.94 tff(916,plain,
% 0.76/0.94 (~c0_1(a8)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[915, 72, 859, 804, 803, 190, 205, 204, 881, 907, 664])).
% 0.76/0.94 tff(917,plain,
% 0.76/0.94 (~hskp6),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[895, 916])).
% 0.76/0.94 tff(918,plain,
% 0.76/0.94 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a8) | c2_1(a8) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a8) | c2_1(a8) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a8)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(919,plain,
% 0.76/0.94 ((hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8))) <=> (hskp6 | c0_1(a8) | c2_1(a8) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a8)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(920,plain,
% 0.76/0.94 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a8) | c2_1(a8) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a8))))),
% 0.76/0.94 inference(monotonicity,[status(thm)],[919])).
% 0.76/0.94 tff(921,plain,
% 0.76/0.94 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a8) | c2_1(a8) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a8)))),
% 0.76/0.94 inference(transitivity,[status(thm)],[920, 918])).
% 0.76/0.94 tff(922,plain,
% 0.76/0.94 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a8) | c0_1(a8) | (~c1_1(a8)))),
% 0.76/0.94 inference(quant_inst,[status(thm)],[])).
% 0.76/0.94 tff(923,plain,
% 0.76/0.94 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a8) | c2_1(a8) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c1_1(a8))),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[922, 921])).
% 0.76/0.94 tff(924,plain,
% 0.76/0.94 (hskp6 | c0_1(a8) | c2_1(a4) | (~c3_1(a4))),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[923, 72, 804, 205, 723, 858])).
% 0.76/0.94 tff(925,plain,
% 0.76/0.94 ($false),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[924, 917, 916, 909, 907])).
% 0.76/0.94 tff(926,plain,(c2_1(a4) | c2_1(a8) | c0_1(a4) | (~c1_1(a8)) | c2_1(a5) | c3_1(a8) | c1_1(a5) | c1_1(a4) | (~c0_1(a5))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.94 tff(927,plain,
% 0.76/0.94 (c2_1(a4)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[926, 859, 205, 858, 804, 803, 190, 204, 906])).
% 0.76/0.94 tff(928,plain,
% 0.76/0.94 (hskp5),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[777, 927, 909])).
% 0.76/0.94 tff(929,plain,
% 0.76/0.94 (c0_1(a6)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[247, 928])).
% 0.76/0.94 tff(930,plain,
% 0.76/0.94 (c2_1(a6)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[255, 928])).
% 0.76/0.94 tff(931,plain,
% 0.76/0.94 ($false),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[787, 930, 929, 909, 927])).
% 0.76/0.94 tff(932,plain,(c2_1(a5) | (~c0_1(a3)) | (~c2_1(a3)) | c3_1(a6) | c0_1(a4) | c1_1(a3) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | c1_1(a5) | c1_1(a4) | (~c3_1(a5))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.94 tff(933,plain,
% 0.76/0.94 (c2_1(a5)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[932, 849, 165, 206, 205, 157, 857, 804, 803, 190, 204, 173])).
% 0.76/0.94 tff(934,plain,
% 0.76/0.94 (c0_1(a5)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[265, 933, 849, 173, 165, 206, 157])).
% 0.76/0.94 tff(935,plain,
% 0.76/0.94 (c3_1(a4)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[502, 494, 123, 122, 205, 204])).
% 0.76/0.94 tff(936,plain,
% 0.76/0.94 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(937,plain,
% 0.76/0.94 ((hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4)) <=> (hskp1 | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(938,plain,
% 0.76/0.94 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c2_1(a5)) | (~c0_1(a5))))),
% 0.76/0.94 inference(monotonicity,[status(thm)],[937])).
% 0.76/0.94 tff(939,plain,
% 0.76/0.94 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.76/0.94 inference(transitivity,[status(thm)],[938, 936])).
% 0.76/0.94 tff(940,plain,
% 0.76/0.94 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a4) | c1_1(a4) | c0_1(a4))),
% 0.76/0.94 inference(quant_inst,[status(thm)],[])).
% 0.76/0.94 tff(941,plain,
% 0.76/0.94 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a5) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c2_1(a5)) | (~c0_1(a5))),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.76/0.94 tff(942,plain,
% 0.76/0.94 (hskp1),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[941, 72, 233, 190, 205, 204, 674, 907, 664])).
% 0.76/0.94 tff(943,plain,
% 0.76/0.94 (~c2_1(a2)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[551, 942])).
% 0.76/0.94 tff(944,plain,
% 0.76/0.94 (c3_1(a2)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[559, 942])).
% 0.76/0.94 tff(945,plain,
% 0.76/0.94 (c0_1(a2)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[567, 942])).
% 0.76/0.94 tff(946,plain,
% 0.76/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(947,plain,
% 0.76/0.94 (((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5))) <=> (c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(948,plain,
% 0.76/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a5)) | (~c0_1(a5))))),
% 0.76/0.94 inference(monotonicity,[status(thm)],[947])).
% 0.76/0.94 tff(949,plain,
% 0.76/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.76/0.94 inference(transitivity,[status(thm)],[948, 946])).
% 0.76/0.94 tff(950,plain,
% 0.76/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.76/0.94 inference(quant_inst,[status(thm)],[])).
% 0.76/0.94 tff(951,plain,
% 0.76/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a5) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a5)) | (~c0_1(a5))),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[950, 949])).
% 0.76/0.94 tff(952,plain,
% 0.76/0.94 (~c1_1(a2)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[951, 72, 233, 945, 944, 190, 943, 527, 664])).
% 0.76/0.94 tff(953,plain,
% 0.76/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a8)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a8)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(954,plain,
% 0.76/0.94 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4)) <=> (c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a8)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(955,plain,
% 0.76/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a8))))),
% 0.76/0.94 inference(monotonicity,[status(thm)],[954])).
% 0.76/0.94 tff(956,plain,
% 0.76/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a8)))),
% 0.76/0.94 inference(transitivity,[status(thm)],[955, 953])).
% 0.76/0.94 tff(957,plain,
% 0.76/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4))),
% 0.76/0.94 inference(quant_inst,[status(thm)],[])).
% 0.76/0.94 tff(958,plain,
% 0.76/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a8))),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[957, 956])).
% 0.76/0.94 tff(959,plain,
% 0.76/0.94 (~c0_1(a8)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[958, 72, 945, 804, 803, 205, 204, 943, 881, 907, 952])).
% 0.76/0.94 tff(960,plain,
% 0.76/0.94 (~hskp6),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[895, 959])).
% 0.76/0.94 tff(961,plain,
% 0.76/0.94 ($false),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[924, 960, 959, 725, 907])).
% 0.76/0.94 tff(962,plain,(c2_1(a4) | (~c3_1(a4)) | c2_1(a8) | c0_1(a4) | (~c1_1(a8)) | c3_1(a8) | c1_1(a4) | (~c2_1(a5)) | c1_1(a5) | (~c0_1(a5))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.94 tff(963,plain,
% 0.76/0.94 (c2_1(a4)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[962, 935, 804, 205, 857, 803, 204, 933, 190, 934])).
% 0.76/0.94 tff(964,plain,
% 0.76/0.94 (hskp5 | (~c2_1(a4)) | (~c3_1(a4))),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[776, 72, 173, 165, 205, 157, 228])).
% 0.76/0.94 tff(965,plain,
% 0.76/0.94 (hskp5),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[964, 963, 935])).
% 0.76/0.94 tff(966,plain,
% 0.76/0.94 (c0_1(a6)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[247, 965])).
% 0.76/0.94 tff(967,plain,
% 0.76/0.94 (c2_1(a6)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[255, 965])).
% 0.76/0.94 tff(968,plain,
% 0.76/0.94 ((~c2_1(a4)) | (~c3_1(a4)) | (~c2_1(a6)) | (~c0_1(a6))),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[786, 72, 173, 165, 206, 205, 157, 91])).
% 0.76/0.94 tff(969,plain,
% 0.76/0.94 ($false),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[968, 967, 966, 935, 963])).
% 0.76/0.94 tff(970,plain,(hskp9 | c3_1(a6) | c0_1(a4) | c2_1(a8) | c3_1(a8) | c1_1(a4) | c1_1(a5) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/0.94 tff(971,plain,
% 0.76/0.94 (hskp9),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[970, 804, 205, 206, 803, 204, 190, 123, 122])).
% 0.76/0.94 tff(972,plain,
% 0.76/0.94 (~c3_1(a12)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[516, 971])).
% 0.76/0.94 tff(973,plain,
% 0.76/0.94 (((~hskp9) | (~c2_1(a12))) <=> ((~hskp9) | (~c2_1(a12)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(974,plain,
% 0.76/0.94 (((~c2_1(a12)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a12)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(975,axiom,((~c2_1(a12)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.76/0.94 tff(976,plain,
% 0.76/0.94 ((~hskp9) | (~c2_1(a12))),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[975, 974])).
% 0.76/0.94 tff(977,plain,
% 0.76/0.94 ((~hskp9) | (~c2_1(a12))),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[976, 973])).
% 0.76/0.94 tff(978,plain,
% 0.76/0.94 (~c2_1(a12)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[977, 971])).
% 0.76/0.94 tff(979,plain,
% 0.76/0.94 (hskp1),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[941, 72, 823, 190, 205, 204, 674, 830, 814])).
% 0.76/0.94 tff(980,plain,
% 0.76/0.94 (~c2_1(a2)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[551, 979])).
% 0.76/0.94 tff(981,plain,
% 0.76/0.94 (c3_1(a2)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[559, 979])).
% 0.76/0.94 tff(982,plain,
% 0.76/0.94 (c0_1(a2)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[567, 979])).
% 0.76/0.94 tff(983,plain,
% 0.76/0.94 (~c1_1(a2)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[951, 72, 823, 982, 981, 190, 980, 527, 814])).
% 0.76/0.94 tff(984,plain,
% 0.76/0.94 (~c0_1(a8)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[958, 72, 982, 804, 803, 205, 204, 980, 881, 830, 983])).
% 0.76/0.94 tff(985,assumption,(~c2_1(a12)), introduced(assumption)).
% 0.76/0.94 tff(986,plain,
% 0.76/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a12) | c3_1(a12) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a12)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a12) | c3_1(a12) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a12)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(987,plain,
% 0.76/0.94 (((~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4)) <=> (c2_1(a12) | c3_1(a12) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a12)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(988,plain,
% 0.76/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a12) | c3_1(a12) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a12))))),
% 0.76/0.94 inference(monotonicity,[status(thm)],[987])).
% 0.76/0.94 tff(989,plain,
% 0.76/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a12) | c3_1(a12) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a12)))),
% 0.76/0.94 inference(transitivity,[status(thm)],[988, 986])).
% 0.76/0.94 tff(990,plain,
% 0.76/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c0_1(a12)) | c2_1(a2) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | c1_1(a4) | c0_1(a4))),
% 0.76/0.94 inference(quant_inst,[status(thm)],[])).
% 0.76/0.94 tff(991,plain,
% 0.76/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a12) | c3_1(a12) | c0_1(a4) | c1_1(a4) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)) | c2_1(a4) | (~c0_1(a12))),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[990, 989])).
% 0.76/0.94 tff(992,plain,
% 0.76/0.94 (~c0_1(a12)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[991, 72, 982, 985, 586, 205, 204, 980, 881, 830, 983])).
% 0.76/0.94 tff(993,plain,
% 0.76/0.94 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(994,plain,
% 0.76/0.94 ((hskp30 | hskp18 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12)) <=> (hskp30 | hskp18 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(995,plain,
% 0.76/0.94 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0)))),
% 0.76/0.94 inference(monotonicity,[status(thm)],[994])).
% 0.76/0.94 tff(996,plain,
% 0.76/0.94 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))),
% 0.76/0.94 inference(transitivity,[status(thm)],[995, 993])).
% 0.76/0.94 tff(997,plain,
% 0.76/0.94 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12))),
% 0.76/0.94 inference(quant_inst,[status(thm)],[])).
% 0.76/0.94 tff(998,plain,
% 0.76/0.94 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0)),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[997, 996])).
% 0.76/0.94 tff(999,plain,
% 0.76/0.94 (c1_1(a12) | c2_1(a12)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[998, 123, 72, 122, 586, 276])).
% 0.76/0.94 tff(1000,plain,
% 0.76/0.94 (c1_1(a12)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[999, 985])).
% 0.76/0.94 tff(1001,plain,
% 0.76/0.94 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a12) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | c0_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a12) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | c0_1(a12) | (~c1_1(a12)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(1002,plain,
% 0.76/0.94 ((hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12))) <=> (hskp6 | c2_1(a12) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | c0_1(a12) | (~c1_1(a12)))),
% 0.76/0.94 inference(rewrite,[status(thm)],[])).
% 0.76/0.94 tff(1003,plain,
% 0.76/0.94 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a12) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | c0_1(a12) | (~c1_1(a12))))),
% 0.76/0.94 inference(monotonicity,[status(thm)],[1002])).
% 0.76/0.94 tff(1004,plain,
% 0.76/0.94 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a12) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | c0_1(a12) | (~c1_1(a12)))),
% 0.76/0.94 inference(transitivity,[status(thm)],[1003, 1001])).
% 0.76/0.94 tff(1005,plain,
% 0.76/0.94 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a4) | c2_1(a4) | (~c3_1(a4)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12)))),
% 0.76/0.94 inference(quant_inst,[status(thm)],[])).
% 0.76/0.94 tff(1006,plain,
% 0.76/0.94 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a12) | c0_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | c0_1(a12) | (~c1_1(a12))),
% 0.76/0.94 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 0.76/0.94 tff(1007,plain,
% 0.76/0.94 (hskp6 | c2_1(a4) | (~c3_1(a4)) | c0_1(a12)),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[1006, 72, 1000, 985, 205, 723])).
% 0.76/0.94 tff(1008,plain,
% 0.76/0.94 (hskp6),
% 0.76/0.94 inference(unit_resolution,[status(thm)],[1007, 992, 815, 830])).
% 0.76/0.95 tff(1009,plain,
% 0.76/0.95 ($false),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[895, 1008, 984])).
% 0.76/0.95 tff(1010,plain,(c3_1(a5) | c2_1(a12) | c0_1(a4) | c2_1(a8) | c3_1(a8) | c1_1(a4) | c3_1(a12) | c1_1(a5) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/0.95 tff(1011,plain,
% 0.76/0.95 (c3_1(a5)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1010, 978, 205, 804, 803, 204, 972, 190, 123, 122])).
% 0.76/0.95 tff(1012,plain,
% 0.76/0.95 (c2_1(a5)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[932, 1011, 165, 206, 205, 157, 857, 804, 803, 190, 204, 173])).
% 0.76/0.95 tff(1013,plain,
% 0.76/0.95 (c0_1(a5)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[265, 1012, 1011, 173, 165, 206, 157])).
% 0.76/0.95 tff(1014,plain,
% 0.76/0.95 (c1_1(a12)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[510, 971])).
% 0.76/0.95 tff(1015,plain,
% 0.76/0.95 (hskp0),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[639, 1012, 972, 1014, 1011, 190, 173, 165, 157])).
% 0.76/0.95 tff(1016,plain,
% 0.76/0.95 (~c0_1(a1)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[645, 1015])).
% 0.76/0.95 tff(1017,plain,
% 0.76/0.95 (c2_1(a1)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[661, 1015])).
% 0.76/0.95 tff(1018,plain,
% 0.76/0.95 (c1_1(a1)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[653, 1015])).
% 0.76/0.95 tff(1019,plain,
% 0.76/0.95 (~hskp14),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[710, 1018, 1017, 1016, 1012, 1011, 190, 123, 122, 1013])).
% 0.76/0.95 tff(1020,plain,
% 0.76/0.95 (c3_1(a4)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[449, 1019, 122, 205, 123, 204])).
% 0.76/0.95 tff(1021,plain,
% 0.76/0.95 (c2_1(a4)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[962, 1020, 804, 205, 857, 803, 204, 1012, 190, 1013])).
% 0.76/0.95 tff(1022,plain,
% 0.76/0.95 (hskp5),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[964, 1020, 1021])).
% 0.76/0.95 tff(1023,plain,
% 0.76/0.95 (c0_1(a6)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[247, 1022])).
% 0.76/0.95 tff(1024,plain,
% 0.76/0.95 (c2_1(a6)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[255, 1022])).
% 0.76/0.95 tff(1025,plain,
% 0.76/0.95 ($false),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[968, 1024, 1023, 1020, 1021])).
% 0.76/0.95 tff(1026,plain,(c2_1(a8) | c3_1(a6) | c0_1(a4) | c3_1(a8) | c1_1(a4) | c1_1(a5) | hskp18 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.76/0.95 tff(1027,plain,
% 0.76/0.95 ($false),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1026, 802, 796, 205, 206, 204, 190, 122, 123])).
% 0.76/0.95 tff(1028,plain,(c3_1(a6) | c0_1(a4) | c1_1(a4) | c1_1(a5) | hskp18 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.76/0.95 tff(1029,plain,
% 0.76/0.95 (c3_1(a6)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1028, 190, 204, 205, 122, 123])).
% 0.76/0.95 tff(1030,plain,
% 0.76/0.95 (((~hskp5) | (~c3_1(a6))) <=> ((~hskp5) | (~c3_1(a6)))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1031,plain,
% 0.76/0.95 (((~c3_1(a6)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a6)))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1032,axiom,((~c3_1(a6)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.76/0.95 tff(1033,plain,
% 0.76/0.95 ((~hskp5) | (~c3_1(a6))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1032, 1031])).
% 0.76/0.95 tff(1034,plain,
% 0.76/0.95 ((~hskp5) | (~c3_1(a6))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1033, 1030])).
% 0.76/0.95 tff(1035,plain,
% 0.76/0.95 (~hskp5),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1034, 1029])).
% 0.76/0.95 tff(1036,plain,
% 0.76/0.95 (~c2_1(a4)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[964, 909, 1035])).
% 0.76/0.95 tff(1037,plain,
% 0.76/0.95 (hskp7),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[742, 724, 725, 205])).
% 0.76/0.95 tff(1038,plain,
% 0.76/0.95 (~c2_1(a9)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[748, 1037])).
% 0.76/0.95 tff(1039,plain,
% 0.76/0.95 (~c0_1(a9)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[754, 1037])).
% 0.76/0.95 tff(1040,plain,
% 0.76/0.95 (c1_1(a9)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[762, 1037])).
% 0.76/0.95 tff(1041,plain,
% 0.76/0.95 ($false),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[769, 72, 724, 1040, 725, 1039, 1038, 205, 723, 907])).
% 0.76/0.95 tff(1042,plain,(hskp6 | (~c3_1(a4)) | c0_1(a4) | c2_1(a4) | c1_1(a4)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.95 tff(1043,plain,
% 0.76/0.95 (hskp6),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1042, 909, 205, 1036, 204])).
% 0.76/0.95 tff(1044,plain,
% 0.76/0.95 (~c2_1(a8)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[795, 1043])).
% 0.76/0.95 tff(1045,plain,
% 0.76/0.95 (~c3_1(a8)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[801, 1043])).
% 0.76/0.95 tff(1046,plain,
% 0.76/0.95 (c3_1(a5)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[822, 859])).
% 0.76/0.95 tff(1047,plain,
% 0.76/0.95 (~c1_1(a8)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[905, 804, 1046, 218, 803, 859, 190, 173, 165, 157])).
% 0.76/0.95 tff(1048,plain,
% 0.76/0.95 ($false),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[856, 1047, 804])).
% 0.76/0.95 tff(1049,plain,(c2_1(a8) | hskp30 | hskp18 | c3_1(a8) | c0_1(a5) | c2_1(a5) | c1_1(a5)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.95 tff(1050,plain,
% 0.76/0.95 (c0_1(a5)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1049, 1045, 122, 123, 1044, 859, 190])).
% 0.76/0.95 tff(1051,plain,
% 0.76/0.95 (~c1_1(a8)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[926, 1050, 205, 1036, 859, 1045, 190, 204, 1044])).
% 0.76/0.95 tff(1052,plain,
% 0.76/0.95 (c0_1(a8)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[895, 1043])).
% 0.76/0.95 tff(1053,plain,
% 0.76/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a8)) | c1_1(a8))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a8)) | c1_1(a8))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1054,plain,
% 0.76/0.95 (((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a8) | c1_1(a8) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | c0_1(a4)) <=> (c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a8)) | c1_1(a8))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1055,plain,
% 0.76/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a8) | c1_1(a8) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a8)) | c1_1(a8)))),
% 0.76/0.95 inference(monotonicity,[status(thm)],[1054])).
% 0.76/0.95 tff(1056,plain,
% 0.76/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a8) | c1_1(a8) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a8)) | c1_1(a8))),
% 0.76/0.95 inference(transitivity,[status(thm)],[1055, 1053])).
% 0.76/0.95 tff(1057,plain,
% 0.76/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c0_1(a8)) | c2_1(a8) | c1_1(a8) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | c0_1(a4))),
% 0.76/0.95 inference(quant_inst,[status(thm)],[])).
% 0.76/0.95 tff(1058,plain,
% 0.76/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a8) | c3_1(a8) | c0_1(a4) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c0_1(a8)) | c1_1(a8)),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 0.76/0.95 tff(1059,plain,
% 0.76/0.95 ($false),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1058, 72, 1052, 1044, 1045, 205, 204, 881, 1036, 1051])).
% 0.76/0.95 tff(1060,plain,(c2_1(a5) | c0_1(a4) | c1_1(a4) | c1_1(a5) | hskp18 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.76/0.95 tff(1061,plain,
% 0.76/0.95 (c2_1(a5)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1060, 190, 204, 205, 122, 123])).
% 0.76/0.95 tff(1062,assumption,(~hskp5), introduced(assumption)).
% 0.76/0.95 tff(1063,plain,
% 0.76/0.95 (~c3_1(a5)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[239, 72, 1062, 233, 231, 230, 229, 228, 218])).
% 0.76/0.95 tff(1064,plain,
% 0.76/0.95 (~hskp4),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[180, 1063])).
% 0.76/0.95 tff(1065,plain,
% 0.76/0.95 ($false),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[813, 1064, 1063, 218])).
% 0.76/0.95 tff(1066,plain,(c0_1(a5) | c1_1(a5) | hskp5 | (~c2_1(a5)) | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.95 tff(1067,plain,
% 0.76/0.95 (c0_1(a5)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1066, 190, 1035, 1061, 173, 165, 157])).
% 0.76/0.95 tff(1068,plain,
% 0.76/0.95 (^[U: $i] : refl((hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.76/0.95 inference(bind,[status(th)],[])).
% 0.76/0.95 tff(1069,plain,
% 0.76/0.95 (![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.95 inference(quant_intro,[status(thm)],[1068])).
% 0.76/0.95 tff(1070,plain,
% 0.76/0.95 (![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1071,plain,
% 0.76/0.95 (^[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)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp0) <=> ((hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp0))), rewrite(((hskp5 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp0) <=> (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp0) <=> (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.76/0.95 inference(bind,[status(th)],[])).
% 0.76/0.95 tff(1072,plain,
% 0.76/0.95 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp0) <=> ![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.95 inference(quant_intro,[status(thm)],[1071])).
% 0.76/0.95 tff(1073,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp5) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.76/0.95 tff(1074,plain,
% 0.76/0.95 (![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1073, 1072])).
% 0.76/0.95 tff(1075,plain,
% 0.76/0.95 (![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1074, 1070])).
% 0.76/0.95 tff(1076,plain,(
% 0.76/0.95 ![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.95 inference(skolemize,[status(sab)],[1075])).
% 0.76/0.95 tff(1077,plain,
% 0.76/0.95 (![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1076, 1069])).
% 0.76/0.95 tff(1078,plain,
% 0.76/0.95 (((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c2_1(a4)))) <=> ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp0 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c2_1(a4)))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1079,plain,
% 0.76/0.95 ((hskp5 | hskp0 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c2_1(a4))) <=> (hskp5 | hskp0 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c2_1(a4)))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1080,plain,
% 0.76/0.95 (((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c2_1(a4)))) <=> ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c2_1(a4))))),
% 0.76/0.95 inference(monotonicity,[status(thm)],[1079])).
% 0.76/0.95 tff(1081,plain,
% 0.76/0.95 (((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c2_1(a4)))) <=> ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp0 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c2_1(a4)))),
% 0.76/0.95 inference(transitivity,[status(thm)],[1080, 1078])).
% 0.76/0.95 tff(1082,plain,
% 0.76/0.95 ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | (~ndr1_0) | c1_1(a4) | c0_1(a4) | (~c2_1(a4)))),
% 0.76/0.95 inference(quant_inst,[status(thm)],[])).
% 0.76/0.95 tff(1083,plain,
% 0.76/0.95 ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp0 | c0_1(a4) | c1_1(a4) | (~ndr1_0) | (~c2_1(a4))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 0.76/0.95 tff(1084,plain,
% 0.76/0.95 (hskp5 | hskp0 | c0_1(a4) | (~c2_1(a4))),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1083, 72, 204, 1077])).
% 0.76/0.95 tff(1085,plain,
% 0.76/0.95 (hskp0),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1084, 285, 205, 1035])).
% 0.76/0.95 tff(1086,plain,
% 0.76/0.95 (c2_1(a1)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[661, 1085])).
% 0.76/0.95 tff(1087,plain,
% 0.76/0.95 (hskp9),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[848, 805, 190, 205, 204, 123, 122])).
% 0.76/0.95 tff(1088,plain,
% 0.76/0.95 (~c3_1(a12)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[516, 1087])).
% 0.76/0.95 tff(1089,plain,
% 0.76/0.95 (~c2_1(a12)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[977, 1087])).
% 0.76/0.95 tff(1090,plain,
% 0.76/0.95 (~c2_1(a4)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[964, 815, 1035])).
% 0.76/0.95 tff(1091,plain,
% 0.76/0.95 (hskp6),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1042, 815, 205, 1090, 204])).
% 0.76/0.95 tff(1092,plain,
% 0.76/0.95 (~c2_1(a8)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[795, 1091])).
% 0.76/0.95 tff(1093,plain,
% 0.76/0.95 (~c3_1(a8)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[801, 1091])).
% 0.76/0.95 tff(1094,plain,
% 0.76/0.95 ($false),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1010, 1093, 1092, 205, 805, 1089, 204, 1088, 190, 123, 122])).
% 0.76/0.95 tff(1095,plain,(c3_1(a5) | c0_1(a4) | c1_1(a4) | c1_1(a5) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/0.95 tff(1096,plain,
% 0.76/0.95 (c3_1(a5)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1095, 190, 204, 205, 123, 122])).
% 0.76/0.95 tff(1097,plain,
% 0.76/0.95 (c1_1(a1)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[653, 1085])).
% 0.76/0.95 tff(1098,plain,
% 0.76/0.95 (~c0_1(a1)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[645, 1085])).
% 0.76/0.95 tff(1099,plain,
% 0.76/0.95 ($false),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[710, 1098, 1097, 1096, 450, 1061, 1086, 190, 123, 122, 1067])).
% 0.76/0.95 tff(1100,plain,(c3_1(a4) | c1_1(a5) | hskp30 | hskp18 | c0_1(a4) | c1_1(a4)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.95 tff(1101,plain,
% 0.76/0.95 (c3_1(a4)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1100, 190, 123, 122, 205, 204])).
% 0.76/0.95 tff(1102,plain,
% 0.76/0.95 (~c2_1(a4)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[964, 1101, 1035])).
% 0.76/0.95 tff(1103,plain,
% 0.76/0.95 (hskp6),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1042, 1101, 205, 1102, 204])).
% 0.76/0.95 tff(1104,plain,
% 0.76/0.95 (~c3_1(a8)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[801, 1103])).
% 0.76/0.95 tff(1105,plain,
% 0.76/0.95 (~c2_1(a8)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[795, 1103])).
% 0.76/0.95 tff(1106,plain,
% 0.76/0.95 (~c1_1(a8)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[962, 1105, 1067, 205, 1102, 1104, 204, 1061, 190, 1101])).
% 0.76/0.95 tff(1107,plain,
% 0.76/0.95 (c0_1(a8)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[895, 1103])).
% 0.76/0.95 tff(1108,plain,
% 0.76/0.95 ($false),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1058, 72, 1107, 1105, 1104, 205, 204, 881, 1102, 1106])).
% 0.76/0.95 tff(1109,plain,(c1_1(a5) | c0_1(a4) | c1_1(a4) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/0.95 tff(1110,plain,
% 0.76/0.95 ($false),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1109, 203, 197, 190, 123, 122])).
% 0.76/0.95 tff(1111,plain,((~hskp3) | c1_1(a5) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/0.95 tff(1112,plain,
% 0.76/0.95 (~hskp3),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1111, 150, 123, 122])).
% 0.76/0.95 tff(1113,plain,
% 0.76/0.95 (^[U: $i] : refl((hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.76/0.95 inference(bind,[status(th)],[])).
% 0.76/0.95 tff(1114,plain,
% 0.76/0.95 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.76/0.95 inference(quant_intro,[status(thm)],[1113])).
% 0.76/0.95 tff(1115,plain,
% 0.76/0.95 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1116,plain,
% 0.76/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp21) <=> ((hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp21))), rewrite(((hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp21) <=> (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp21) <=> (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.76/0.95 inference(bind,[status(th)],[])).
% 0.76/0.95 tff(1117,plain,
% 0.76/0.95 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp21) <=> ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.76/0.95 inference(quant_intro,[status(thm)],[1116])).
% 0.76/0.95 tff(1118,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp0) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 0.76/0.95 tff(1119,plain,
% 0.76/0.95 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 0.76/0.95 tff(1120,plain,
% 0.76/0.95 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1119, 1115])).
% 0.76/0.95 tff(1121,plain,(
% 0.76/0.95 ![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.76/0.95 inference(skolemize,[status(sab)],[1120])).
% 0.76/0.95 tff(1122,plain,
% 0.76/0.95 (![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1121, 1114])).
% 0.76/0.95 tff(1123,plain,
% 0.76/0.95 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1124,plain,
% 0.76/0.95 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2))) <=> (hskp21 | hskp0 | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1125,plain,
% 0.76/0.95 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2))))),
% 0.76/0.95 inference(monotonicity,[status(thm)],[1124])).
% 0.76/0.95 tff(1126,plain,
% 0.76/0.95 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2)))),
% 0.76/0.95 inference(transitivity,[status(thm)],[1125, 1123])).
% 0.76/0.95 tff(1127,plain,
% 0.76/0.95 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a2) | c2_1(a2) | (~c0_1(a2)))),
% 0.76/0.95 inference(quant_inst,[status(thm)],[])).
% 0.76/0.95 tff(1128,plain,
% 0.76/0.95 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c0_1(a2))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 0.76/0.95 tff(1129,plain,
% 0.76/0.95 (hskp21 | c1_1(a2)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1128, 72, 528, 568, 552, 1122])).
% 0.76/0.95 tff(1130,plain,
% 0.76/0.95 (hskp21),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1129, 575])).
% 0.76/0.95 tff(1131,plain,
% 0.76/0.95 (((~hskp21) | (~c0_1(a42))) <=> ((~hskp21) | (~c0_1(a42)))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1132,plain,
% 0.76/0.95 (((~c0_1(a42)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a42)))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1133,axiom,((~c0_1(a42)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 0.76/0.95 tff(1134,plain,
% 0.76/0.95 ((~hskp21) | (~c0_1(a42))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 0.76/0.95 tff(1135,plain,
% 0.76/0.95 ((~hskp21) | (~c0_1(a42))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1134, 1131])).
% 0.76/0.95 tff(1136,plain,
% 0.76/0.95 (~c0_1(a42)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1135, 1130])).
% 0.76/0.95 tff(1137,plain,
% 0.76/0.95 (((~hskp21) | c3_1(a42)) <=> ((~hskp21) | c3_1(a42))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1138,axiom,((~hskp21) | c3_1(a42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 0.76/0.95 tff(1139,plain,
% 0.76/0.95 ((~hskp21) | c3_1(a42)),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 0.76/0.95 tff(1140,plain,
% 0.76/0.95 ((~hskp21) | c3_1(a42)),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1139, 1137])).
% 0.76/0.95 tff(1141,plain,
% 0.76/0.95 ((~hskp21) | c3_1(a42)),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1140, 1137])).
% 0.76/0.95 tff(1142,plain,
% 0.76/0.95 ((~hskp21) | c3_1(a42)),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1141, 1137])).
% 0.76/0.95 tff(1143,plain,
% 0.76/0.95 ((~hskp21) | c3_1(a42)),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1142, 1137])).
% 0.76/0.95 tff(1144,plain,
% 0.76/0.95 (c3_1(a42)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1143, 1130])).
% 0.76/0.95 tff(1145,plain,
% 0.76/0.95 (((~hskp21) | c2_1(a42)) <=> ((~hskp21) | c2_1(a42))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1146,axiom,((~hskp21) | c2_1(a42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.76/0.95 tff(1147,plain,
% 0.76/0.95 ((~hskp21) | c2_1(a42)),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 0.76/0.95 tff(1148,plain,
% 0.76/0.95 ((~hskp21) | c2_1(a42)),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1147, 1145])).
% 0.76/0.95 tff(1149,plain,
% 0.76/0.95 ((~hskp21) | c2_1(a42)),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1148, 1145])).
% 0.76/0.95 tff(1150,plain,
% 0.76/0.95 ((~hskp21) | c2_1(a42)),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1149, 1145])).
% 0.76/0.95 tff(1151,plain,
% 0.76/0.95 ((~hskp21) | c2_1(a42)),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1150, 1145])).
% 0.76/0.95 tff(1152,plain,
% 0.76/0.95 (c2_1(a42)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1151, 1130])).
% 0.76/0.95 tff(1153,plain,
% 0.76/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1154,plain,
% 0.76/0.95 (((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42))) <=> (c1_1(a43) | c3_1(a43) | c0_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1155,plain,
% 0.76/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a42) | (~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)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 0.76/0.95 inference(monotonicity,[status(thm)],[1154])).
% 0.76/0.95 tff(1156,plain,
% 0.76/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a42) | (~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)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.95 inference(transitivity,[status(thm)],[1155, 1153])).
% 0.76/0.95 tff(1157,plain,
% 0.76/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))),
% 0.76/0.95 inference(quant_inst,[status(thm)],[])).
% 0.76/0.95 tff(1158,plain,
% 0.76/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a42) | (~ndr1_0) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a43)) | (~c0_1(a43))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 0.76/0.95 tff(1159,plain,
% 0.76/0.95 (~c0_1(a43)),
% 0.76/0.95 inference(unit_resolution,[status(thm)],[1158, 72, 631, 1152, 1144, 623, 617, 1136, 91])).
% 0.76/0.95 tff(1160,plain,
% 0.76/0.95 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.76/0.95 inference(bind,[status(th)],[])).
% 0.76/0.95 tff(1161,plain,
% 0.76/0.95 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.76/0.95 inference(quant_intro,[status(thm)],[1160])).
% 0.76/0.95 tff(1162,plain,
% 0.76/0.95 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1163,plain,
% 0.76/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.76/0.95 inference(bind,[status(th)],[])).
% 0.76/0.95 tff(1164,plain,
% 0.76/0.95 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.76/0.95 inference(quant_intro,[status(thm)],[1163])).
% 0.76/0.95 tff(1165,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.76/0.95 tff(1166,plain,
% 0.76/0.95 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 0.76/0.95 tff(1167,plain,
% 0.76/0.95 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1166, 1162])).
% 0.76/0.95 tff(1168,plain,(
% 0.76/0.95 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.76/0.95 inference(skolemize,[status(sab)],[1167])).
% 0.76/0.95 tff(1169,plain,
% 0.76/0.95 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.76/0.95 inference(modus_ponens,[status(thm)],[1168, 1161])).
% 0.76/0.95 tff(1170,assumption,(~hskp3), introduced(assumption)).
% 0.76/0.95 tff(1171,plain,
% 0.76/0.95 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c1_1(a43) | c3_1(a43) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a43))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a43) | c3_1(a43) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a43))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1172,plain,
% 0.76/0.95 ((hskp3 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c0_1(a43) | c3_1(a43)) <=> (hskp3 | c1_1(a43) | c3_1(a43) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a43))),
% 0.76/0.95 inference(rewrite,[status(thm)],[])).
% 0.76/0.95 tff(1173,plain,
% 0.76/0.95 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c0_1(a43) | c3_1(a43))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | c1_1(a43) | c3_1(a43) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a43)))),
% 0.76/0.95 inference(monotonicity,[status(thm)],[1172])).
% 0.76/0.95 tff(1174,plain,
% 0.76/0.95 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c0_1(a43) | c3_1(a43))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a43) | c3_1(a43) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a43))),
% 0.76/0.96 inference(transitivity,[status(thm)],[1173, 1171])).
% 0.76/0.96 tff(1175,plain,
% 0.76/0.96 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)) | c1_1(a43) | c0_1(a43) | c3_1(a43))),
% 0.76/0.96 inference(quant_inst,[status(thm)],[])).
% 0.76/0.96 tff(1176,plain,
% 0.76/0.96 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp3 | c1_1(a43) | c3_1(a43) | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)) | c0_1(a43)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 0.76/0.96 tff(1177,plain,
% 0.76/0.96 ($false),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1176, 72, 1170, 568, 560, 623, 617, 552, 1169, 1159])).
% 0.76/0.96 tff(1178,plain,(hskp0 | hskp3 | (~c2_1(a5)) | (~c3_1(a5)) | c1_1(a5) | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.96 tff(1179,plain,
% 0.76/0.96 (hskp0),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1178, 1112, 189, 181, 150, 173, 165, 157])).
% 0.76/0.96 tff(1180,plain,
% 0.76/0.96 (c2_1(a1)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[661, 1179])).
% 0.76/0.96 tff(1181,plain,
% 0.76/0.96 (c1_1(a1)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[653, 1179])).
% 0.76/0.96 tff(1182,assumption,(hskp19), introduced(assumption)).
% 0.76/0.96 tff(1183,plain,
% 0.76/0.96 (((~hskp19) | (~c3_1(a36))) <=> ((~hskp19) | (~c3_1(a36)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1184,plain,
% 0.76/0.96 (((~c3_1(a36)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a36)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1185,axiom,((~c3_1(a36)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 0.76/0.96 tff(1186,plain,
% 0.76/0.96 ((~hskp19) | (~c3_1(a36))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 0.76/0.96 tff(1187,plain,
% 0.76/0.96 ((~hskp19) | (~c3_1(a36))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1186, 1183])).
% 0.76/0.96 tff(1188,plain,
% 0.76/0.96 (~c3_1(a36)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1187, 1182])).
% 0.76/0.96 tff(1189,plain,
% 0.76/0.96 (((~hskp19) | (~c2_1(a36))) <=> ((~hskp19) | (~c2_1(a36)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1190,plain,
% 0.76/0.96 (((~c2_1(a36)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a36)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1191,axiom,((~c2_1(a36)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.76/0.96 tff(1192,plain,
% 0.76/0.96 ((~hskp19) | (~c2_1(a36))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 0.76/0.96 tff(1193,plain,
% 0.76/0.96 ((~hskp19) | (~c2_1(a36))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1192, 1189])).
% 0.76/0.96 tff(1194,plain,
% 0.76/0.96 (~c2_1(a36)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1193, 1182])).
% 0.76/0.96 tff(1195,plain,
% 0.76/0.96 (((~hskp19) | (~c1_1(a36))) <=> ((~hskp19) | (~c1_1(a36)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1196,plain,
% 0.76/0.96 (((~c1_1(a36)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a36)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1197,axiom,((~c1_1(a36)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.76/0.96 tff(1198,plain,
% 0.76/0.96 ((~hskp19) | (~c1_1(a36))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 0.76/0.96 tff(1199,plain,
% 0.76/0.96 ((~hskp19) | (~c1_1(a36))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1198, 1195])).
% 0.76/0.96 tff(1200,plain,
% 0.76/0.96 (~c1_1(a36)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1199, 1182])).
% 0.76/0.96 tff(1201,plain,
% 0.76/0.96 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1202,plain,
% 0.76/0.96 ((hskp30 | hskp18 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c2_1(a36)) <=> (hskp30 | hskp18 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1203,plain,
% 0.76/0.96 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c2_1(a36))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0)))),
% 0.76/0.96 inference(monotonicity,[status(thm)],[1202])).
% 0.76/0.96 tff(1204,plain,
% 0.76/0.96 (((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c2_1(a36))) <=> ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0))),
% 0.76/0.96 inference(transitivity,[status(thm)],[1203, 1201])).
% 0.76/0.96 tff(1205,plain,
% 0.76/0.96 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp30 | hskp18 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c2_1(a36))),
% 0.76/0.96 inference(quant_inst,[status(thm)],[])).
% 0.76/0.96 tff(1206,plain,
% 0.76/0.96 ((~![U: $i] : (hskp30 | hskp18 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp30 | hskp18 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1205, 1204])).
% 0.76/0.96 tff(1207,plain,
% 0.76/0.96 ($false),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1206, 123, 72, 122, 1200, 1194, 1188, 276])).
% 0.76/0.96 tff(1208,plain,((~hskp19) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/0.96 tff(1209,plain,
% 0.76/0.96 (~hskp19),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1208, 123, 122])).
% 0.76/0.96 tff(1210,plain,
% 0.76/0.96 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a5) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | (~c2_1(a5)) | (~c3_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a5) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1211,plain,
% 0.76/0.96 ((hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5))) <=> (hskp19 | c1_1(a5) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1212,plain,
% 0.76/0.96 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a5) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | (~c2_1(a5)) | (~c3_1(a5))))),
% 0.76/0.96 inference(monotonicity,[status(thm)],[1211])).
% 0.76/0.96 tff(1213,plain,
% 0.76/0.96 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a5) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | (~c2_1(a5)) | (~c3_1(a5)))),
% 0.76/0.96 inference(transitivity,[status(thm)],[1212, 1210])).
% 0.76/0.96 tff(1214,plain,
% 0.76/0.96 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))),
% 0.76/0.96 inference(quant_inst,[status(thm)],[])).
% 0.76/0.96 tff(1215,plain,
% 0.76/0.96 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a5) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | (~c2_1(a5)) | (~c3_1(a5))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 0.76/0.96 tff(1216,plain,
% 0.76/0.96 (~c3_1(a1)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1215, 72, 1209, 189, 181, 1181, 1180, 150, 143])).
% 0.76/0.96 tff(1217,plain,
% 0.76/0.96 (~c0_1(a1)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[645, 1179])).
% 0.76/0.96 tff(1218,plain,
% 0.76/0.96 (c3_1(a6)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[265, 218, 233, 231, 230, 232, 229])).
% 0.76/0.96 tff(1219,plain,
% 0.76/0.96 (hskp5),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1066, 218, 233, 190, 231, 230, 229])).
% 0.76/0.96 tff(1220,plain,
% 0.76/0.96 ($false),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1034, 1219, 1218])).
% 0.76/0.96 tff(1221,plain,(c0_1(a5) | (~c2_1(a5)) | c1_1(a5) | (~c0_1(a3)) | (~c2_1(a3)) | c1_1(a3) | (~c3_1(a5))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.96 tff(1222,plain,
% 0.76/0.96 (c0_1(a5)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1221, 181, 150, 173, 165, 157, 189])).
% 0.76/0.96 tff(1223,plain,
% 0.76/0.96 (~hskp14),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[710, 1180, 1222, 1217, 189, 181, 150, 123, 122, 1181])).
% 0.76/0.96 tff(1224,plain,
% 0.76/0.96 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1225,plain,
% 0.76/0.96 ((hskp29 | hskp14 | (~ndr1_0) | c3_1(a1) | c0_1(a1) | (~c2_1(a1))) <=> (hskp29 | hskp14 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1226,plain,
% 0.76/0.96 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1)))),
% 0.76/0.96 inference(monotonicity,[status(thm)],[1225])).
% 0.76/0.96 tff(1227,plain,
% 0.76/0.96 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1))),
% 0.76/0.96 inference(transitivity,[status(thm)],[1226, 1224])).
% 0.76/0.96 tff(1228,plain,
% 0.76/0.96 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a1) | c0_1(a1) | (~c2_1(a1)))),
% 0.76/0.96 inference(quant_inst,[status(thm)],[])).
% 0.76/0.96 tff(1229,plain,
% 0.76/0.96 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 0.76/0.96 tff(1230,plain,
% 0.76/0.96 (hskp29),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1229, 72, 1223, 1180, 1217, 306, 1216])).
% 0.76/0.96 tff(1231,plain,
% 0.76/0.96 (c0_1(a25)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[321, 1230])).
% 0.76/0.96 tff(1232,plain,
% 0.76/0.96 (c2_1(a25)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[329, 1230])).
% 0.76/0.96 tff(1233,plain,
% 0.76/0.96 (c1_1(a25)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[347, 1230])).
% 0.76/0.96 tff(1234,plain,
% 0.76/0.96 (~c3_1(a25)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[354, 72, 1231, 1233, 1232, 340])).
% 0.76/0.96 tff(1235,plain,
% 0.76/0.96 (~hskp27),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[398, 1234, 1232, 173, 165, 157, 1231])).
% 0.76/0.96 tff(1236,plain,
% 0.76/0.96 ((hskp30 | hskp27 | hskp7) <=> (hskp30 | hskp27 | hskp7)),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1237,plain,
% 0.76/0.96 (((hskp30 | hskp27) | hskp7) <=> (hskp30 | hskp27 | hskp7)),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1238,plain,
% 0.76/0.96 ((hskp30 | hskp27) <=> (hskp30 | hskp27)),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1239,plain,
% 0.76/0.96 (((hskp30 | hskp27) | hskp7) <=> ((hskp30 | hskp27) | hskp7)),
% 0.76/0.96 inference(monotonicity,[status(thm)],[1238])).
% 0.76/0.96 tff(1240,plain,
% 0.76/0.96 (((hskp30 | hskp27) | hskp7) <=> (hskp30 | hskp27 | hskp7)),
% 0.76/0.96 inference(transitivity,[status(thm)],[1239, 1237])).
% 0.76/0.96 tff(1241,axiom,((hskp30 | hskp27) | hskp7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 0.76/0.96 tff(1242,plain,
% 0.76/0.96 (hskp30 | hskp27 | hskp7),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 0.76/0.96 tff(1243,plain,
% 0.76/0.96 (hskp30 | hskp27 | hskp7),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1242, 1236])).
% 0.76/0.96 tff(1244,plain,
% 0.76/0.96 (hskp30 | hskp27 | hskp7),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1243, 1236])).
% 0.76/0.96 tff(1245,plain,
% 0.76/0.96 (hskp30 | hskp27 | hskp7),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1244, 1236])).
% 0.76/0.96 tff(1246,plain,
% 0.76/0.96 (hskp30 | hskp27 | hskp7),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1245, 1236])).
% 0.76/0.96 tff(1247,plain,
% 0.76/0.96 (hskp7),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1246, 1235, 123])).
% 0.76/0.96 tff(1248,plain,
% 0.76/0.96 (~c2_1(a9)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[748, 1247])).
% 0.76/0.96 tff(1249,plain,
% 0.76/0.96 (~c0_1(a9)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[754, 1247])).
% 0.76/0.96 tff(1250,plain,
% 0.76/0.96 (c1_1(a9)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[762, 1247])).
% 0.76/0.96 tff(1251,assumption,(hskp28), introduced(assumption)).
% 0.76/0.96 tff(1252,plain,
% 0.76/0.96 (((~hskp28) | c3_1(a15)) <=> ((~hskp28) | c3_1(a15))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1253,axiom,((~hskp28) | c3_1(a15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.76/0.96 tff(1254,plain,
% 0.76/0.96 ((~hskp28) | c3_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 0.76/0.96 tff(1255,plain,
% 0.76/0.96 ((~hskp28) | c3_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1254, 1252])).
% 0.76/0.96 tff(1256,plain,
% 0.76/0.96 ((~hskp28) | c3_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1255, 1252])).
% 0.76/0.96 tff(1257,plain,
% 0.76/0.96 ((~hskp28) | c3_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1256, 1252])).
% 0.76/0.96 tff(1258,plain,
% 0.76/0.96 ((~hskp28) | c3_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1257, 1252])).
% 0.76/0.96 tff(1259,plain,
% 0.76/0.96 (c3_1(a15)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1258, 1251])).
% 0.76/0.96 tff(1260,plain,
% 0.76/0.96 (((~hskp28) | c1_1(a15)) <=> ((~hskp28) | c1_1(a15))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1261,axiom,((~hskp28) | c1_1(a15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.76/0.96 tff(1262,plain,
% 0.76/0.96 ((~hskp28) | c1_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1261, 1260])).
% 0.76/0.96 tff(1263,plain,
% 0.76/0.96 ((~hskp28) | c1_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1262, 1260])).
% 0.76/0.96 tff(1264,plain,
% 0.76/0.96 ((~hskp28) | c1_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1263, 1260])).
% 0.76/0.96 tff(1265,plain,
% 0.76/0.96 ((~hskp28) | c1_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1264, 1260])).
% 0.76/0.96 tff(1266,plain,
% 0.76/0.96 ((~hskp28) | c1_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1265, 1260])).
% 0.76/0.96 tff(1267,plain,
% 0.76/0.96 (c1_1(a15)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1266, 1251])).
% 0.76/0.96 tff(1268,plain,
% 0.76/0.96 (((~hskp28) | c0_1(a15)) <=> ((~hskp28) | c0_1(a15))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1269,axiom,((~hskp28) | c0_1(a15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.76/0.96 tff(1270,plain,
% 0.76/0.96 ((~hskp28) | c0_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 0.76/0.96 tff(1271,plain,
% 0.76/0.96 ((~hskp28) | c0_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1270, 1268])).
% 0.76/0.96 tff(1272,plain,
% 0.76/0.96 ((~hskp28) | c0_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1271, 1268])).
% 0.76/0.96 tff(1273,plain,
% 0.76/0.96 ((~hskp28) | c0_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1272, 1268])).
% 0.76/0.96 tff(1274,plain,
% 0.76/0.96 ((~hskp28) | c0_1(a15)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1273, 1268])).
% 0.76/0.96 tff(1275,plain,
% 0.76/0.96 (c0_1(a15)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1274, 1251])).
% 0.76/0.96 tff(1276,assumption,(c2_1(a15)), introduced(assumption)).
% 0.76/0.96 tff(1277,assumption,(c3_1(a15)), introduced(assumption)).
% 0.76/0.96 tff(1278,assumption,(c1_1(a15)), introduced(assumption)).
% 0.76/0.96 tff(1279,assumption,(c0_1(a15)), introduced(assumption)).
% 0.76/0.96 tff(1280,plain,
% 0.76/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1281,plain,
% 0.76/0.96 (((~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a15)) | (~c2_1(a15)) | (~c0_1(a15))) <=> ((~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1282,plain,
% 0.76/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a15)) | (~c2_1(a15)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15))))),
% 0.76/0.96 inference(monotonicity,[status(thm)],[1281])).
% 0.76/0.96 tff(1283,plain,
% 0.76/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a15)) | (~c2_1(a15)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.76/0.96 inference(transitivity,[status(thm)],[1282, 1280])).
% 0.76/0.96 tff(1284,plain,
% 0.76/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a15)) | (~c3_1(a15)) | (~c1_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a15)) | (~c2_1(a15)) | (~c0_1(a15)))),
% 0.76/0.96 inference(quant_inst,[status(thm)],[])).
% 0.76/0.96 tff(1285,plain,
% 0.76/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c2_1(a15)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 0.76/0.96 tff(1286,plain,
% 0.76/0.96 ($false),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1285, 72, 1279, 1278, 1277, 340, 1276])).
% 0.76/0.96 tff(1287,plain,((~c2_1(a15)) | (~c0_1(a15)) | (~c1_1(a15)) | (~c3_1(a15))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.96 tff(1288,plain,
% 0.76/0.96 (~c2_1(a15)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1287, 1275, 1267, 1259])).
% 0.76/0.96 tff(1289,plain,
% 0.76/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1290,plain,
% 0.76/0.96 (((~ndr1_0) | (~c3_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5))) <=> (c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1291,plain,
% 0.76/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15))))),
% 0.76/0.96 inference(monotonicity,[status(thm)],[1290])).
% 0.76/0.96 tff(1292,plain,
% 0.76/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.76/0.96 inference(transitivity,[status(thm)],[1291, 1289])).
% 0.76/0.96 tff(1293,plain,
% 0.76/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a15)) | (~c1_1(a15)) | (~c0_1(a15)) | c2_1(a15) | (~c1_1(a15)) | (~c0_1(a15)) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)))),
% 0.76/0.96 inference(quant_inst,[status(thm)],[])).
% 0.76/0.96 tff(1294,plain,
% 0.76/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 0.76/0.96 tff(1295,plain,
% 0.76/0.96 ($false),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1294, 72, 1275, 1267, 1259, 233, 190, 527, 664, 1288])).
% 0.76/0.96 tff(1296,plain,((~hskp28) | (~c2_1(a5)) | c1_1(a5) | (~c0_1(a5))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.96 tff(1297,plain,
% 0.76/0.96 (~hskp28),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1296, 1222, 150, 189])).
% 0.76/0.96 tff(1298,plain,
% 0.76/0.96 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp28 | hskp27 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a9)))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp28 | hskp27 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a9)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1299,plain,
% 0.76/0.96 ((hskp28 | hskp27 | (~ndr1_0) | c0_1(a9) | c2_1(a9) | (~c1_1(a9))) <=> (hskp28 | hskp27 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a9)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1300,plain,
% 0.76/0.96 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp28 | hskp27 | (~ndr1_0) | c0_1(a9) | c2_1(a9) | (~c1_1(a9)))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp28 | hskp27 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a9))))),
% 0.76/0.96 inference(monotonicity,[status(thm)],[1299])).
% 0.76/0.96 tff(1301,plain,
% 0.76/0.96 (((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp28 | hskp27 | (~ndr1_0) | c0_1(a9) | c2_1(a9) | (~c1_1(a9)))) <=> ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp28 | hskp27 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a9)))),
% 0.76/0.96 inference(transitivity,[status(thm)],[1300, 1298])).
% 0.76/0.96 tff(1302,plain,
% 0.76/0.96 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp28 | hskp27 | (~ndr1_0) | c0_1(a9) | c2_1(a9) | (~c1_1(a9)))),
% 0.76/0.96 inference(quant_inst,[status(thm)],[])).
% 0.76/0.96 tff(1303,plain,
% 0.76/0.96 ((~![U: $i] : (hskp28 | hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp28 | hskp27 | c0_1(a9) | c2_1(a9) | (~ndr1_0) | (~c1_1(a9))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 0.76/0.96 tff(1304,plain,
% 0.76/0.96 ($false),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1303, 72, 1297, 1235, 1250, 1249, 1248, 133])).
% 0.76/0.96 tff(1305,plain,((~hskp4) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/0.96 tff(1306,plain,
% 0.76/0.96 (~hskp4),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1305, 123, 122])).
% 0.76/0.96 tff(1307,assumption,(~hskp24), introduced(assumption)).
% 0.76/0.96 tff(1308,assumption,(~hskp4), introduced(assumption)).
% 0.76/0.96 tff(1309,plain,
% 0.76/0.96 (^[U: $i] : refl((hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.76/0.96 inference(bind,[status(th)],[])).
% 0.76/0.96 tff(1310,plain,
% 0.76/0.96 (![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.96 inference(quant_intro,[status(thm)],[1309])).
% 0.76/0.96 tff(1311,plain,
% 0.76/0.96 (![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1312,plain,
% 0.76/0.96 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp19) <=> ((hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp19))), rewrite(((hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp19) <=> (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.76/0.96 inference(bind,[status(th)],[])).
% 0.76/0.96 tff(1313,plain,
% 0.76/0.96 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp19) <=> ![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.96 inference(quant_intro,[status(thm)],[1312])).
% 0.76/0.96 tff(1314,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 0.76/0.96 tff(1315,plain,
% 0.76/0.96 (![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 0.76/0.96 tff(1316,plain,
% 0.76/0.96 (![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1315, 1311])).
% 0.76/0.96 tff(1317,plain,(
% 0.76/0.96 ![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.96 inference(skolemize,[status(sab)],[1316])).
% 0.76/0.96 tff(1318,plain,
% 0.76/0.96 (![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1317, 1310])).
% 0.76/0.96 tff(1319,assumption,(~hskp19), introduced(assumption)).
% 0.76/0.96 tff(1320,plain,
% 0.76/0.96 (~c2_1(a15)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1287, 1259, 1267, 1275])).
% 0.76/0.96 tff(1321,plain,
% 0.76/0.96 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1322,plain,
% 0.76/0.96 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.76/0.96 inference(quant_inst,[status(thm)],[])).
% 0.76/0.96 tff(1323,plain,
% 0.76/0.96 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c0_1(a15))),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1322, 1321])).
% 0.76/0.96 tff(1324,plain,
% 0.76/0.96 ($false),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1323, 1, 72, 1319, 1275, 1259, 1318, 1320])).
% 0.76/0.96 tff(1325,plain,((~hskp28) | hskp22 | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.76/0.96 tff(1326,plain,
% 0.76/0.96 (~hskp28),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1325, 1, 1319])).
% 0.76/0.96 tff(1327,assumption,(hskp24), introduced(assumption)).
% 0.76/0.96 tff(1328,plain,
% 0.76/0.96 (((~hskp24) | c3_1(a58)) <=> ((~hskp24) | c3_1(a58))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1329,axiom,((~hskp24) | c3_1(a58)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.76/0.96 tff(1330,plain,
% 0.76/0.96 ((~hskp24) | c3_1(a58)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 0.76/0.96 tff(1331,plain,
% 0.76/0.96 ((~hskp24) | c3_1(a58)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1330, 1328])).
% 0.76/0.96 tff(1332,plain,
% 0.76/0.96 ((~hskp24) | c3_1(a58)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1331, 1328])).
% 0.76/0.96 tff(1333,plain,
% 0.76/0.96 ((~hskp24) | c3_1(a58)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1332, 1328])).
% 0.76/0.96 tff(1334,plain,
% 0.76/0.96 ((~hskp24) | c3_1(a58)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1333, 1328])).
% 0.76/0.96 tff(1335,plain,
% 0.76/0.96 (c3_1(a58)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1334, 1327])).
% 0.76/0.96 tff(1336,plain,
% 0.76/0.96 (((~hskp24) | c0_1(a58)) <=> ((~hskp24) | c0_1(a58))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.96 tff(1337,axiom,((~hskp24) | c0_1(a58)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 0.76/0.96 tff(1338,plain,
% 0.76/0.96 ((~hskp24) | c0_1(a58)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1337, 1336])).
% 0.76/0.96 tff(1339,plain,
% 0.76/0.96 ((~hskp24) | c0_1(a58)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1338, 1336])).
% 0.76/0.96 tff(1340,plain,
% 0.76/0.96 ((~hskp24) | c0_1(a58)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1339, 1336])).
% 0.76/0.96 tff(1341,plain,
% 0.76/0.96 ((~hskp24) | c0_1(a58)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1340, 1336])).
% 0.76/0.96 tff(1342,plain,
% 0.76/0.96 ((~hskp24) | c0_1(a58)),
% 0.76/0.96 inference(modus_ponens,[status(thm)],[1341, 1336])).
% 0.76/0.96 tff(1343,plain,
% 0.76/0.96 (c0_1(a58)),
% 0.76/0.96 inference(unit_resolution,[status(thm)],[1342, 1327])).
% 0.76/0.96 tff(1344,plain,
% 0.76/0.96 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))),
% 0.76/0.96 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1345,plain,
% 0.76/0.97 ((hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58))) <=> (hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1346,plain,
% 0.76/0.97 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58))))),
% 0.76/0.97 inference(monotonicity,[status(thm)],[1345])).
% 0.76/0.97 tff(1347,plain,
% 0.76/0.97 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))),
% 0.76/0.97 inference(transitivity,[status(thm)],[1346, 1344])).
% 0.76/0.97 tff(1348,plain,
% 0.76/0.97 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))),
% 0.76/0.97 inference(quant_inst,[status(thm)],[])).
% 0.76/0.97 tff(1349,plain,
% 0.76/0.97 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 0.76/0.97 tff(1350,plain,
% 0.76/0.97 (c2_1(a58)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1349, 1, 72, 1319, 1343, 1335, 1318])).
% 0.76/0.97 tff(1351,plain,
% 0.76/0.97 (((~hskp24) | (~c1_1(a58))) <=> ((~hskp24) | (~c1_1(a58)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1352,plain,
% 0.76/0.97 (((~c1_1(a58)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a58)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1353,axiom,((~c1_1(a58)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.76/0.97 tff(1354,plain,
% 0.76/0.97 ((~hskp24) | (~c1_1(a58))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 0.76/0.97 tff(1355,plain,
% 0.76/0.97 ((~hskp24) | (~c1_1(a58))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1354, 1351])).
% 0.76/0.97 tff(1356,plain,
% 0.76/0.97 (~c1_1(a58)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1355, 1327])).
% 0.76/0.97 tff(1357,assumption,(~hskp21), introduced(assumption)).
% 0.76/0.97 tff(1358,plain,
% 0.76/0.97 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | c1_1(a58) | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c1_1(a58) | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1359,plain,
% 0.76/0.97 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58))) <=> (hskp21 | hskp0 | c1_1(a58) | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1360,plain,
% 0.76/0.97 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | c1_1(a58) | (~ndr1_0) | c2_1(a58) | (~c0_1(a58))))),
% 0.76/0.97 inference(monotonicity,[status(thm)],[1359])).
% 0.76/0.97 tff(1361,plain,
% 0.76/0.97 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c1_1(a58) | (~ndr1_0) | c2_1(a58) | (~c0_1(a58)))),
% 0.76/0.97 inference(transitivity,[status(thm)],[1360, 1358])).
% 0.76/0.97 tff(1362,plain,
% 0.76/0.97 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a58) | c2_1(a58) | (~c0_1(a58)))),
% 0.76/0.97 inference(quant_inst,[status(thm)],[])).
% 0.76/0.97 tff(1363,plain,
% 0.76/0.97 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c1_1(a58) | (~ndr1_0) | c2_1(a58) | (~c0_1(a58))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 0.76/0.97 tff(1364,plain,
% 0.76/0.97 (c2_1(a58)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1363, 72, 1357, 528, 1343, 1356, 1122])).
% 0.76/0.97 tff(1365,plain,
% 0.76/0.97 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1366,plain,
% 0.76/0.97 ((hskp1 | hskp0 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58))) <=> (hskp1 | hskp0 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1367,plain,
% 0.76/0.97 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58))))),
% 0.76/0.97 inference(monotonicity,[status(thm)],[1366])).
% 0.76/0.97 tff(1368,plain,
% 0.76/0.97 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58)))),
% 0.76/0.97 inference(transitivity,[status(thm)],[1367, 1365])).
% 0.76/0.97 tff(1369,plain,
% 0.76/0.97 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)))),
% 0.76/0.97 inference(quant_inst,[status(thm)],[])).
% 0.76/0.97 tff(1370,plain,
% 0.76/0.97 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | c1_1(a58) | (~ndr1_0) | (~c2_1(a58)) | (~c3_1(a58))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 0.76/0.97 tff(1371,plain,
% 0.76/0.97 (hskp1),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1370, 72, 528, 1335, 1356, 538, 1364])).
% 0.76/0.97 tff(1372,plain,
% 0.76/0.97 (~c2_1(a2)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[551, 1371])).
% 0.76/0.97 tff(1373,plain,
% 0.76/0.97 (c3_1(a2)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[559, 1371])).
% 0.76/0.97 tff(1374,plain,
% 0.76/0.97 (c0_1(a2)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[567, 1371])).
% 0.76/0.97 tff(1375,plain,
% 0.76/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a58) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a58)) | (~c0_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a58) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a58)) | (~c0_1(a58)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1376,plain,
% 0.76/0.97 (((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58))) <=> (c1_1(a58) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a58)) | (~c0_1(a58)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1377,plain,
% 0.76/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a58) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a58)) | (~c0_1(a58))))),
% 0.76/0.97 inference(monotonicity,[status(thm)],[1376])).
% 0.76/0.97 tff(1378,plain,
% 0.76/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a58) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a58)) | (~c0_1(a58)))),
% 0.76/0.97 inference(transitivity,[status(thm)],[1377, 1375])).
% 0.76/0.97 tff(1379,plain,
% 0.76/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)))),
% 0.76/0.97 inference(quant_inst,[status(thm)],[])).
% 0.76/0.97 tff(1380,plain,
% 0.76/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a58) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a58)) | (~c0_1(a58))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1379, 1378])).
% 0.76/0.97 tff(1381,plain,
% 0.76/0.97 (~c1_1(a2)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1380, 72, 1343, 1374, 1373, 1356, 1372, 527, 1364])).
% 0.76/0.97 tff(1382,plain,
% 0.76/0.97 ($false),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1128, 72, 1357, 528, 1374, 1372, 1122, 1381])).
% 0.76/0.97 tff(1383,plain,((~hskp24) | hskp21 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.76/0.97 tff(1384,plain,
% 0.76/0.97 (hskp21),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1383, 1327, 528])).
% 0.76/0.97 tff(1385,plain,
% 0.76/0.97 (~c0_1(a42)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1135, 1384])).
% 0.76/0.97 tff(1386,plain,
% 0.76/0.97 (c3_1(a42)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1143, 1384])).
% 0.76/0.97 tff(1387,plain,
% 0.76/0.97 (c2_1(a42)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1151, 1384])).
% 0.76/0.97 tff(1388,plain,
% 0.76/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a58) | c0_1(a42) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a58)) | (~c0_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)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a58) | c0_1(a42) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a58)) | (~c0_1(a58)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1389,plain,
% 0.76/0.97 (((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42))) <=> (c1_1(a58) | c0_1(a42) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a58)) | (~c0_1(a58)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1390,plain,
% 0.76/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c0_1(a42) | (~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)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a58) | c0_1(a42) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a58)) | (~c0_1(a58))))),
% 0.76/0.97 inference(monotonicity,[status(thm)],[1389])).
% 0.76/0.97 tff(1391,plain,
% 0.76/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c0_1(a42) | (~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)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a58) | c0_1(a42) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a58)) | (~c0_1(a58)))),
% 0.76/0.97 inference(transitivity,[status(thm)],[1390, 1388])).
% 0.76/0.97 tff(1392,plain,
% 0.76/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))),
% 0.76/0.97 inference(quant_inst,[status(thm)],[])).
% 0.76/0.97 tff(1393,plain,
% 0.76/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a58) | c0_1(a42) | c3_1(a19) | (~ndr1_0) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a42)) | (~c3_1(a42)) | (~c2_1(a58)) | (~c0_1(a58))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 0.76/0.97 tff(1394,plain,
% 0.76/0.97 ($false),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1393, 72, 1343, 1387, 1386, 38, 1356, 1385, 22, 91, 81, 1350])).
% 0.76/0.97 tff(1395,plain,((~hskp24) | hskp22 | hskp19 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.76/0.97 tff(1396,plain,
% 0.76/0.97 (~hskp24),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1395, 1, 1319, 528])).
% 0.76/0.97 tff(1397,assumption,(~hskp1), introduced(assumption)).
% 0.76/0.97 tff(1398,assumption,(c2_1(a19)), introduced(assumption)).
% 0.76/0.97 tff(1399,assumption,(~c3_1(a19)), introduced(assumption)).
% 0.76/0.97 tff(1400,assumption,(c0_1(a19)), introduced(assumption)).
% 0.76/0.97 tff(1401,assumption,(~hskp28), introduced(assumption)).
% 0.76/0.97 tff(1402,plain,
% 0.76/0.97 ((hskp28 | hskp9 | hskp1) <=> (hskp28 | hskp9 | hskp1)),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1403,plain,
% 0.76/0.97 (((hskp28 | hskp1) | hskp9) <=> (hskp28 | hskp9 | hskp1)),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1404,plain,
% 0.76/0.97 ((hskp28 | hskp1) <=> (hskp28 | hskp1)),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1405,plain,
% 0.76/0.97 (((hskp28 | hskp1) | hskp9) <=> ((hskp28 | hskp1) | hskp9)),
% 0.76/0.97 inference(monotonicity,[status(thm)],[1404])).
% 0.76/0.97 tff(1406,plain,
% 0.76/0.97 (((hskp28 | hskp1) | hskp9) <=> (hskp28 | hskp9 | hskp1)),
% 0.76/0.97 inference(transitivity,[status(thm)],[1405, 1403])).
% 0.76/0.97 tff(1407,axiom,((hskp28 | hskp1) | hskp9), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 0.76/0.97 tff(1408,plain,
% 0.76/0.97 (hskp28 | hskp9 | hskp1),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1407, 1406])).
% 0.76/0.97 tff(1409,plain,
% 0.76/0.97 (hskp28 | hskp9 | hskp1),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1408, 1402])).
% 0.76/0.97 tff(1410,plain,
% 0.76/0.97 (hskp28 | hskp9 | hskp1),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1409, 1402])).
% 0.76/0.97 tff(1411,plain,
% 0.76/0.97 (hskp28 | hskp9 | hskp1),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1410, 1402])).
% 0.76/0.97 tff(1412,plain,
% 0.76/0.97 (hskp28 | hskp9 | hskp1),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1411, 1402])).
% 0.76/0.97 tff(1413,plain,
% 0.76/0.97 (hskp9),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1412, 1397, 1401])).
% 0.76/0.97 tff(1414,plain,
% 0.76/0.97 (~c2_1(a12)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[977, 1413])).
% 0.76/0.97 tff(1415,plain,
% 0.76/0.97 (~c3_1(a12)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[516, 1413])).
% 0.76/0.97 tff(1416,plain,
% 0.76/0.97 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.76/0.97 inference(bind,[status(th)],[])).
% 0.76/0.97 tff(1417,plain,
% 0.76/0.97 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.97 inference(quant_intro,[status(thm)],[1416])).
% 0.76/0.97 tff(1418,plain,
% 0.76/0.97 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1419,plain,
% 0.76/0.97 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp24) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp24))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.76/0.97 inference(bind,[status(th)],[])).
% 0.76/0.97 tff(1420,plain,
% 0.76/0.97 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.97 inference(quant_intro,[status(thm)],[1419])).
% 0.76/0.97 tff(1421,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 0.76/0.97 tff(1422,plain,
% 0.76/0.97 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 0.76/0.97 tff(1423,plain,
% 0.76/0.97 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1422, 1418])).
% 0.76/0.97 tff(1424,plain,(
% 0.76/0.97 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.97 inference(skolemize,[status(sab)],[1423])).
% 0.76/0.97 tff(1425,plain,
% 0.76/0.97 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1424, 1417])).
% 0.76/0.97 tff(1426,plain,
% 0.76/0.97 (^[U: $i] : refl((hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))),
% 0.76/0.97 inference(bind,[status(th)],[])).
% 0.76/0.97 tff(1427,plain,
% 0.76/0.97 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.76/0.97 inference(quant_intro,[status(thm)],[1426])).
% 0.76/0.97 tff(1428,plain,
% 0.76/0.97 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1429,plain,
% 0.76/0.97 (^[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)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp19) <=> ((hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp19))), rewrite(((hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp19) <=> (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp19) <=> (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))))),
% 0.76/0.97 inference(bind,[status(th)],[])).
% 0.76/0.97 tff(1430,plain,
% 0.76/0.97 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp19) <=> ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.76/0.97 inference(quant_intro,[status(thm)],[1429])).
% 0.76/0.97 tff(1431,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 0.76/0.97 tff(1432,plain,
% 0.76/0.97 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 0.76/0.97 tff(1433,plain,
% 0.76/0.97 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1432, 1428])).
% 0.76/0.97 tff(1434,plain,(
% 0.76/0.97 ![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.76/0.97 inference(skolemize,[status(sab)],[1433])).
% 0.76/0.97 tff(1435,plain,
% 0.76/0.97 (![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1434, 1427])).
% 0.76/0.97 tff(1436,plain,
% 0.76/0.97 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp19 | hskp1 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1437,plain,
% 0.76/0.97 ((hskp19 | hskp1 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12)) <=> (hskp19 | hskp1 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1438,plain,
% 0.76/0.97 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0)))),
% 0.76/0.97 inference(monotonicity,[status(thm)],[1437])).
% 0.76/0.97 tff(1439,plain,
% 0.76/0.97 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp19 | hskp1 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0))),
% 0.76/0.97 inference(transitivity,[status(thm)],[1438, 1436])).
% 0.76/0.97 tff(1440,plain,
% 0.76/0.97 ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | (~ndr1_0) | c3_1(a12) | c1_1(a12) | c2_1(a12))),
% 0.76/0.97 inference(quant_inst,[status(thm)],[])).
% 0.76/0.97 tff(1441,plain,
% 0.76/0.97 ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp19 | hskp1 | c1_1(a12) | c2_1(a12) | c3_1(a12) | (~ndr1_0)),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 0.76/0.97 tff(1442,plain,
% 0.76/0.97 (c1_1(a12) | c2_1(a12)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1441, 72, 1319, 1397, 586, 1435])).
% 0.76/0.97 tff(1443,plain,
% 0.76/0.97 (c1_1(a12)),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1442, 985])).
% 0.76/0.97 tff(1444,plain,
% 0.76/0.97 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a19) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a19)) | (~c0_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a19) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a19)) | (~c0_1(a19)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1445,plain,
% 0.76/0.97 ((hskp24 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12))) <=> (hskp24 | c3_1(a19) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a19)) | (~c0_1(a19)))),
% 0.76/0.97 inference(rewrite,[status(thm)],[])).
% 0.76/0.97 tff(1446,plain,
% 0.76/0.97 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a19) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a19)) | (~c0_1(a19))))),
% 0.76/0.97 inference(monotonicity,[status(thm)],[1445])).
% 0.76/0.97 tff(1447,plain,
% 0.76/0.97 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a19) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a19)) | (~c0_1(a19)))),
% 0.76/0.97 inference(transitivity,[status(thm)],[1446, 1444])).
% 0.76/0.97 tff(1448,plain,
% 0.76/0.97 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))),
% 0.76/0.97 inference(quant_inst,[status(thm)],[])).
% 0.76/0.97 tff(1449,plain,
% 0.76/0.97 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a19) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a19)) | (~c0_1(a19))),
% 0.76/0.97 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 0.76/0.97 tff(1450,plain,
% 0.76/0.97 ($false),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1449, 72, 1307, 1400, 1443, 1399, 985, 586, 1425, 1398])).
% 0.76/0.97 tff(1451,plain,(c2_1(a12) | hskp24 | (~c0_1(a19)) | c3_1(a19) | c3_1(a12) | (~c2_1(a19)) | hskp19 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.76/0.97 tff(1452,plain,
% 0.76/0.97 ($false),
% 0.76/0.97 inference(unit_resolution,[status(thm)],[1451, 1415, 1414, 1400, 1399, 1307, 1398, 1319, 1397])).
% 0.76/0.98 tff(1453,plain,(hskp1 | (~c0_1(a19)) | c3_1(a19) | hskp24 | (~c2_1(a19)) | hskp19 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.76/0.98 tff(1454,plain,
% 0.76/0.98 (hskp1),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1453, 38, 22, 1396, 81, 1319, 1326])).
% 0.76/0.98 tff(1455,plain,
% 0.76/0.98 (~c2_1(a2)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[551, 1454])).
% 0.76/0.98 tff(1456,plain,
% 0.76/0.98 (c3_1(a2)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[559, 1454])).
% 0.76/0.98 tff(1457,plain,
% 0.76/0.98 (c0_1(a2)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[567, 1454])).
% 0.76/0.98 tff(1458,plain,
% 0.76/0.98 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1459,plain,
% 0.76/0.98 ((hskp22 | hskp19 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2))) <=> (hskp22 | hskp19 | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1460,plain,
% 0.76/0.98 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2))))),
% 0.76/0.98 inference(monotonicity,[status(thm)],[1459])).
% 0.76/0.98 tff(1461,plain,
% 0.76/0.98 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2)))),
% 0.76/0.98 inference(transitivity,[status(thm)],[1460, 1458])).
% 0.76/0.98 tff(1462,plain,
% 0.76/0.98 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a2) | (~c3_1(a2)) | (~c0_1(a2)))),
% 0.76/0.98 inference(quant_inst,[status(thm)],[])).
% 0.76/0.98 tff(1463,plain,
% 0.76/0.98 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | c2_1(a2) | (~ndr1_0) | (~c3_1(a2)) | (~c0_1(a2))),
% 0.76/0.98 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 0.76/0.98 tff(1464,plain,
% 0.76/0.98 ($false),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1463, 1, 72, 1319, 1457, 1456, 1455, 1318])).
% 0.76/0.98 tff(1465,plain,(hskp22 | hskp19 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.76/0.98 tff(1466,plain,
% 0.76/0.98 (hskp22),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1465, 528, 1209])).
% 0.76/0.98 tff(1467,plain,
% 0.76/0.98 (~c3_1(a43)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[616, 1466])).
% 0.76/0.98 tff(1468,plain,
% 0.76/0.98 (~c1_1(a43)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[622, 1466])).
% 0.76/0.98 tff(1469,plain,
% 0.76/0.98 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c1_1(a43) | c3_1(a43) | (~ndr1_0) | c0_1(a43))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c1_1(a43) | c3_1(a43) | (~ndr1_0) | c0_1(a43))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1470,plain,
% 0.76/0.98 ((hskp4 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | c0_1(a43)) <=> (hskp4 | c1_1(a43) | c3_1(a43) | (~ndr1_0) | c0_1(a43))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1471,plain,
% 0.76/0.98 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | c0_1(a43))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c1_1(a43) | c3_1(a43) | (~ndr1_0) | c0_1(a43)))),
% 0.76/0.98 inference(monotonicity,[status(thm)],[1470])).
% 0.76/0.98 tff(1472,plain,
% 0.76/0.98 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | c0_1(a43))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c1_1(a43) | c3_1(a43) | (~ndr1_0) | c0_1(a43))),
% 0.76/0.98 inference(transitivity,[status(thm)],[1471, 1469])).
% 0.76/0.98 tff(1473,plain,
% 0.76/0.98 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | c0_1(a43))),
% 0.76/0.98 inference(quant_inst,[status(thm)],[])).
% 0.76/0.98 tff(1474,plain,
% 0.76/0.98 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c1_1(a43) | c3_1(a43) | (~ndr1_0) | c0_1(a43)),
% 0.76/0.98 inference(modus_ponens,[status(thm)],[1473, 1472])).
% 0.76/0.98 tff(1475,plain,
% 0.76/0.98 (c0_1(a43)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1474, 72, 1308, 1468, 1467, 101])).
% 0.76/0.98 tff(1476,plain,
% 0.76/0.98 (c2_1(a43)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[630, 1466])).
% 0.76/0.98 tff(1477,assumption,(c0_1(a43)), introduced(assumption)).
% 0.76/0.98 tff(1478,assumption,(c2_1(a43)), introduced(assumption)).
% 0.76/0.98 tff(1479,assumption,(~c3_1(a43)), introduced(assumption)).
% 0.76/0.98 tff(1480,assumption,(hskp6), introduced(assumption)).
% 0.76/0.98 tff(1481,plain,
% 0.76/0.98 (~c2_1(a8)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[795, 1480])).
% 0.76/0.98 tff(1482,plain,
% 0.76/0.98 (~c3_1(a8)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[801, 1480])).
% 0.76/0.98 tff(1483,plain,
% 0.76/0.98 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a43) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1484,plain,
% 0.76/0.98 ((hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a8) | c3_1(a8) | (~c1_1(a8))) <=> (hskp24 | c3_1(a43) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1485,plain,
% 0.76/0.98 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a8) | c3_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a43) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 0.76/0.98 inference(monotonicity,[status(thm)],[1484])).
% 0.76/0.98 tff(1486,plain,
% 0.76/0.98 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a8) | c3_1(a8) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.98 inference(transitivity,[status(thm)],[1485, 1483])).
% 0.76/0.98 tff(1487,plain,
% 0.76/0.98 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a8) | c3_1(a8) | (~c1_1(a8)))),
% 0.76/0.98 inference(quant_inst,[status(thm)],[])).
% 0.76/0.98 tff(1488,plain,
% 0.76/0.98 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c1_1(a8)) | (~c2_1(a43)) | (~c0_1(a43))),
% 0.76/0.98 inference(modus_ponens,[status(thm)],[1487, 1486])).
% 0.76/0.98 tff(1489,plain,
% 0.76/0.98 ($false),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1488, 72, 1307, 1478, 1479, 804, 803, 1425, 857, 1477])).
% 0.76/0.98 tff(1490,plain,(c2_1(a8) | hskp24 | (~c2_1(a43)) | c3_1(a43) | c3_1(a8) | (~c0_1(a43)) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/0.98 tff(1491,plain,
% 0.76/0.98 ($false),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1490, 1482, 1481, 122, 1479, 1478, 1477, 123, 1307])).
% 0.76/0.98 tff(1492,plain,((~hskp6) | hskp18 | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | hskp30 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.76/0.98 tff(1493,plain,
% 0.76/0.98 (~hskp6),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1492, 1467, 122, 1476, 1475, 123, 1307])).
% 0.76/0.98 tff(1494,plain,
% 0.76/0.98 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | c3_1(a26))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | c3_1(a26))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1495,plain,
% 0.76/0.98 ((hskp4 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c0_1(a26)) <=> (hskp4 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | c3_1(a26))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1496,plain,
% 0.76/0.98 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c0_1(a26))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | c3_1(a26)))),
% 0.76/0.98 inference(monotonicity,[status(thm)],[1495])).
% 0.76/0.98 tff(1497,plain,
% 0.76/0.98 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c0_1(a26))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | c3_1(a26))),
% 0.76/0.98 inference(transitivity,[status(thm)],[1496, 1494])).
% 0.76/0.98 tff(1498,plain,
% 0.76/0.98 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a26) | c1_1(a26) | c0_1(a26))),
% 0.76/0.98 inference(quant_inst,[status(thm)],[])).
% 0.76/0.98 tff(1499,plain,
% 0.76/0.98 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c0_1(a26) | c1_1(a26) | (~ndr1_0) | c3_1(a26)),
% 0.76/0.98 inference(modus_ponens,[status(thm)],[1498, 1497])).
% 0.76/0.98 tff(1500,plain,
% 0.76/0.98 (c3_1(a26)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1499, 72, 1308, 678, 677, 101])).
% 0.76/0.98 tff(1501,plain,
% 0.76/0.98 (^[U: $i] : refl((hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))),
% 0.76/0.98 inference(bind,[status(th)],[])).
% 0.76/0.98 tff(1502,plain,
% 0.76/0.98 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.76/0.98 inference(quant_intro,[status(thm)],[1501])).
% 0.76/0.98 tff(1503,plain,
% 0.76/0.98 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1504,plain,
% 0.76/0.98 (^[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)) | hskp11) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp11))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) | hskp6) <=> ((hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp6))), rewrite(((hskp11 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp6) <=> (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) | hskp6) <=> (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))))),
% 0.76/0.98 inference(bind,[status(th)],[])).
% 0.76/0.98 tff(1505,plain,
% 0.76/0.98 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) | hskp6) <=> ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.76/0.98 inference(quant_intro,[status(thm)],[1504])).
% 0.76/0.98 tff(1506,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp11) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 0.76/0.98 tff(1507,plain,
% 0.76/0.98 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.76/0.98 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 0.76/0.98 tff(1508,plain,
% 0.76/0.98 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.76/0.98 inference(modus_ponens,[status(thm)],[1507, 1503])).
% 0.76/0.98 tff(1509,plain,(
% 0.76/0.98 ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.76/0.98 inference(skolemize,[status(sab)],[1508])).
% 0.76/0.98 tff(1510,plain,
% 0.76/0.98 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.76/0.98 inference(modus_ponens,[status(thm)],[1509, 1502])).
% 0.76/0.98 tff(1511,assumption,(~hskp11), introduced(assumption)).
% 0.76/0.98 tff(1512,plain,
% 0.76/0.98 (((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | c0_1(a26) | c2_1(a26) | (~ndr1_0) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp11 | hskp6 | c0_1(a26) | c2_1(a26) | (~ndr1_0) | (~c3_1(a26)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1513,plain,
% 0.76/0.98 ((hskp11 | hskp6 | (~ndr1_0) | c0_1(a26) | c2_1(a26) | (~c3_1(a26))) <=> (hskp11 | hskp6 | c0_1(a26) | c2_1(a26) | (~ndr1_0) | (~c3_1(a26)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1514,plain,
% 0.76/0.98 (((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | (~ndr1_0) | c0_1(a26) | c2_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | c0_1(a26) | c2_1(a26) | (~ndr1_0) | (~c3_1(a26))))),
% 0.76/0.98 inference(monotonicity,[status(thm)],[1513])).
% 0.76/0.98 tff(1515,plain,
% 0.76/0.98 (((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | (~ndr1_0) | c0_1(a26) | c2_1(a26) | (~c3_1(a26)))) <=> ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp11 | hskp6 | c0_1(a26) | c2_1(a26) | (~ndr1_0) | (~c3_1(a26)))),
% 0.76/0.98 inference(transitivity,[status(thm)],[1514, 1512])).
% 0.76/0.98 tff(1516,plain,
% 0.76/0.98 ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | (~ndr1_0) | c0_1(a26) | c2_1(a26) | (~c3_1(a26)))),
% 0.76/0.98 inference(quant_inst,[status(thm)],[])).
% 0.76/0.98 tff(1517,plain,
% 0.76/0.98 ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp11 | hskp6 | c0_1(a26) | c2_1(a26) | (~ndr1_0) | (~c3_1(a26))),
% 0.76/0.98 inference(modus_ponens,[status(thm)],[1516, 1515])).
% 0.76/0.98 tff(1518,plain,
% 0.76/0.98 (~c3_1(a26)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1517, 1511, 72, 724, 678, 676, 1510])).
% 0.76/0.98 tff(1519,plain,
% 0.76/0.98 ($false),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1499, 72, 1308, 678, 677, 101, 1518])).
% 0.76/0.98 tff(1520,plain,((~hskp14) | hskp4 | hskp11 | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.76/0.98 tff(1521,plain,
% 0.76/0.98 (hskp11),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1520, 675, 1308, 724])).
% 0.76/0.98 tff(1522,plain,
% 0.76/0.98 (~c3_1(a19)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[21, 1521])).
% 0.76/0.98 tff(1523,plain,
% 0.76/0.98 (c1_1(a19)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[29, 1521])).
% 0.76/0.98 tff(1524,plain,
% 0.76/0.98 (c0_1(a19)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[37, 1521])).
% 0.76/0.98 tff(1525,plain,
% 0.76/0.98 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a26) | c2_1(a26) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a26) | c2_1(a26) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a26)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1526,plain,
% 0.76/0.98 ((hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26))) <=> (hskp0 | c1_1(a26) | c2_1(a26) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a26)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1527,plain,
% 0.76/0.98 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a26) | c2_1(a26) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a26))))),
% 0.76/0.98 inference(monotonicity,[status(thm)],[1526])).
% 0.76/0.98 tff(1528,plain,
% 0.76/0.98 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a26) | c2_1(a26) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a26)))),
% 0.76/0.98 inference(transitivity,[status(thm)],[1527, 1525])).
% 0.76/0.98 tff(1529,plain,
% 0.76/0.98 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a26) | c1_1(a26) | (~c3_1(a26)))),
% 0.76/0.98 inference(quant_inst,[status(thm)],[])).
% 0.76/0.98 tff(1530,plain,
% 0.76/0.98 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a26) | c2_1(a26) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a26))),
% 0.76/0.98 inference(modus_ponens,[status(thm)],[1529, 1528])).
% 0.76/0.98 tff(1531,plain,
% 0.76/0.98 ($false),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1530, 72, 528, 1524, 1523, 677, 676, 1522, 585, 1500])).
% 0.76/0.98 tff(1532,plain,((~hskp14) | hskp0 | hskp4 | hskp6), inference(lemma,lemma(discharge,[]))).
% 0.76/0.98 tff(1533,plain,
% 0.76/0.98 (~hskp14),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1532, 1493, 1308, 528])).
% 0.76/0.98 tff(1534,plain,
% 0.76/0.98 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | (~ndr1_0) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1535,plain,
% 0.76/0.98 ((hskp18 | hskp14 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15))) <=> (hskp18 | hskp14 | (~ndr1_0) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1536,plain,
% 0.76/0.98 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15))))),
% 0.76/0.98 inference(monotonicity,[status(thm)],[1535])).
% 0.76/0.98 tff(1537,plain,
% 0.76/0.98 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | (~ndr1_0) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15)))),
% 0.76/0.98 inference(transitivity,[status(thm)],[1536, 1534])).
% 0.76/0.98 tff(1538,plain,
% 0.76/0.98 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a15) | (~c3_1(a15)) | (~c1_1(a15)))),
% 0.76/0.98 inference(quant_inst,[status(thm)],[])).
% 0.76/0.98 tff(1539,plain,
% 0.76/0.98 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | (~ndr1_0) | (~c1_1(a15)) | c2_1(a15) | (~c3_1(a15))),
% 0.76/0.98 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 0.76/0.98 tff(1540,plain,
% 0.76/0.98 ($false),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1539, 72, 122, 277, 1267, 1259, 295, 1320])).
% 0.76/0.98 tff(1541,plain,((~hskp28) | hskp18 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.76/0.98 tff(1542,plain,
% 0.76/0.98 (~hskp28),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1541, 1533, 122])).
% 0.76/0.98 tff(1543,assumption,(hskp9), introduced(assumption)).
% 0.76/0.98 tff(1544,plain,
% 0.76/0.98 (~c2_1(a12)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[977, 1543])).
% 0.76/0.98 tff(1545,plain,
% 0.76/0.98 (~c3_1(a12)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[516, 1543])).
% 0.76/0.98 tff(1546,plain,
% 0.76/0.98 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a43) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1547,plain,
% 0.76/0.98 ((hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12))) <=> (hskp24 | c3_1(a43) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1548,plain,
% 0.76/0.98 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a43) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 0.76/0.98 inference(monotonicity,[status(thm)],[1547])).
% 0.76/0.98 tff(1549,plain,
% 0.76/0.98 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.98 inference(transitivity,[status(thm)],[1548, 1546])).
% 0.76/0.98 tff(1550,plain,
% 0.76/0.98 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))),
% 0.76/0.98 inference(quant_inst,[status(thm)],[])).
% 0.76/0.98 tff(1551,plain,
% 0.76/0.98 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c2_1(a43)) | (~c0_1(a43))),
% 0.76/0.98 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 0.76/0.98 tff(1552,plain,
% 0.76/0.98 ($false),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1551, 72, 1307, 1478, 1443, 1479, 985, 586, 1425, 1477])).
% 0.76/0.98 tff(1553,plain,(c2_1(a12) | hskp24 | (~c2_1(a43)) | c3_1(a43) | c3_1(a12) | (~c0_1(a43)) | hskp19 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.76/0.98 tff(1554,plain,
% 0.76/0.98 ($false),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1553, 1545, 1544, 1478, 1479, 1397, 1477, 1319, 1307])).
% 0.76/0.98 tff(1555,plain,((~hskp9) | (~c2_1(a43)) | c3_1(a43) | hskp1 | (~c0_1(a43)) | hskp19 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.76/0.98 tff(1556,plain,
% 0.76/0.98 (~hskp9),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1555, 1397, 1479, 1478, 1477, 1319, 1307])).
% 0.76/0.98 tff(1557,plain,
% 0.76/0.98 ($false),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1412, 1556, 1397, 1401])).
% 0.76/0.98 tff(1558,plain,(hskp1 | hskp28 | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | hskp19 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.76/0.98 tff(1559,plain,
% 0.76/0.98 (hskp1),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1558, 1542, 1467, 1476, 1475, 1209, 1307])).
% 0.76/0.98 tff(1560,plain,
% 0.76/0.98 (~c2_1(a2)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[551, 1559])).
% 0.76/0.98 tff(1561,plain,
% 0.76/0.98 (c0_1(a2)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[567, 1559])).
% 0.76/0.98 tff(1562,assumption,(hskp21), introduced(assumption)).
% 0.76/0.98 tff(1563,plain,
% 0.76/0.98 (~c0_1(a42)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1135, 1562])).
% 0.76/0.98 tff(1564,assumption,(~c1_1(a43)), introduced(assumption)).
% 0.76/0.98 tff(1565,plain,
% 0.76/0.98 (c3_1(a42)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1143, 1562])).
% 0.76/0.98 tff(1566,plain,
% 0.76/0.98 (c2_1(a42)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1151, 1562])).
% 0.76/0.98 tff(1567,plain,
% 0.76/0.98 ($false),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1158, 72, 1478, 1566, 1565, 1564, 1479, 1563, 91, 1477])).
% 0.76/0.98 tff(1568,plain,((~hskp21) | (~c2_1(a43)) | c1_1(a43) | c3_1(a43) | (~c0_1(a43))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.98 tff(1569,plain,
% 0.76/0.98 (~hskp21),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1568, 1476, 1468, 1467, 1475])).
% 0.76/0.98 tff(1570,plain,
% 0.76/0.98 (c1_1(a2)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[1128, 72, 1569, 528, 1561, 1560, 1122])).
% 0.76/0.98 tff(1571,plain,
% 0.76/0.98 (c3_1(a2)),
% 0.76/0.98 inference(unit_resolution,[status(thm)],[559, 1559])).
% 0.76/0.98 tff(1572,plain,
% 0.76/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a43) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a43) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1573,plain,
% 0.76/0.98 (((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43))) <=> (c1_1(a43) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.98 inference(rewrite,[status(thm)],[])).
% 0.76/0.98 tff(1574,plain,
% 0.76/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a43) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 0.76/0.98 inference(monotonicity,[status(thm)],[1573])).
% 0.76/0.98 tff(1575,plain,
% 0.76/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a43) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.98 inference(transitivity,[status(thm)],[1574, 1572])).
% 0.76/0.98 tff(1576,plain,
% 0.76/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.98 inference(quant_inst,[status(thm)],[])).
% 0.76/0.98 tff(1577,plain,
% 0.76/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a43) | c2_1(a2) | (~ndr1_0) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c2_1(a43)) | (~c0_1(a43))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 0.76/0.99 tff(1578,plain,
% 0.76/0.99 ($false),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1577, 72, 1476, 1561, 1571, 1468, 1560, 527, 1475, 1570])).
% 0.76/0.99 tff(1579,plain,(hskp0 | hskp24 | hskp18 | hskp4 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.76/0.99 tff(1580,plain,
% 0.76/0.99 (hskp0),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1579, 1308, 122, 1307, 123])).
% 0.76/0.99 tff(1581,plain,
% 0.76/0.99 (~c0_1(a1)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[645, 1580])).
% 0.76/0.99 tff(1582,plain,
% 0.76/0.99 (^[U: $i] : refl((hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.76/0.99 inference(bind,[status(th)],[])).
% 0.76/0.99 tff(1583,plain,
% 0.76/0.99 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.99 inference(quant_intro,[status(thm)],[1582])).
% 0.76/0.99 tff(1584,plain,
% 0.76/0.99 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1585,plain,
% 0.76/0.99 (^[U: $i] : 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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp4) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp4))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp4) <=> (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.76/0.99 inference(bind,[status(th)],[])).
% 0.76/0.99 tff(1586,plain,
% 0.76/0.99 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp4) <=> ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.99 inference(quant_intro,[status(thm)],[1585])).
% 0.76/0.99 tff(1587,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 0.76/0.99 tff(1588,plain,
% 0.76/0.99 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1587, 1586])).
% 0.76/0.99 tff(1589,plain,
% 0.76/0.99 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1588, 1584])).
% 0.76/0.99 tff(1590,plain,(
% 0.76/0.99 ![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.99 inference(skolemize,[status(sab)],[1589])).
% 0.76/0.99 tff(1591,plain,
% 0.76/0.99 (![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1590, 1583])).
% 0.76/0.99 tff(1592,plain,
% 0.76/0.99 (c2_1(a1)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[661, 1580])).
% 0.76/0.99 tff(1593,plain,
% 0.76/0.99 (c1_1(a1)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[653, 1580])).
% 0.76/0.99 tff(1594,plain,
% 0.76/0.99 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp4 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp4 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1595,plain,
% 0.76/0.99 ((hskp15 | hskp4 | (~ndr1_0) | c0_1(a1) | (~c2_1(a1)) | (~c1_1(a1))) <=> (hskp15 | hskp4 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1596,plain,
% 0.76/0.99 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c0_1(a1) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp4 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))))),
% 0.76/0.99 inference(monotonicity,[status(thm)],[1595])).
% 0.76/0.99 tff(1597,plain,
% 0.76/0.99 (((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c0_1(a1) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp4 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)))),
% 0.76/0.99 inference(transitivity,[status(thm)],[1596, 1594])).
% 0.76/0.99 tff(1598,plain,
% 0.76/0.99 ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp4 | (~ndr1_0) | c0_1(a1) | (~c2_1(a1)) | (~c1_1(a1)))),
% 0.76/0.99 inference(quant_inst,[status(thm)],[])).
% 0.76/0.99 tff(1599,plain,
% 0.76/0.99 ((~![U: $i] : (hskp15 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp4 | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 0.76/0.99 tff(1600,plain,
% 0.76/0.99 (hskp15),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1599, 72, 1308, 1593, 1592, 1581, 1591])).
% 0.76/0.99 tff(1601,plain,
% 0.76/0.99 (((~hskp15) | (~c2_1(a27))) <=> ((~hskp15) | (~c2_1(a27)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1602,plain,
% 0.76/0.99 (((~c2_1(a27)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a27)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1603,axiom,((~c2_1(a27)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.76/0.99 tff(1604,plain,
% 0.76/0.99 ((~hskp15) | (~c2_1(a27))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 0.76/0.99 tff(1605,plain,
% 0.76/0.99 ((~hskp15) | (~c2_1(a27))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1604, 1601])).
% 0.76/0.99 tff(1606,plain,
% 0.76/0.99 (~c2_1(a27)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1605, 1600])).
% 0.76/0.99 tff(1607,plain,
% 0.76/0.99 (((~hskp15) | c0_1(a27)) <=> ((~hskp15) | c0_1(a27))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1608,axiom,((~hskp15) | c0_1(a27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 0.76/0.99 tff(1609,plain,
% 0.76/0.99 ((~hskp15) | c0_1(a27)),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 0.76/0.99 tff(1610,plain,
% 0.76/0.99 ((~hskp15) | c0_1(a27)),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1609, 1607])).
% 0.76/0.99 tff(1611,plain,
% 0.76/0.99 ((~hskp15) | c0_1(a27)),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1610, 1607])).
% 0.76/0.99 tff(1612,plain,
% 0.76/0.99 ((~hskp15) | c0_1(a27)),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1611, 1607])).
% 0.76/0.99 tff(1613,plain,
% 0.76/0.99 ((~hskp15) | c0_1(a27)),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1612, 1607])).
% 0.76/0.99 tff(1614,plain,
% 0.76/0.99 (c0_1(a27)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1613, 1600])).
% 0.76/0.99 tff(1615,plain,
% 0.76/0.99 (((~hskp15) | c1_1(a27)) <=> ((~hskp15) | c1_1(a27))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1616,axiom,((~hskp15) | c1_1(a27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 0.76/0.99 tff(1617,plain,
% 0.76/0.99 ((~hskp15) | c1_1(a27)),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1616, 1615])).
% 0.76/0.99 tff(1618,plain,
% 0.76/0.99 ((~hskp15) | c1_1(a27)),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1617, 1615])).
% 0.76/0.99 tff(1619,plain,
% 0.76/0.99 ((~hskp15) | c1_1(a27)),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1618, 1615])).
% 0.76/0.99 tff(1620,plain,
% 0.76/0.99 ((~hskp15) | c1_1(a27)),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1619, 1615])).
% 0.76/0.99 tff(1621,plain,
% 0.76/0.99 ((~hskp15) | c1_1(a27)),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1620, 1615])).
% 0.76/0.99 tff(1622,plain,
% 0.76/0.99 (c1_1(a27)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1621, 1600])).
% 0.76/0.99 tff(1623,assumption,(~c2_1(a27)), introduced(assumption)).
% 0.76/0.99 tff(1624,assumption,(c0_1(a27)), introduced(assumption)).
% 0.76/0.99 tff(1625,plain,
% 0.76/0.99 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | c2_1(a27) | (~ndr1_0) | (~c3_1(a27)) | (~c0_1(a27)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | c2_1(a27) | (~ndr1_0) | (~c3_1(a27)) | (~c0_1(a27)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1626,plain,
% 0.76/0.99 ((hskp22 | hskp19 | (~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27))) <=> (hskp22 | hskp19 | c2_1(a27) | (~ndr1_0) | (~c3_1(a27)) | (~c0_1(a27)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1627,plain,
% 0.76/0.99 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | c2_1(a27) | (~ndr1_0) | (~c3_1(a27)) | (~c0_1(a27))))),
% 0.76/0.99 inference(monotonicity,[status(thm)],[1626])).
% 0.76/0.99 tff(1628,plain,
% 0.76/0.99 (((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)))) <=> ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | c2_1(a27) | (~ndr1_0) | (~c3_1(a27)) | (~c0_1(a27)))),
% 0.76/0.99 inference(transitivity,[status(thm)],[1627, 1625])).
% 0.76/0.99 tff(1629,plain,
% 0.76/0.99 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp19 | (~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)))),
% 0.76/0.99 inference(quant_inst,[status(thm)],[])).
% 0.76/0.99 tff(1630,plain,
% 0.76/0.99 ((~![U: $i] : (hskp22 | hskp19 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp19 | c2_1(a27) | (~ndr1_0) | (~c3_1(a27)) | (~c0_1(a27))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1629, 1628])).
% 0.76/0.99 tff(1631,plain,
% 0.76/0.99 (hskp22 | (~c3_1(a27))),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1630, 72, 1319, 1624, 1623, 1318])).
% 0.76/0.99 tff(1632,plain,
% 0.76/0.99 (~c3_1(a27)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1631, 1])).
% 0.76/0.99 tff(1633,assumption,(c1_1(a27)), introduced(assumption)).
% 0.76/0.99 tff(1634,plain,
% 0.76/0.99 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c0_1(a27)) | (~c1_1(a27)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c0_1(a27)) | (~c1_1(a27)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1635,plain,
% 0.76/0.99 ((hskp22 | (~ndr1_0) | c3_1(a27) | c2_1(a27) | (~c1_1(a27)) | c2_1(a27) | c3_1(a27) | (~c0_1(a27))) <=> (hskp22 | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c0_1(a27)) | (~c1_1(a27)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1636,plain,
% 0.76/0.99 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a27) | c2_1(a27) | (~c1_1(a27)) | c2_1(a27) | c3_1(a27) | (~c0_1(a27)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c0_1(a27)) | (~c1_1(a27))))),
% 0.76/0.99 inference(monotonicity,[status(thm)],[1635])).
% 0.76/0.99 tff(1637,plain,
% 0.76/0.99 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a27) | c2_1(a27) | (~c1_1(a27)) | c2_1(a27) | c3_1(a27) | (~c0_1(a27)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c0_1(a27)) | (~c1_1(a27)))),
% 0.76/0.99 inference(transitivity,[status(thm)],[1636, 1634])).
% 0.76/0.99 tff(1638,plain,
% 0.76/0.99 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a27) | c2_1(a27) | (~c1_1(a27)) | c2_1(a27) | c3_1(a27) | (~c0_1(a27)))),
% 0.76/0.99 inference(quant_inst,[status(thm)],[])).
% 0.76/0.99 tff(1639,plain,
% 0.76/0.99 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c0_1(a27)) | (~c1_1(a27))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 0.76/0.99 tff(1640,plain,
% 0.76/0.99 ($false),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1639, 1, 72, 1624, 1633, 1623, 12, 1632])).
% 0.76/0.99 tff(1641,plain,(hskp22 | (~c0_1(a27)) | (~c1_1(a27)) | c2_1(a27) | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.76/0.99 tff(1642,plain,
% 0.76/0.99 (hskp22),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1641, 1622, 1614, 1606, 1209])).
% 0.76/0.99 tff(1643,plain,
% 0.76/0.99 (~c3_1(a43)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[616, 1642])).
% 0.76/0.99 tff(1644,plain,
% 0.76/0.99 (~c1_1(a43)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[622, 1642])).
% 0.76/0.99 tff(1645,plain,
% 0.76/0.99 (c2_1(a43)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[630, 1642])).
% 0.76/0.99 tff(1646,plain,
% 0.76/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c2_1(a27) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a27)) | (~c0_1(a27)) | (~c2_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a27) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a27)) | (~c0_1(a27)) | (~c2_1(a43)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1647,plain,
% 0.76/0.99 (((~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1))) <=> (c1_1(a43) | c3_1(a43) | c2_1(a27) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a27)) | (~c0_1(a27)) | (~c2_1(a43)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1648,plain,
% 0.76/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c2_1(a27) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a27)) | (~c0_1(a27)) | (~c2_1(a43))))),
% 0.76/0.99 inference(monotonicity,[status(thm)],[1647])).
% 0.76/0.99 tff(1649,plain,
% 0.76/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a27) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a27)) | (~c0_1(a27)) | (~c2_1(a43)))),
% 0.76/0.99 inference(transitivity,[status(thm)],[1648, 1646])).
% 0.76/0.99 tff(1650,plain,
% 0.76/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a27) | (~c3_1(a27)) | (~c0_1(a27)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))),
% 0.76/0.99 inference(quant_inst,[status(thm)],[])).
% 0.76/0.99 tff(1651,plain,
% 0.76/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a27) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a27)) | (~c0_1(a27)) | (~c2_1(a43))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 0.76/0.99 tff(1652,plain,
% 0.76/0.99 (~c3_1(a27)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1651, 72, 1645, 1614, 1593, 1592, 1644, 1643, 1606, 1581, 121])).
% 0.76/0.99 tff(1653,plain,
% 0.76/0.99 (c0_1(a43)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1474, 72, 1308, 1644, 1643, 101])).
% 0.76/0.99 tff(1654,plain,
% 0.76/0.99 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a43) | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c1_1(a27)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c1_1(a27)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1655,plain,
% 0.76/0.99 ((hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a27) | c3_1(a27) | (~c1_1(a27))) <=> (hskp24 | c3_1(a43) | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c1_1(a27)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1656,plain,
% 0.76/0.99 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a27) | c3_1(a27) | (~c1_1(a27)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c3_1(a43) | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c1_1(a27)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 0.76/0.99 inference(monotonicity,[status(thm)],[1655])).
% 0.76/0.99 tff(1657,plain,
% 0.76/0.99 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a27) | c3_1(a27) | (~c1_1(a27)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c1_1(a27)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.99 inference(transitivity,[status(thm)],[1656, 1654])).
% 0.76/0.99 tff(1658,plain,
% 0.76/0.99 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a27) | c3_1(a27) | (~c1_1(a27)))),
% 0.76/0.99 inference(quant_inst,[status(thm)],[])).
% 0.76/0.99 tff(1659,plain,
% 0.76/0.99 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c3_1(a43) | c2_1(a27) | (~ndr1_0) | c3_1(a27) | (~c1_1(a27)) | (~c2_1(a43)) | (~c0_1(a43))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 0.76/0.99 tff(1660,plain,
% 0.76/0.99 ($false),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1659, 72, 1307, 1645, 1622, 1643, 1606, 1425, 1653, 1652])).
% 0.76/0.99 tff(1661,plain,(hskp4 | hskp24 | hskp18 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.76/0.99 tff(1662,plain,
% 0.76/0.99 (hskp24),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1661, 1306, 122, 123])).
% 0.76/0.99 tff(1663,plain,
% 0.76/0.99 (hskp0),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1395, 1, 1319, 1327])).
% 0.76/0.99 tff(1664,plain,
% 0.76/0.99 (~c0_1(a1)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[645, 1663])).
% 0.76/0.99 tff(1665,plain,
% 0.76/0.99 (c2_1(a1)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[661, 1663])).
% 0.76/0.99 tff(1666,plain,
% 0.76/0.99 (c1_1(a1)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[653, 1663])).
% 0.76/0.99 tff(1667,plain,
% 0.76/0.99 (hskp15),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1599, 72, 1308, 1666, 1665, 1664, 1591])).
% 0.76/0.99 tff(1668,plain,
% 0.76/0.99 (~c2_1(a27)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1605, 1667])).
% 0.76/0.99 tff(1669,plain,
% 0.76/0.99 (c0_1(a27)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1613, 1667])).
% 0.76/0.99 tff(1670,plain,
% 0.76/0.99 (c1_1(a27)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1621, 1667])).
% 0.76/0.99 tff(1671,plain,
% 0.76/0.99 ($false),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1641, 1670, 1669, 1, 1668, 1319])).
% 0.76/0.99 tff(1672,plain,(hskp22 | hskp19 | hskp4 | (~hskp24)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.99 tff(1673,plain,
% 0.76/0.99 (hskp22),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1672, 1209, 1306, 1662])).
% 0.76/0.99 tff(1674,plain,
% 0.76/0.99 (~c3_1(a43)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[616, 1673])).
% 0.76/0.99 tff(1675,plain,
% 0.76/0.99 (~c1_1(a43)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[622, 1673])).
% 0.76/0.99 tff(1676,plain,
% 0.76/0.99 (c0_1(a43)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1474, 72, 1306, 1675, 1674, 101])).
% 0.76/0.99 tff(1677,plain,
% 0.76/0.99 (c2_1(a43)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[630, 1673])).
% 0.76/0.99 tff(1678,plain,
% 0.76/0.99 (~hskp21),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1568, 1676, 1675, 1674, 1677])).
% 0.76/0.99 tff(1679,plain,
% 0.76/0.99 (hskp0),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1383, 1678, 1662])).
% 0.76/0.99 tff(1680,plain,
% 0.76/0.99 (~c0_1(a1)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[645, 1679])).
% 0.76/0.99 tff(1681,plain,
% 0.76/0.99 (c2_1(a1)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[661, 1679])).
% 0.76/0.99 tff(1682,plain,
% 0.76/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1683,plain,
% 0.76/0.99 (((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a1) | (~c2_1(a1)) | (~c3_1(a1))) <=> (c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1684,plain,
% 0.76/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a1) | (~c2_1(a1)) | (~c3_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c2_1(a43)) | (~c0_1(a43))))),
% 0.76/0.99 inference(monotonicity,[status(thm)],[1683])).
% 0.76/0.99 tff(1685,plain,
% 0.76/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a1) | (~c2_1(a1)) | (~c3_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.76/0.99 inference(transitivity,[status(thm)],[1684, 1682])).
% 0.76/0.99 tff(1686,plain,
% 0.76/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c0_1(a1) | (~c2_1(a1)) | (~c3_1(a1)))),
% 0.76/0.99 inference(quant_inst,[status(thm)],[])).
% 0.76/0.99 tff(1687,plain,
% 0.76/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c2_1(a43)) | (~c0_1(a43))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1686, 1685])).
% 0.76/0.99 tff(1688,plain,
% 0.76/0.99 (~c3_1(a1)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1687, 72, 1677, 1681, 1675, 1674, 1680, 91, 1676])).
% 0.76/0.99 tff(1689,plain,
% 0.76/0.99 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 0.76/0.99 inference(bind,[status(th)],[])).
% 0.76/0.99 tff(1690,plain,
% 0.76/0.99 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.76/0.99 inference(quant_intro,[status(thm)],[1689])).
% 0.76/0.99 tff(1691,plain,
% 0.76/0.99 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1692,plain,
% 0.76/0.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~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)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 0.76/0.99 inference(bind,[status(th)],[])).
% 0.76/0.99 tff(1693,plain,
% 0.76/0.99 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.76/0.99 inference(quant_intro,[status(thm)],[1692])).
% 0.76/0.99 tff(1694,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 0.76/0.99 tff(1695,plain,
% 0.76/0.99 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1694, 1693])).
% 0.76/0.99 tff(1696,plain,
% 0.76/0.99 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1695, 1691])).
% 0.76/0.99 tff(1697,plain,(
% 0.76/0.99 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.76/0.99 inference(skolemize,[status(sab)],[1696])).
% 0.76/0.99 tff(1698,plain,
% 0.76/0.99 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1697, 1690])).
% 0.76/0.99 tff(1699,plain,
% 0.76/0.99 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a43)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1700,plain,
% 0.76/0.99 ((hskp3 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | c3_1(a1) | (~c2_1(a1))) <=> (hskp3 | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a43)))),
% 0.76/0.99 inference(rewrite,[status(thm)],[])).
% 0.76/0.99 tff(1701,plain,
% 0.76/0.99 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | c3_1(a1) | (~c2_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a43))))),
% 0.76/0.99 inference(monotonicity,[status(thm)],[1700])).
% 0.76/0.99 tff(1702,plain,
% 0.76/0.99 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | c3_1(a1) | (~c2_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a43)))),
% 0.76/0.99 inference(transitivity,[status(thm)],[1701, 1699])).
% 0.76/0.99 tff(1703,plain,
% 0.76/0.99 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | c3_1(a1) | (~c2_1(a1)))),
% 0.76/0.99 inference(quant_inst,[status(thm)],[])).
% 0.76/0.99 tff(1704,plain,
% 0.76/0.99 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c0_1(a43))),
% 0.76/0.99 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 0.76/0.99 tff(1705,plain,
% 0.76/0.99 (hskp3),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1704, 72, 1681, 1675, 1674, 1680, 1698, 1688, 1676])).
% 0.76/0.99 tff(1706,plain,
% 0.76/0.99 (~c0_1(a4)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[196, 1705])).
% 0.76/0.99 tff(1707,plain,
% 0.76/0.99 (~c1_1(a4)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[202, 1705])).
% 0.76/0.99 tff(1708,plain,
% 0.76/0.99 (c1_1(a5)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1109, 205, 204, 123, 122])).
% 0.76/0.99 tff(1709,plain,
% 0.76/0.99 (~hskp4),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[149, 1708])).
% 0.76/0.99 tff(1710,plain,
% 0.76/0.99 (c3_1(a4)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[214, 1709, 205])).
% 0.76/0.99 tff(1711,plain,
% 0.76/0.99 (hskp5),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[777, 296, 725])).
% 0.76/0.99 tff(1712,plain,
% 0.76/0.99 (~c3_1(a6)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1034, 1711])).
% 0.76/0.99 tff(1713,plain,
% 0.76/0.99 (c2_1(a6)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[255, 1711])).
% 0.76/0.99 tff(1714,plain,
% 0.76/0.99 (c0_1(a6)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[247, 1711])).
% 0.76/0.99 tff(1715,plain,
% 0.76/0.99 ($false),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[786, 72, 1714, 1713, 725, 231, 230, 1712, 205, 229, 91, 296])).
% 0.76/0.99 tff(1716,plain,((~c2_1(a4)) | (~c3_1(a4)) | (~c0_1(a3)) | (~c2_1(a3)) | c0_1(a4) | c1_1(a3)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.99 tff(1717,plain,
% 0.76/0.99 (~c2_1(a4)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1716, 1710, 173, 165, 205, 157])).
% 0.76/0.99 tff(1718,plain,
% 0.76/0.99 (hskp6),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1042, 1717, 205, 1710, 204])).
% 0.76/0.99 tff(1719,plain,
% 0.76/0.99 (~c3_1(a8)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[801, 1718])).
% 0.76/0.99 tff(1720,plain,
% 0.76/0.99 (~c2_1(a8)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[795, 1718])).
% 0.76/0.99 tff(1721,plain,
% 0.76/0.99 (c0_1(a8)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[895, 1718])).
% 0.76/0.99 tff(1722,plain,
% 0.76/0.99 (c1_1(a8)),
% 0.76/0.99 inference(unit_resolution,[status(thm)],[1058, 72, 1721, 1720, 1719, 205, 204, 881, 1717])).
% 0.76/1.00 tff(1723,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c3_1(a8) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a8)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a8) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a8)) | (~c1_1(a8)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1724,plain,
% 0.76/1.00 ((hskp0 | (~ndr1_0) | c3_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | (~c3_1(a4))) <=> (hskp0 | c3_1(a8) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a8)) | (~c1_1(a8)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1725,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c3_1(a8) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a8)) | (~c1_1(a8))))),
% 0.76/1.00 inference(monotonicity,[status(thm)],[1724])).
% 0.76/1.00 tff(1726,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | (~c3_1(a4)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a8) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a8)) | (~c1_1(a8)))),
% 0.76/1.00 inference(transitivity,[status(thm)],[1725, 1723])).
% 0.76/1.00 tff(1727,plain,
% 0.76/1.00 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a8) | (~c1_1(a8)) | (~c0_1(a8)) | c2_1(a4) | c1_1(a4) | (~c3_1(a4)))),
% 0.76/1.00 inference(quant_inst,[status(thm)],[])).
% 0.76/1.00 tff(1728,plain,
% 0.76/1.00 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a8) | c1_1(a4) | (~ndr1_0) | c2_1(a4) | (~c3_1(a4)) | (~c0_1(a8)) | (~c1_1(a8))),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1727, 1726])).
% 0.76/1.00 tff(1729,plain,
% 0.76/1.00 (hskp0),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1728, 72, 1721, 1710, 1719, 204, 585, 1717, 1722])).
% 0.76/1.00 tff(1730,plain,
% 0.76/1.00 (~c0_1(a1)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[645, 1729])).
% 0.76/1.00 tff(1731,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a4) | c1_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a4) | c1_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1732,plain,
% 0.76/1.00 ((hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4) | c1_1(a4) | c0_1(a4)) <=> (hskp1 | c0_1(a4) | c1_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1733,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a4) | c1_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4)))),
% 0.76/1.00 inference(monotonicity,[status(thm)],[1732])).
% 0.76/1.00 tff(1734,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4) | c1_1(a4) | c0_1(a4))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a4) | c1_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4))),
% 0.76/1.00 inference(transitivity,[status(thm)],[1733, 1731])).
% 0.76/1.00 tff(1735,plain,
% 0.76/1.00 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4) | c1_1(a4) | c0_1(a4))),
% 0.76/1.00 inference(quant_inst,[status(thm)],[])).
% 0.76/1.00 tff(1736,plain,
% 0.76/1.00 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a4) | c1_1(a4) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | c2_1(a4)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 0.76/1.00 tff(1737,plain,
% 0.76/1.00 (hskp1),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1736, 72, 173, 165, 205, 204, 157, 674, 1717])).
% 0.76/1.00 tff(1738,plain,
% 0.76/1.00 (~c2_1(a2)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[551, 1737])).
% 0.76/1.00 tff(1739,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c1_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c1_1(a8)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1740,plain,
% 0.76/1.00 ((hskp22 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8))) <=> (hskp22 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c1_1(a8)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1741,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c1_1(a8))))),
% 0.76/1.00 inference(monotonicity,[status(thm)],[1740])).
% 0.76/1.00 tff(1742,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c1_1(a8)))),
% 0.76/1.00 inference(transitivity,[status(thm)],[1741, 1739])).
% 0.76/1.00 tff(1743,plain,
% 0.76/1.00 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a8) | c2_1(a8) | (~c1_1(a8)) | c2_1(a8) | c3_1(a8) | (~c0_1(a8)))),
% 0.76/1.00 inference(quant_inst,[status(thm)],[])).
% 0.76/1.00 tff(1744,plain,
% 0.76/1.00 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a8) | c3_1(a8) | (~ndr1_0) | (~c0_1(a8)) | (~c1_1(a8))),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 0.76/1.00 tff(1745,plain,
% 0.76/1.00 (hskp22),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1744, 72, 1721, 1720, 1719, 12, 1722])).
% 0.76/1.00 tff(1746,plain,
% 0.76/1.00 (~c3_1(a43)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[616, 1745])).
% 0.76/1.00 tff(1747,plain,
% 0.76/1.00 (~c1_1(a43)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[622, 1745])).
% 0.76/1.00 tff(1748,plain,
% 0.76/1.00 (c2_1(a1)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[661, 1729])).
% 0.76/1.00 tff(1749,plain,
% 0.76/1.00 (c1_1(a1)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[653, 1729])).
% 0.76/1.00 tff(1750,plain,
% 0.76/1.00 (c3_1(a2)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[559, 1737])).
% 0.76/1.00 tff(1751,plain,
% 0.76/1.00 (c0_1(a2)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[567, 1737])).
% 0.76/1.00 tff(1752,plain,
% 0.76/1.00 (c2_1(a43)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[630, 1745])).
% 0.76/1.00 tff(1753,plain,
% 0.76/1.00 ($false),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[708, 72, 1752, 1751, 1750, 1749, 1748, 1747, 1746, 1738, 1730, 121])).
% 0.76/1.00 tff(1754,plain,(c0_1(a4) | c1_1(a4) | hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/1.00 tff(1755,plain,
% 0.76/1.00 ($false),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1754, 1707, 1706, 123, 122])).
% 0.76/1.00 tff(1756,plain,(hskp30 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/1.00 tff(1757,plain,
% 0.76/1.00 (hskp30),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1756, 122])).
% 0.76/1.00 tff(1758,plain,
% 0.76/1.00 (((~hskp30) | c0_1(a33)) <=> ((~hskp30) | c0_1(a33))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1759,axiom,((~hskp30) | c0_1(a33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.76/1.00 tff(1760,plain,
% 0.76/1.00 ((~hskp30) | c0_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 0.76/1.00 tff(1761,plain,
% 0.76/1.00 ((~hskp30) | c0_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1760, 1758])).
% 0.76/1.00 tff(1762,plain,
% 0.76/1.00 ((~hskp30) | c0_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1761, 1758])).
% 0.76/1.00 tff(1763,plain,
% 0.76/1.00 ((~hskp30) | c0_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1762, 1758])).
% 0.76/1.00 tff(1764,plain,
% 0.76/1.00 ((~hskp30) | c0_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1763, 1758])).
% 0.76/1.00 tff(1765,plain,
% 0.76/1.00 (c0_1(a33)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1764, 1757])).
% 0.76/1.00 tff(1766,plain,
% 0.76/1.00 (((~hskp30) | c3_1(a33)) <=> ((~hskp30) | c3_1(a33))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1767,axiom,((~hskp30) | c3_1(a33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.76/1.00 tff(1768,plain,
% 0.76/1.00 ((~hskp30) | c3_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1767, 1766])).
% 0.76/1.00 tff(1769,plain,
% 0.76/1.00 ((~hskp30) | c3_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1768, 1766])).
% 0.76/1.00 tff(1770,plain,
% 0.76/1.00 ((~hskp30) | c3_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1769, 1766])).
% 0.76/1.00 tff(1771,plain,
% 0.76/1.00 ((~hskp30) | c3_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1770, 1766])).
% 0.76/1.00 tff(1772,plain,
% 0.76/1.00 ((~hskp30) | c3_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1771, 1766])).
% 0.76/1.00 tff(1773,plain,
% 0.76/1.00 (c3_1(a33)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1772, 1757])).
% 0.76/1.00 tff(1774,plain,
% 0.76/1.00 (((~hskp30) | c2_1(a33)) <=> ((~hskp30) | c2_1(a33))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1775,axiom,((~hskp30) | c2_1(a33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.76/1.00 tff(1776,plain,
% 0.76/1.00 ((~hskp30) | c2_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 0.76/1.00 tff(1777,plain,
% 0.76/1.00 ((~hskp30) | c2_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1776, 1774])).
% 0.76/1.00 tff(1778,plain,
% 0.76/1.00 ((~hskp30) | c2_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1777, 1774])).
% 0.76/1.00 tff(1779,plain,
% 0.76/1.00 ((~hskp30) | c2_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1778, 1774])).
% 0.76/1.00 tff(1780,plain,
% 0.76/1.00 ((~hskp30) | c2_1(a33)),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1779, 1774])).
% 0.76/1.00 tff(1781,plain,
% 0.76/1.00 (c2_1(a33)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1780, 1757])).
% 0.76/1.00 tff(1782,assumption,(c1_1(a33)), introduced(assumption)).
% 0.76/1.00 tff(1783,assumption,(c3_1(a33)), introduced(assumption)).
% 0.76/1.00 tff(1784,assumption,(c2_1(a33)), introduced(assumption)).
% 0.76/1.00 tff(1785,assumption,(c0_1(a33)), introduced(assumption)).
% 0.76/1.00 tff(1786,plain,
% 0.76/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1787,plain,
% 0.76/1.00 (((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33))) <=> ((~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1788,plain,
% 0.76/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33))))),
% 0.76/1.00 inference(monotonicity,[status(thm)],[1787])).
% 0.76/1.00 tff(1789,plain,
% 0.76/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)))),
% 0.76/1.00 inference(transitivity,[status(thm)],[1788, 1786])).
% 0.76/1.00 tff(1790,plain,
% 0.76/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)))),
% 0.76/1.00 inference(quant_inst,[status(thm)],[])).
% 0.76/1.00 tff(1791,plain,
% 0.76/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33))),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1790, 1789])).
% 0.76/1.00 tff(1792,plain,
% 0.76/1.00 ($false),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1791, 72, 1785, 1784, 1783, 340, 1782])).
% 0.76/1.00 tff(1793,plain,((~c1_1(a33)) | (~c0_1(a33)) | (~c2_1(a33)) | (~c3_1(a33))), inference(lemma,lemma(discharge,[]))).
% 0.76/1.00 tff(1794,plain,
% 0.76/1.00 (~c1_1(a33)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1793, 1765, 1781, 1773])).
% 0.76/1.00 tff(1795,plain,
% 0.76/1.00 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1796,plain,
% 0.76/1.00 ((hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33))) <=> (hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1797,plain,
% 0.76/1.00 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33))))),
% 0.76/1.00 inference(monotonicity,[status(thm)],[1796])).
% 0.76/1.00 tff(1798,plain,
% 0.76/1.00 (((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)))) <=> ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 0.76/1.00 inference(transitivity,[status(thm)],[1797, 1795])).
% 0.76/1.00 tff(1799,plain,
% 0.76/1.00 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)))),
% 0.76/1.00 inference(quant_inst,[status(thm)],[])).
% 0.76/1.00 tff(1800,plain,
% 0.76/1.00 ((~![U: $i] : (hskp1 | hskp0 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp1 | hskp0 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33))),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1799, 1798])).
% 0.76/1.00 tff(1801,plain,
% 0.76/1.00 (hskp1 | hskp0 | c1_1(a33)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1800, 72, 1781, 1773, 538])).
% 0.76/1.00 tff(1802,plain,
% 0.76/1.00 (hskp0),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1801, 1397, 1794])).
% 0.76/1.00 tff(1803,plain,
% 0.76/1.00 (c2_1(a1)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[661, 1802])).
% 0.76/1.00 tff(1804,plain,
% 0.76/1.00 (c1_1(a1)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[653, 1802])).
% 0.76/1.00 tff(1805,assumption,(~c1_1(a33)), introduced(assumption)).
% 0.76/1.00 tff(1806,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1807,plain,
% 0.76/1.00 ((hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a26) | c1_1(a26) | c0_1(a26)) <=> (hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1808,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a26) | c1_1(a26) | c0_1(a26))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33))))),
% 0.76/1.00 inference(monotonicity,[status(thm)],[1807])).
% 0.76/1.00 tff(1809,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a26) | c1_1(a26) | c0_1(a26))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))),
% 0.76/1.00 inference(transitivity,[status(thm)],[1808, 1806])).
% 0.76/1.00 tff(1810,plain,
% 0.76/1.00 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a26) | c1_1(a26) | c0_1(a26))),
% 0.76/1.00 inference(quant_inst,[status(thm)],[])).
% 0.76/1.00 tff(1811,plain,
% 0.76/1.00 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a26) | c1_1(a26) | c2_1(a26) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33))),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1810, 1809])).
% 0.76/1.00 tff(1812,plain,
% 0.76/1.00 ($false),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1811, 72, 1397, 1785, 1784, 678, 677, 676, 674, 1805])).
% 0.76/1.00 tff(1813,plain,((~hskp14) | hskp1 | (~c0_1(a33)) | (~c2_1(a33)) | c1_1(a33)), inference(lemma,lemma(discharge,[]))).
% 0.76/1.00 tff(1814,plain,
% 0.76/1.00 (~hskp14),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1813, 1397, 1765, 1781, 1794])).
% 0.76/1.00 tff(1815,assumption,(hskp25), introduced(assumption)).
% 0.76/1.00 tff(1816,plain,
% 0.76/1.00 (~c2_1(a64)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[422, 1815])).
% 0.76/1.00 tff(1817,plain,
% 0.76/1.00 (c3_1(a64)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[430, 1815])).
% 0.76/1.00 tff(1818,plain,
% 0.76/1.00 (c1_1(a64)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[438, 1815])).
% 0.76/1.00 tff(1819,plain,
% 0.76/1.00 ($false),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[445, 72, 122, 277, 1818, 1817, 1816, 295])).
% 0.76/1.00 tff(1820,plain,((~hskp25) | hskp18 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.76/1.00 tff(1821,plain,
% 0.76/1.00 (~hskp25),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1820, 1814, 122])).
% 0.76/1.00 tff(1822,assumption,(~hskp25), introduced(assumption)).
% 0.76/1.00 tff(1823,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a1)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a1)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1824,plain,
% 0.76/1.00 ((hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a1)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1825,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a1))))),
% 0.76/1.00 inference(monotonicity,[status(thm)],[1824])).
% 0.76/1.00 tff(1826,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a1)))),
% 0.76/1.00 inference(transitivity,[status(thm)],[1825, 1823])).
% 0.76/1.00 tff(1827,plain,
% 0.76/1.00 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | (~c1_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 0.76/1.00 inference(quant_inst,[status(thm)],[])).
% 0.76/1.00 tff(1828,plain,
% 0.76/1.00 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | (~ndr1_0) | (~c2_1(a1)) | (~c3_1(a1)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a1))),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1827, 1826])).
% 0.76/1.00 tff(1829,plain,
% 0.76/1.00 (hskp19 | (~c3_1(a1))),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1828, 72, 1784, 1783, 699, 698, 143, 1805])).
% 0.76/1.00 tff(1830,plain,
% 0.76/1.00 (~c3_1(a1)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1829, 1319])).
% 0.76/1.00 tff(1831,plain,
% 0.76/1.00 (((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp25 | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1832,plain,
% 0.76/1.00 ((hskp27 | hskp25 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1))) <=> (hskp27 | hskp25 | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1833,plain,
% 0.76/1.00 (((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1))))),
% 0.76/1.00 inference(monotonicity,[status(thm)],[1832])).
% 0.76/1.00 tff(1834,plain,
% 0.76/1.00 (((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)))) <=> ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp25 | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1)))),
% 0.76/1.00 inference(transitivity,[status(thm)],[1833, 1831])).
% 0.76/1.00 tff(1835,plain,
% 0.76/1.00 ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp27 | hskp25 | (~ndr1_0) | c3_1(a1) | (~c2_1(a1)) | (~c1_1(a1)))),
% 0.76/1.00 inference(quant_inst,[status(thm)],[])).
% 0.76/1.00 tff(1836,plain,
% 0.76/1.00 ((~![U: $i] : (hskp27 | hskp25 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp27 | hskp25 | (~ndr1_0) | (~c2_1(a1)) | c3_1(a1) | (~c1_1(a1))),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 0.76/1.00 tff(1837,plain,
% 0.76/1.00 (hskp27 | hskp25 | c3_1(a1)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1836, 72, 699, 698, 409])).
% 0.76/1.00 tff(1838,plain,
% 0.76/1.00 (hskp27),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1837, 1830, 1822])).
% 0.76/1.00 tff(1839,plain,
% 0.76/1.00 (c3_1(a10)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[363, 1838])).
% 0.76/1.00 tff(1840,plain,
% 0.76/1.00 (c2_1(a10)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[371, 1838])).
% 0.76/1.00 tff(1841,plain,
% 0.76/1.00 (c1_1(a10)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[379, 1838])).
% 0.76/1.00 tff(1842,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1843,plain,
% 0.76/1.00 ((hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33))) <=> (hskp19 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1844,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10))))),
% 0.76/1.00 inference(monotonicity,[status(thm)],[1843])).
% 0.76/1.00 tff(1845,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10)))),
% 0.76/1.00 inference(transitivity,[status(thm)],[1844, 1842])).
% 0.76/1.00 tff(1846,plain,
% 0.76/1.00 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a10)) | (~c3_1(a10)) | (~c1_1(a10)) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)))),
% 0.76/1.00 inference(quant_inst,[status(thm)],[])).
% 0.76/1.00 tff(1847,plain,
% 0.76/1.00 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | (~c1_1(a10)) | (~c2_1(a10)) | (~c3_1(a10))),
% 0.76/1.00 inference(modus_ponens,[status(thm)],[1846, 1845])).
% 0.76/1.00 tff(1848,plain,
% 0.76/1.00 ($false),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1847, 72, 1319, 1784, 1783, 1841, 1840, 1839, 143, 1805])).
% 0.76/1.00 tff(1849,plain,(hskp19 | (~c2_1(a33)) | (~c3_1(a33)) | c1_1(a33) | hskp25 | (~c1_1(a1)) | (~c2_1(a1))), inference(lemma,lemma(discharge,[]))).
% 0.76/1.00 tff(1850,plain,
% 0.76/1.00 (hskp19),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1849, 1821, 1773, 1794, 1781, 1804, 1803])).
% 0.76/1.00 tff(1851,plain,
% 0.76/1.00 (~c2_1(a36)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1193, 1850])).
% 0.76/1.00 tff(1852,plain,
% 0.76/1.00 (~c1_1(a36)),
% 0.76/1.00 inference(unit_resolution,[status(thm)],[1199, 1850])).
% 0.76/1.00 tff(1853,plain,
% 0.76/1.00 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a36))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a36))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.00 tff(1854,plain,
% 0.76/1.00 ((hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a36) | c1_1(a36) | c0_1(a36)) <=> (hskp1 | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a36))),
% 0.76/1.00 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1855,plain,
% 0.76/1.01 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a36) | c1_1(a36) | c0_1(a36))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a36)))),
% 0.76/1.01 inference(monotonicity,[status(thm)],[1854])).
% 0.76/1.01 tff(1856,plain,
% 0.76/1.01 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a36) | c1_1(a36) | c0_1(a36))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a36))),
% 0.76/1.01 inference(transitivity,[status(thm)],[1855, 1853])).
% 0.76/1.01 tff(1857,plain,
% 0.76/1.01 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c2_1(a36) | c1_1(a36) | c0_1(a36))),
% 0.76/1.01 inference(quant_inst,[status(thm)],[])).
% 0.76/1.01 tff(1858,plain,
% 0.76/1.01 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a36)),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1857, 1856])).
% 0.76/1.01 tff(1859,plain,
% 0.76/1.01 (c0_1(a36)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1858, 72, 1397, 1765, 1781, 1852, 1851, 674, 1794])).
% 0.76/1.01 tff(1860,plain,
% 0.76/1.01 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(1861,plain,
% 0.76/1.01 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[1860])).
% 0.76/1.01 tff(1862,plain,
% 0.76/1.01 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1863,plain,
% 0.76/1.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | 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)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(1864,plain,
% 0.76/1.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[1863])).
% 0.76/1.01 tff(1865,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 0.76/1.01 tff(1866,plain,
% 0.76/1.01 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1865, 1864])).
% 0.76/1.01 tff(1867,plain,
% 0.76/1.01 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1866, 1862])).
% 0.76/1.01 tff(1868,plain,(
% 0.76/1.01 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.76/1.01 inference(skolemize,[status(sab)],[1867])).
% 0.76/1.01 tff(1869,plain,
% 0.76/1.01 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1868, 1861])).
% 0.76/1.01 tff(1870,plain,
% 0.76/1.01 (~c3_1(a36)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1187, 1850])).
% 0.76/1.01 tff(1871,plain,
% 0.76/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp17 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1872,plain,
% 0.76/1.01 ((hskp17 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | c3_1(a36)) <=> (hskp17 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1873,plain,
% 0.76/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | c3_1(a36))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36))))),
% 0.76/1.01 inference(monotonicity,[status(thm)],[1872])).
% 0.76/1.01 tff(1874,plain,
% 0.76/1.01 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | c3_1(a36))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp17 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 0.76/1.01 inference(transitivity,[status(thm)],[1873, 1871])).
% 0.76/1.01 tff(1875,plain,
% 0.76/1.01 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp17 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | c3_1(a36))),
% 0.76/1.01 inference(quant_inst,[status(thm)],[])).
% 0.76/1.01 tff(1876,plain,
% 0.76/1.01 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp17 | c1_1(a36) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 0.76/1.01 tff(1877,plain,
% 0.76/1.01 (hskp17),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1876, 72, 1852, 1851, 1870, 1869, 1859])).
% 0.76/1.01 tff(1878,plain,
% 0.76/1.01 (((~hskp17) | (~c2_1(a32))) <=> ((~hskp17) | (~c2_1(a32)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1879,plain,
% 0.76/1.01 (((~c2_1(a32)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a32)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1880,axiom,((~c2_1(a32)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.76/1.01 tff(1881,plain,
% 0.76/1.01 ((~hskp17) | (~c2_1(a32))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1880, 1879])).
% 0.76/1.01 tff(1882,plain,
% 0.76/1.01 ((~hskp17) | (~c2_1(a32))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1881, 1878])).
% 0.76/1.01 tff(1883,plain,
% 0.76/1.01 (~c2_1(a32)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1882, 1877])).
% 0.76/1.01 tff(1884,plain,
% 0.76/1.01 (((~hskp17) | c3_1(a32)) <=> ((~hskp17) | c3_1(a32))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1885,axiom,((~hskp17) | c3_1(a32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 0.76/1.01 tff(1886,plain,
% 0.76/1.01 ((~hskp17) | c3_1(a32)),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 0.76/1.01 tff(1887,plain,
% 0.76/1.01 ((~hskp17) | c3_1(a32)),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1886, 1884])).
% 0.76/1.01 tff(1888,plain,
% 0.76/1.01 ((~hskp17) | c3_1(a32)),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1887, 1884])).
% 0.76/1.01 tff(1889,plain,
% 0.76/1.01 ((~hskp17) | c3_1(a32)),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1888, 1884])).
% 0.76/1.01 tff(1890,plain,
% 0.76/1.01 ((~hskp17) | c3_1(a32)),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1889, 1884])).
% 0.76/1.01 tff(1891,plain,
% 0.76/1.01 (c3_1(a32)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1890, 1877])).
% 0.76/1.01 tff(1892,plain,
% 0.76/1.01 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | c2_1(a32) | (~ndr1_0) | (~c3_1(a32)) | (~c1_1(a32)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c2_1(a32) | (~ndr1_0) | (~c3_1(a32)) | (~c1_1(a32)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1893,plain,
% 0.76/1.01 ((hskp18 | hskp14 | (~ndr1_0) | c2_1(a32) | (~c3_1(a32)) | (~c1_1(a32))) <=> (hskp18 | hskp14 | c2_1(a32) | (~ndr1_0) | (~c3_1(a32)) | (~c1_1(a32)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1894,plain,
% 0.76/1.01 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a32) | (~c3_1(a32)) | (~c1_1(a32)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | c2_1(a32) | (~ndr1_0) | (~c3_1(a32)) | (~c1_1(a32))))),
% 0.76/1.01 inference(monotonicity,[status(thm)],[1893])).
% 0.76/1.01 tff(1895,plain,
% 0.76/1.01 (((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a32) | (~c3_1(a32)) | (~c1_1(a32)))) <=> ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c2_1(a32) | (~ndr1_0) | (~c3_1(a32)) | (~c1_1(a32)))),
% 0.76/1.01 inference(transitivity,[status(thm)],[1894, 1892])).
% 0.76/1.01 tff(1896,plain,
% 0.76/1.01 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp14 | (~ndr1_0) | c2_1(a32) | (~c3_1(a32)) | (~c1_1(a32)))),
% 0.76/1.01 inference(quant_inst,[status(thm)],[])).
% 0.76/1.01 tff(1897,plain,
% 0.76/1.01 ((~![U: $i] : (hskp18 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp14 | c2_1(a32) | (~ndr1_0) | (~c3_1(a32)) | (~c1_1(a32))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 0.76/1.01 tff(1898,plain,
% 0.76/1.01 (~c1_1(a32)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1897, 72, 122, 1814, 1891, 1883, 295])).
% 0.76/1.01 tff(1899,plain,
% 0.76/1.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(1900,plain,
% 0.76/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | 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)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[1899])).
% 0.76/1.01 tff(1901,plain,
% 0.76/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | 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)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1902,plain,
% 0.76/1.01 (^[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)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(1903,plain,
% 0.76/1.01 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[1902])).
% 0.76/1.01 tff(1904,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 0.76/1.01 tff(1905,plain,
% 0.76/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1904, 1903])).
% 0.76/1.01 tff(1906,plain,
% 0.76/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1905, 1901])).
% 0.76/1.01 tff(1907,plain,(
% 0.76/1.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/1.01 inference(skolemize,[status(sab)],[1906])).
% 0.76/1.01 tff(1908,plain,
% 0.76/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1907, 1900])).
% 0.76/1.01 tff(1909,plain,
% 0.76/1.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(1910,plain,
% 0.76/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[1909])).
% 0.76/1.01 tff(1911,plain,
% 0.76/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1912,plain,
% 0.76/1.01 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(1913,plain,
% 0.76/1.01 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[1912])).
% 0.76/1.01 tff(1914,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 0.76/1.01 tff(1915,plain,
% 0.76/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 0.76/1.01 tff(1916,plain,
% 0.76/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1915, 1911])).
% 0.76/1.01 tff(1917,plain,(
% 0.76/1.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.76/1.01 inference(skolemize,[status(sab)],[1916])).
% 0.76/1.01 tff(1918,plain,
% 0.76/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1917, 1910])).
% 0.76/1.01 tff(1919,plain,
% 0.76/1.01 (~c0_1(a1)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[645, 1802])).
% 0.76/1.01 tff(1920,plain,
% 0.76/1.01 (~hskp28),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1541, 1814, 122])).
% 0.76/1.01 tff(1921,plain,
% 0.76/1.01 (hskp9),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1412, 1920, 1397])).
% 0.76/1.01 tff(1922,plain,
% 0.76/1.01 (~c2_1(a12)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[977, 1921])).
% 0.76/1.01 tff(1923,plain,
% 0.76/1.01 (c1_1(a12)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[510, 1921])).
% 0.76/1.01 tff(1924,plain,
% 0.76/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a36) | c3_1(a36) | c2_1(a12) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a12) | (~c1_1(a12)) | (~c0_1(a36)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a36) | c3_1(a36) | c2_1(a12) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a12) | (~c1_1(a12)) | (~c0_1(a36)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1925,plain,
% 0.76/1.01 (((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12))) <=> (c1_1(a36) | c3_1(a36) | c2_1(a12) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a12) | (~c1_1(a12)) | (~c0_1(a36)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1926,plain,
% 0.76/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a36) | c3_1(a36) | c2_1(a12) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a12) | (~c1_1(a12)) | (~c0_1(a36))))),
% 0.76/1.01 inference(monotonicity,[status(thm)],[1925])).
% 0.76/1.01 tff(1927,plain,
% 0.76/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a36) | c3_1(a36) | c2_1(a12) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a12) | (~c1_1(a12)) | (~c0_1(a36)))),
% 0.76/1.01 inference(transitivity,[status(thm)],[1926, 1924])).
% 0.76/1.01 tff(1928,plain,
% 0.76/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a12) | c0_1(a12) | (~c1_1(a12)))),
% 0.76/1.01 inference(quant_inst,[status(thm)],[])).
% 0.76/1.01 tff(1929,plain,
% 0.76/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a36) | c3_1(a36) | c2_1(a12) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | c0_1(a12) | (~c1_1(a12)) | (~c0_1(a36))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1928, 1927])).
% 0.76/1.01 tff(1930,plain,
% 0.76/1.01 (c0_1(a12)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1929, 72, 1923, 1804, 1803, 1852, 1870, 1922, 1919, 1918, 1859])).
% 0.76/1.01 tff(1931,plain,
% 0.76/1.01 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(1932,plain,
% 0.76/1.01 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[1931])).
% 0.76/1.01 tff(1933,plain,
% 0.76/1.01 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1934,plain,
% 0.76/1.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~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))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~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))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~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))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.76/1.01 inference(bind,[status(th)],[])).
% 0.76/1.01 tff(1935,plain,
% 0.76/1.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.76/1.01 inference(quant_intro,[status(thm)],[1934])).
% 0.76/1.01 tff(1936,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 0.76/1.01 tff(1937,plain,
% 0.76/1.01 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 0.76/1.01 tff(1938,plain,
% 0.76/1.01 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1937, 1933])).
% 0.76/1.01 tff(1939,plain,(
% 0.76/1.01 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.76/1.01 inference(skolemize,[status(sab)],[1938])).
% 0.76/1.01 tff(1940,plain,
% 0.76/1.01 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1939, 1932])).
% 0.76/1.01 tff(1941,plain,
% 0.76/1.01 (~c3_1(a12)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[516, 1921])).
% 0.76/1.01 tff(1942,plain,
% 0.76/1.01 (hskp1 | hskp0 | c1_1(a33)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1800, 72, 1784, 1783, 538])).
% 0.76/1.01 tff(1943,plain,
% 0.76/1.01 (c1_1(a33)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1942, 1397, 528])).
% 0.76/1.01 tff(1944,plain,
% 0.76/1.01 (hskp22),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1465, 528, 1319])).
% 0.76/1.01 tff(1945,plain,
% 0.76/1.01 (c2_1(a43)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[630, 1944])).
% 0.76/1.01 tff(1946,plain,
% 0.76/1.01 (~c3_1(a43)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[616, 1944])).
% 0.76/1.01 tff(1947,plain,
% 0.76/1.01 (hskp28),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1558, 1397, 1477, 1946, 1945, 1319, 1307])).
% 0.76/1.01 tff(1948,plain,
% 0.76/1.01 (c3_1(a15)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1258, 1947])).
% 0.76/1.01 tff(1949,plain,
% 0.76/1.01 (c1_1(a15)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1266, 1947])).
% 0.76/1.01 tff(1950,plain,
% 0.76/1.01 (c0_1(a15)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1274, 1947])).
% 0.76/1.01 tff(1951,plain,
% 0.76/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1952,plain,
% 0.76/1.01 (((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33))) <=> ((~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1953,plain,
% 0.76/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15))))),
% 0.76/1.01 inference(monotonicity,[status(thm)],[1952])).
% 0.76/1.01 tff(1954,plain,
% 0.76/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)))),
% 0.76/1.01 inference(transitivity,[status(thm)],[1953, 1951])).
% 0.76/1.01 tff(1955,plain,
% 0.76/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15)) | (~c1_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)))),
% 0.76/1.01 inference(quant_inst,[status(thm)],[])).
% 0.76/1.01 tff(1956,plain,
% 0.76/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c2_1(W)) | (~c0_1(W)))) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c1_1(a33)) | (~c1_1(a15)) | (~c3_1(a15)) | (~c0_1(a15))),
% 0.76/1.01 inference(modus_ponens,[status(thm)],[1955, 1954])).
% 0.76/1.01 tff(1957,plain,
% 0.76/1.01 ($false),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1956, 72, 1785, 1784, 1783, 1950, 1949, 1948, 340, 1943])).
% 0.76/1.01 tff(1958,plain,(hskp1 | (~c0_1(a33)) | (~c2_1(a33)) | (~c3_1(a33)) | hskp0 | (~c0_1(a43)) | hskp19 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.76/1.01 tff(1959,plain,
% 0.76/1.01 (hskp1),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1958, 1477, 1784, 1783, 528, 1785, 1319, 1307])).
% 0.76/1.01 tff(1960,plain,
% 0.76/1.01 (~c2_1(a2)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[551, 1959])).
% 0.76/1.01 tff(1961,plain,
% 0.76/1.01 (c0_1(a2)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[567, 1959])).
% 0.76/1.01 tff(1962,plain,
% 0.76/1.01 (~c1_1(a43)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[622, 1944])).
% 0.76/1.01 tff(1963,plain,
% 0.76/1.01 (~hskp21),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1568, 1477, 1962, 1946, 1945])).
% 0.76/1.01 tff(1964,plain,
% 0.76/1.01 (c1_1(a2)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1128, 72, 1963, 528, 1961, 1960, 1122])).
% 0.76/1.01 tff(1965,plain,
% 0.76/1.01 (c3_1(a2)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[559, 1959])).
% 0.76/1.01 tff(1966,plain,
% 0.76/1.01 ($false),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1577, 72, 1945, 1961, 1965, 1962, 1960, 527, 1477, 1964])).
% 0.76/1.01 tff(1967,plain,((~c0_1(a43)) | hskp0 | (~c2_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | hskp19 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.76/1.01 tff(1968,plain,
% 0.76/1.01 (~c0_1(a43)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1967, 528, 1784, 1783, 1785, 1319, 1307])).
% 0.76/1.01 tff(1969,plain,
% 0.76/1.01 (hskp4 | c0_1(a43)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1474, 72, 1962, 1946, 101])).
% 0.76/1.01 tff(1970,plain,
% 0.76/1.01 (hskp4),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[1969, 1968])).
% 0.76/1.01 tff(1971,plain,
% 0.76/1.01 (~c1_1(a5)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[149, 1970])).
% 0.76/1.01 tff(1972,plain,
% 0.76/1.01 (c3_1(a5)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[180, 1970])).
% 0.76/1.01 tff(1973,plain,
% 0.76/1.01 (c2_1(a5)),
% 0.76/1.01 inference(unit_resolution,[status(thm)],[188, 1970])).
% 0.76/1.01 tff(1974,plain,
% 0.76/1.01 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a5) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a5) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a33)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1975,plain,
% 0.76/1.01 ((hskp19 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5))) <=> (hskp19 | c1_1(a5) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a33)))),
% 0.76/1.01 inference(rewrite,[status(thm)],[])).
% 0.76/1.01 tff(1976,plain,
% 0.76/1.01 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a5) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a33))))),
% 0.76/1.02 inference(monotonicity,[status(thm)],[1975])).
% 0.76/1.02 tff(1977,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a5) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a33)))),
% 0.76/1.02 inference(transitivity,[status(thm)],[1976, 1974])).
% 0.76/1.02 tff(1978,plain,
% 0.76/1.02 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c1_1(a33)) | c1_1(a5) | (~c3_1(a5)) | (~c2_1(a5)))),
% 0.76/1.02 inference(quant_inst,[status(thm)],[])).
% 0.76/1.02 tff(1979,plain,
% 0.76/1.02 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a5) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c2_1(a5)) | (~c3_1(a5)) | (~c1_1(a33))),
% 0.76/1.02 inference(modus_ponens,[status(thm)],[1978, 1977])).
% 0.76/1.02 tff(1980,plain,
% 0.76/1.02 (~c1_1(a33)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1979, 72, 1319, 1784, 1783, 1973, 1972, 1971, 143])).
% 0.76/1.02 tff(1981,plain,
% 0.76/1.02 (hskp1),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[544, 72, 528, 1973, 1972, 1971, 538])).
% 0.76/1.02 tff(1982,plain,
% 0.76/1.02 (~c2_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[551, 1981])).
% 0.76/1.02 tff(1983,plain,
% 0.76/1.02 (c3_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[559, 1981])).
% 0.76/1.02 tff(1984,plain,
% 0.76/1.02 (c0_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[567, 1981])).
% 0.76/1.02 tff(1985,plain,
% 0.76/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c0_1(a33)))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(1986,plain,
% 0.76/1.02 (((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33))) <=> (c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c0_1(a33)))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(1987,plain,
% 0.76/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c0_1(a33))))),
% 0.76/1.02 inference(monotonicity,[status(thm)],[1986])).
% 0.76/1.02 tff(1988,plain,
% 0.76/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c0_1(a33)))),
% 0.76/1.02 inference(transitivity,[status(thm)],[1987, 1985])).
% 0.76/1.02 tff(1989,plain,
% 0.76/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2)) | (~c1_1(a2)) | (~c0_1(a2)) | c2_1(a2) | (~c1_1(a2)) | (~c0_1(a2)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)))),
% 0.76/1.02 inference(quant_inst,[status(thm)],[])).
% 0.76/1.02 tff(1990,plain,
% 0.76/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c1_1(a2)) | (~c3_1(a2)) | (~c0_1(a2)) | (~c0_1(a33))),
% 0.76/1.02 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 0.76/1.02 tff(1991,plain,
% 0.76/1.02 (~c1_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1990, 72, 1785, 1784, 1984, 1983, 1982, 527, 1980])).
% 0.76/1.02 tff(1992,plain,
% 0.76/1.02 (((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | c1_1(a43) | (~ndr1_0) | (~c2_1(a43)) | c0_1(a43))) <=> ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp0 | c1_1(a43) | (~ndr1_0) | (~c2_1(a43)) | c0_1(a43))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(1993,plain,
% 0.76/1.02 ((hskp5 | hskp0 | (~ndr1_0) | c1_1(a43) | c0_1(a43) | (~c2_1(a43))) <=> (hskp5 | hskp0 | c1_1(a43) | (~ndr1_0) | (~c2_1(a43)) | c0_1(a43))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(1994,plain,
% 0.76/1.02 (((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | (~ndr1_0) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)))) <=> ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | c1_1(a43) | (~ndr1_0) | (~c2_1(a43)) | c0_1(a43)))),
% 0.76/1.02 inference(monotonicity,[status(thm)],[1993])).
% 0.76/1.02 tff(1995,plain,
% 0.76/1.02 (((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | (~ndr1_0) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)))) <=> ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp0 | c1_1(a43) | (~ndr1_0) | (~c2_1(a43)) | c0_1(a43))),
% 0.76/1.02 inference(transitivity,[status(thm)],[1994, 1992])).
% 0.76/1.02 tff(1996,plain,
% 0.76/1.02 ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp5 | hskp0 | (~ndr1_0) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)))),
% 0.76/1.02 inference(quant_inst,[status(thm)],[])).
% 0.76/1.02 tff(1997,plain,
% 0.76/1.02 ((~![U: $i] : (hskp5 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp5 | hskp0 | c1_1(a43) | (~ndr1_0) | (~c2_1(a43)) | c0_1(a43)),
% 0.76/1.02 inference(modus_ponens,[status(thm)],[1996, 1995])).
% 0.76/1.02 tff(1998,plain,
% 0.76/1.02 (hskp5 | c0_1(a43)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1997, 72, 528, 1945, 1962, 1077])).
% 0.76/1.02 tff(1999,plain,
% 0.76/1.02 (hskp5),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1998, 1968])).
% 0.76/1.02 tff(2000,plain,
% 0.76/1.02 (~c3_1(a6)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1034, 1999])).
% 0.76/1.02 tff(2001,plain,
% 0.76/1.02 (c0_1(a6)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[247, 1999])).
% 0.76/1.02 tff(2002,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c3_1(a6) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a6)) | (~c1_1(a6)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a6) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a6)) | (~c1_1(a6)))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(2003,plain,
% 0.76/1.02 ((hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2))) <=> (hskp0 | c3_1(a6) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a6)) | (~c1_1(a6)))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(2004,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c3_1(a6) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a6)) | (~c1_1(a6))))),
% 0.76/1.02 inference(monotonicity,[status(thm)],[2003])).
% 0.76/1.02 tff(2005,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a6) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a6)) | (~c1_1(a6)))),
% 0.76/1.02 inference(transitivity,[status(thm)],[2004, 2002])).
% 0.76/1.02 tff(2006,plain,
% 0.76/1.02 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))),
% 0.76/1.02 inference(quant_inst,[status(thm)],[])).
% 0.76/1.02 tff(2007,plain,
% 0.76/1.02 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c3_1(a6) | c2_1(a2) | (~ndr1_0) | c1_1(a2) | (~c3_1(a2)) | (~c0_1(a6)) | (~c1_1(a6))),
% 0.76/1.02 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 0.76/1.02 tff(2008,plain,
% 0.76/1.02 (~c1_1(a6)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2007, 72, 528, 2001, 1983, 2000, 1982, 585, 1991])).
% 0.76/1.02 tff(2009,plain,
% 0.76/1.02 (hskp21),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1128, 72, 528, 1984, 1982, 1122, 1991])).
% 0.76/1.02 tff(2010,plain,
% 0.76/1.02 (~c0_1(a42)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1135, 2009])).
% 0.76/1.02 tff(2011,plain,
% 0.76/1.02 (c2_1(a6)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[255, 1999])).
% 0.76/1.02 tff(2012,plain,
% 0.76/1.02 (c3_1(a42)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1143, 2009])).
% 0.76/1.02 tff(2013,plain,
% 0.76/1.02 (c2_1(a42)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1151, 2009])).
% 0.76/1.02 tff(2014,plain,
% 0.76/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a42) | c3_1(a6) | (~ndr1_0) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~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)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a42) | c3_1(a6) | (~ndr1_0) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(2015,plain,
% 0.76/1.02 (((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42))) <=> (c0_1(a42) | c3_1(a6) | (~ndr1_0) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(2016,plain,
% 0.76/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c0_1(a42) | (~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)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a42) | c3_1(a6) | (~ndr1_0) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a42)) | (~c3_1(a42))))),
% 0.76/1.02 inference(monotonicity,[status(thm)],[2015])).
% 0.76/1.02 tff(2017,plain,
% 0.76/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c0_1(a42) | (~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)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a42) | c3_1(a6) | (~ndr1_0) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a42)) | (~c3_1(a42)))),
% 0.76/1.02 inference(transitivity,[status(thm)],[2016, 2014])).
% 0.76/1.02 tff(2018,plain,
% 0.76/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))),
% 0.76/1.02 inference(quant_inst,[status(thm)],[])).
% 0.76/1.02 tff(2019,plain,
% 0.76/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a42) | c3_1(a6) | (~ndr1_0) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a6) | (~c2_1(a42)) | (~c3_1(a42))),
% 0.76/1.02 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 0.76/1.02 tff(2020,plain,
% 0.76/1.02 ($false),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2019, 72, 2013, 2012, 2001, 2011, 2010, 2000, 91, 2008])).
% 0.76/1.02 tff(2021,plain,(hskp0 | (~c0_1(a33)) | (~c2_1(a33)) | hskp19 | (~c3_1(a33)) | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.76/1.02 tff(2022,plain,
% 0.76/1.02 (hskp0),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2021, 1319, 1781, 1765, 1773, 1307])).
% 0.76/1.02 tff(2023,plain,
% 0.76/1.02 (~c0_1(a1)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[645, 2022])).
% 0.76/1.02 tff(2024,plain,
% 0.76/1.02 (hskp1),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1453, 81, 1401, 1307, 22, 1319, 38])).
% 0.76/1.02 tff(2025,plain,
% 0.76/1.02 (~c2_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[551, 2024])).
% 0.76/1.02 tff(2026,plain,
% 0.76/1.02 (c3_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[559, 2024])).
% 0.76/1.02 tff(2027,plain,
% 0.76/1.02 (c0_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[567, 2024])).
% 0.76/1.02 tff(2028,plain,
% 0.76/1.02 ($false),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1463, 1, 72, 1319, 2027, 2026, 2025, 1318])).
% 0.76/1.02 tff(2029,plain,(hskp22 | hskp19 | hskp28 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.76/1.02 tff(2030,plain,
% 0.76/1.02 ($false),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2029, 1326, 1, 1307, 1319])).
% 0.76/1.02 tff(2031,plain,(hskp22 | hskp24 | hskp19), inference(lemma,lemma(discharge,[]))).
% 0.76/1.02 tff(2032,plain,
% 0.76/1.02 (hskp22),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2031, 1319, 1307])).
% 0.76/1.02 tff(2033,plain,
% 0.76/1.02 (~c1_1(a43)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[622, 2032])).
% 0.76/1.02 tff(2034,plain,
% 0.76/1.02 (c2_1(a1)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[661, 2022])).
% 0.76/1.02 tff(2035,plain,
% 0.76/1.02 (c1_1(a1)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[653, 2022])).
% 0.76/1.02 tff(2036,plain,
% 0.76/1.02 (~c3_1(a43)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[616, 2032])).
% 0.76/1.02 tff(2037,plain,
% 0.76/1.02 (c2_1(a43)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[630, 2032])).
% 0.76/1.02 tff(2038,plain,
% 0.76/1.02 (hskp15 | hskp4),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1599, 72, 699, 698, 663, 1591])).
% 0.76/1.02 tff(2039,plain,
% 0.76/1.02 (hskp15),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2038, 1308])).
% 0.76/1.02 tff(2040,plain,
% 0.76/1.02 (~c2_1(a27)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1605, 2039])).
% 0.76/1.02 tff(2041,plain,
% 0.76/1.02 (c0_1(a27)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1613, 2039])).
% 0.76/1.02 tff(2042,plain,
% 0.76/1.02 (~c3_1(a27)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1651, 72, 1478, 2041, 699, 698, 1564, 1479, 2040, 663, 121])).
% 0.76/1.02 tff(2043,plain,
% 0.76/1.02 (hskp4 | c0_1(a43)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1474, 72, 1564, 1479, 101])).
% 0.76/1.02 tff(2044,plain,
% 0.76/1.02 (c0_1(a43)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2043, 1308])).
% 0.76/1.02 tff(2045,plain,
% 0.76/1.02 (c1_1(a27)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1621, 2039])).
% 0.76/1.02 tff(2046,plain,
% 0.76/1.02 ($false),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1659, 72, 1307, 1478, 2045, 1479, 2040, 1425, 2044, 2042])).
% 0.76/1.02 tff(2047,plain,(hskp4 | hskp24 | (~c2_1(a43)) | c3_1(a43) | (~c1_1(a1)) | (~c2_1(a1)) | c1_1(a43) | c0_1(a1)), inference(lemma,lemma(discharge,[]))).
% 0.76/1.02 tff(2048,plain,
% 0.76/1.02 (hskp4),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2047, 2037, 1307, 2036, 2035, 2034, 2033, 2023])).
% 0.76/1.02 tff(2049,plain,
% 0.76/1.02 (~c1_1(a5)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[149, 2048])).
% 0.76/1.02 tff(2050,plain,
% 0.76/1.02 (c3_1(a5)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[180, 2048])).
% 0.76/1.02 tff(2051,plain,
% 0.76/1.02 (c2_1(a5)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[188, 2048])).
% 0.76/1.02 tff(2052,plain,
% 0.76/1.02 (~c1_1(a33)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1979, 72, 1319, 1781, 1773, 2051, 2050, 2049, 143])).
% 0.76/1.02 tff(2053,plain,
% 0.76/1.02 (~c3_1(a1)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1215, 72, 1319, 2051, 2050, 2035, 2034, 2049, 143])).
% 0.76/1.02 tff(2054,plain,
% 0.76/1.02 (~hskp14),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1813, 1397, 1765, 1781, 1805])).
% 0.76/1.02 tff(2055,plain,
% 0.76/1.02 (~hskp28),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1541, 2054, 122])).
% 0.76/1.02 tff(2056,plain,
% 0.76/1.02 (hskp9),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1412, 2055, 1397])).
% 0.76/1.02 tff(2057,plain,
% 0.76/1.02 (~c3_1(a12)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[516, 2056])).
% 0.76/1.02 tff(2058,assumption,(~c3_1(a1)), introduced(assumption)).
% 0.76/1.02 tff(2059,plain,
% 0.76/1.02 (hskp29 | hskp14 | c3_1(a1)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1229, 72, 698, 663, 306])).
% 0.76/1.02 tff(2060,plain,
% 0.76/1.02 (hskp29),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2059, 2054, 2058])).
% 0.76/1.02 tff(2061,plain,
% 0.76/1.02 (c1_1(a12)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[510, 2056])).
% 0.76/1.02 tff(2062,plain,
% 0.76/1.02 (~c2_1(a12)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[977, 2056])).
% 0.76/1.02 tff(2063,assumption,(hskp29), introduced(assumption)).
% 0.76/1.02 tff(2064,plain,
% 0.76/1.02 (c2_1(a25)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[329, 2063])).
% 0.76/1.02 tff(2065,plain,
% 0.76/1.02 (c1_1(a25)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[347, 2063])).
% 0.76/1.02 tff(2066,plain,
% 0.76/1.02 (c0_1(a25)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[321, 2063])).
% 0.76/1.02 tff(2067,plain,
% 0.76/1.02 (~c3_1(a25)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[354, 72, 2066, 2065, 2064, 340])).
% 0.76/1.02 tff(2068,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(2069,plain,
% 0.76/1.02 ((hskp24 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12))) <=> (hskp24 | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(2070,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25)))),
% 0.76/1.02 inference(monotonicity,[status(thm)],[2069])).
% 0.76/1.02 tff(2071,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25))),
% 0.76/1.02 inference(transitivity,[status(thm)],[2070, 2068])).
% 0.76/1.02 tff(2072,plain,
% 0.76/1.02 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp24 | (~ndr1_0) | c3_1(a25) | (~c2_1(a25)) | (~c0_1(a25)) | c2_1(a12) | c3_1(a12) | (~c1_1(a12)))),
% 0.76/1.02 inference(quant_inst,[status(thm)],[])).
% 0.76/1.02 tff(2073,plain,
% 0.76/1.02 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))) | hskp24 | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a25)) | (~c2_1(a25)) | c3_1(a25)),
% 0.76/1.02 inference(modus_ponens,[status(thm)],[2072, 2071])).
% 0.76/1.02 tff(2074,plain,
% 0.76/1.02 ($false),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2073, 72, 1307, 2066, 2064, 587, 985, 586, 1425, 2067])).
% 0.76/1.02 tff(2075,plain,((~hskp29) | hskp24 | (~c1_1(a12)) | c2_1(a12) | c3_1(a12)), inference(lemma,lemma(discharge,[]))).
% 0.76/1.02 tff(2076,plain,
% 0.76/1.02 ($false),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2075, 2062, 2061, 1307, 2060, 2057])).
% 0.76/1.02 tff(2077,plain,(hskp1 | hskp24 | c3_1(a1) | (~c2_1(a1)) | c0_1(a1) | hskp18 | c1_1(a33)), inference(lemma,lemma(discharge,[]))).
% 0.76/1.02 tff(2078,plain,
% 0.76/1.02 (hskp1),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2077, 2053, 1307, 2034, 2023, 122, 2052])).
% 0.76/1.02 tff(2079,plain,
% 0.76/1.02 (~c2_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[551, 2078])).
% 0.76/1.02 tff(2080,plain,
% 0.76/1.02 (c3_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[559, 2078])).
% 0.76/1.02 tff(2081,plain,
% 0.76/1.02 (c0_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[567, 2078])).
% 0.76/1.02 tff(2082,plain,
% 0.76/1.02 ($false),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[708, 72, 2037, 2081, 2080, 2035, 2034, 2033, 2036, 2079, 2023, 121])).
% 0.76/1.02 tff(2083,plain,(hskp19 | hskp24 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/1.02 tff(2084,plain,
% 0.76/1.02 (hskp19),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2083, 1307, 122])).
% 0.76/1.02 tff(2085,plain,
% 0.76/1.02 (~c2_1(a36)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1193, 2084])).
% 0.76/1.02 tff(2086,plain,
% 0.76/1.02 (~c1_1(a36)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1199, 2084])).
% 0.76/1.02 tff(2087,plain,
% 0.76/1.02 (hskp1 | c0_1(a36)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1858, 72, 1765, 1781, 2086, 2085, 674, 1794])).
% 0.76/1.02 tff(2088,plain,
% 0.76/1.02 (c0_1(a36)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2087, 1397])).
% 0.76/1.02 tff(2089,plain,
% 0.76/1.02 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 0.76/1.02 inference(bind,[status(th)],[])).
% 0.76/1.02 tff(2090,plain,
% 0.76/1.02 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.76/1.02 inference(quant_intro,[status(thm)],[2089])).
% 0.76/1.02 tff(2091,plain,
% 0.76/1.02 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(2092,plain,
% 0.76/1.02 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp29) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp29))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 0.76/1.02 inference(bind,[status(th)],[])).
% 0.76/1.02 tff(2093,plain,
% 0.76/1.02 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.76/1.02 inference(quant_intro,[status(thm)],[2092])).
% 0.76/1.02 tff(2094,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.76/1.02 tff(2095,plain,
% 0.76/1.02 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.76/1.02 inference(modus_ponens,[status(thm)],[2094, 2093])).
% 0.76/1.02 tff(2096,plain,
% 0.76/1.02 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.76/1.02 inference(modus_ponens,[status(thm)],[2095, 2091])).
% 0.76/1.02 tff(2097,plain,(
% 0.76/1.02 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.76/1.02 inference(skolemize,[status(sab)],[2096])).
% 0.76/1.02 tff(2098,plain,
% 0.76/1.02 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 0.76/1.02 inference(modus_ponens,[status(thm)],[2097, 2090])).
% 0.76/1.02 tff(2099,plain,
% 0.76/1.02 (~c3_1(a36)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1187, 2084])).
% 0.76/1.02 tff(2100,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp29 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp29 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c0_1(a36)))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(2101,plain,
% 0.76/1.02 ((hskp29 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | c1_1(a36) | c3_1(a36) | (~c0_1(a36))) <=> (hskp29 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c0_1(a36)))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(2102,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | c1_1(a36) | c3_1(a36) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp29 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c0_1(a36))))),
% 0.76/1.02 inference(monotonicity,[status(thm)],[2101])).
% 0.76/1.02 tff(2103,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | c1_1(a36) | c3_1(a36) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp29 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c0_1(a36)))),
% 0.76/1.02 inference(transitivity,[status(thm)],[2102, 2100])).
% 0.76/1.02 tff(2104,plain,
% 0.76/1.02 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c2_1(a33)) | (~c3_1(a33)) | (~c0_1(a33)) | c1_1(a36) | c3_1(a36) | (~c0_1(a36)))),
% 0.76/1.02 inference(quant_inst,[status(thm)],[])).
% 0.76/1.02 tff(2105,plain,
% 0.76/1.02 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp29 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | (~c3_1(a33)) | (~c2_1(a33)) | (~c0_1(a33)) | (~c0_1(a36))),
% 0.76/1.02 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 0.76/1.02 tff(2106,plain,
% 0.76/1.02 (hskp29 | (~c0_1(a36))),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2105, 72, 1765, 1781, 1773, 2086, 2099, 2098])).
% 0.76/1.02 tff(2107,plain,
% 0.76/1.02 (hskp29),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2106, 2088])).
% 0.76/1.02 tff(2108,plain,
% 0.76/1.02 ($false),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2075, 1922, 1923, 1307, 2107, 1941])).
% 0.76/1.02 tff(2109,plain,(hskp1 | hskp24 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/1.02 tff(2110,plain,
% 0.76/1.02 (hskp1),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2109, 1307, 122])).
% 0.76/1.02 tff(2111,plain,
% 0.76/1.02 (~c2_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[551, 2110])).
% 0.76/1.02 tff(2112,plain,
% 0.76/1.02 (c0_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[567, 2110])).
% 0.76/1.02 tff(2113,plain,
% 0.76/1.02 (c3_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[559, 2110])).
% 0.76/1.02 tff(2114,plain,
% 0.76/1.02 (~c1_1(a2)),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[1990, 72, 1765, 1781, 2112, 2113, 2111, 527, 1794])).
% 0.76/1.02 tff(2115,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)) | (~c0_1(a19)) | (~c1_1(a19)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)) | (~c0_1(a19)) | (~c1_1(a19)))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(2116,plain,
% 0.76/1.02 ((hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33))) <=> (hskp16 | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)) | (~c0_1(a19)) | (~c1_1(a19)))),
% 0.76/1.02 inference(rewrite,[status(thm)],[])).
% 0.76/1.02 tff(2117,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)) | (~c0_1(a19)) | (~c1_1(a19))))),
% 0.76/1.02 inference(monotonicity,[status(thm)],[2116])).
% 0.76/1.02 tff(2118,plain,
% 0.76/1.02 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)) | (~c0_1(a19)) | (~c1_1(a19)))),
% 0.76/1.02 inference(transitivity,[status(thm)],[2117, 2115])).
% 0.76/1.02 tff(2119,plain,
% 0.76/1.02 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)))),
% 0.76/1.02 inference(quant_inst,[status(thm)],[])).
% 0.76/1.02 tff(2120,plain,
% 0.76/1.02 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c0_1(a33)) | (~c0_1(a19)) | (~c1_1(a19))),
% 0.76/1.02 inference(modus_ponens,[status(thm)],[2119, 2118])).
% 0.76/1.02 tff(2121,plain,
% 0.76/1.02 (hskp16),
% 0.76/1.02 inference(unit_resolution,[status(thm)],[2120, 72, 1765, 1773, 38, 30, 22, 1940, 1794])).
% 0.76/1.02 tff(2122,plain,
% 0.76/1.02 (((~hskp16) | (~c0_1(a31))) <=> ((~hskp16) | (~c0_1(a31)))),
% 0.76/1.03 inference(rewrite,[status(thm)],[])).
% 0.76/1.03 tff(2123,plain,
% 0.76/1.03 (((~c0_1(a31)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a31)))),
% 0.76/1.03 inference(rewrite,[status(thm)],[])).
% 0.76/1.03 tff(2124,axiom,((~c0_1(a31)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.76/1.03 tff(2125,plain,
% 0.76/1.03 ((~hskp16) | (~c0_1(a31))),
% 0.76/1.03 inference(modus_ponens,[status(thm)],[2124, 2123])).
% 0.76/1.03 tff(2126,plain,
% 0.76/1.03 ((~hskp16) | (~c0_1(a31))),
% 0.76/1.03 inference(modus_ponens,[status(thm)],[2125, 2122])).
% 0.76/1.03 tff(2127,plain,
% 0.76/1.03 (~c0_1(a31)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2126, 2121])).
% 0.76/1.03 tff(2128,plain,
% 0.76/1.03 (((~hskp16) | c2_1(a31)) <=> ((~hskp16) | c2_1(a31))),
% 0.76/1.03 inference(rewrite,[status(thm)],[])).
% 0.76/1.03 tff(2129,axiom,((~hskp16) | c2_1(a31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.76/1.03 tff(2130,plain,
% 0.76/1.03 ((~hskp16) | c2_1(a31)),
% 0.76/1.03 inference(modus_ponens,[status(thm)],[2129, 2128])).
% 0.76/1.03 tff(2131,plain,
% 0.76/1.03 ((~hskp16) | c2_1(a31)),
% 0.76/1.03 inference(modus_ponens,[status(thm)],[2130, 2128])).
% 0.76/1.03 tff(2132,plain,
% 0.76/1.03 ((~hskp16) | c2_1(a31)),
% 0.76/1.03 inference(modus_ponens,[status(thm)],[2131, 2128])).
% 0.76/1.03 tff(2133,plain,
% 0.76/1.03 ((~hskp16) | c2_1(a31)),
% 0.76/1.03 inference(modus_ponens,[status(thm)],[2132, 2128])).
% 0.76/1.03 tff(2134,plain,
% 0.76/1.03 ((~hskp16) | c2_1(a31)),
% 0.76/1.03 inference(modus_ponens,[status(thm)],[2133, 2128])).
% 0.76/1.03 tff(2135,plain,
% 0.76/1.03 (c2_1(a31)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2134, 2121])).
% 0.76/1.03 tff(2136,plain,
% 0.76/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a31) | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a31) | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 0.76/1.03 inference(rewrite,[status(thm)],[])).
% 0.76/1.03 tff(2137,plain,
% 0.76/1.03 (((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31))) <=> (c0_1(a31) | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 0.76/1.03 inference(rewrite,[status(thm)],[])).
% 0.76/1.03 tff(2138,plain,
% 0.76/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a31) | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31))))),
% 0.76/1.03 inference(monotonicity,[status(thm)],[2137])).
% 0.76/1.03 tff(2139,plain,
% 0.76/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a31) | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 0.76/1.03 inference(transitivity,[status(thm)],[2138, 2136])).
% 0.76/1.03 tff(2140,plain,
% 0.76/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31)))),
% 0.76/1.03 inference(quant_inst,[status(thm)],[])).
% 0.76/1.03 tff(2141,plain,
% 0.76/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a31) | c3_1(a19) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31))),
% 0.76/1.03 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 0.76/1.03 tff(2142,plain,
% 0.76/1.03 (~c3_1(a31)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2141, 72, 1765, 1781, 2135, 38, 2127, 22, 91, 81, 1794])).
% 0.76/1.03 tff(2143,assumption,(~c3_1(a31)), introduced(assumption)).
% 0.76/1.03 tff(2144,assumption,(~c0_1(a31)), introduced(assumption)).
% 0.76/1.03 tff(2145,assumption,(c2_1(a31)), introduced(assumption)).
% 0.76/1.03 tff(2146,plain,
% 0.76/1.03 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | c0_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c0_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 0.76/1.03 inference(rewrite,[status(thm)],[])).
% 0.76/1.03 tff(2147,plain,
% 0.76/1.03 ((hskp29 | hskp14 | (~ndr1_0) | c3_1(a31) | c0_1(a31) | (~c2_1(a31))) <=> (hskp29 | hskp14 | c0_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 0.76/1.03 inference(rewrite,[status(thm)],[])).
% 0.76/1.03 tff(2148,plain,
% 0.76/1.03 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | c0_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31)))),
% 0.76/1.03 inference(monotonicity,[status(thm)],[2147])).
% 0.76/1.03 tff(2149,plain,
% 0.76/1.03 (((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)))) <=> ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c0_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31))),
% 0.76/1.03 inference(transitivity,[status(thm)],[2148, 2146])).
% 0.76/1.03 tff(2150,plain,
% 0.76/1.03 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp14 | (~ndr1_0) | c3_1(a31) | c0_1(a31) | (~c2_1(a31)))),
% 0.76/1.03 inference(quant_inst,[status(thm)],[])).
% 0.76/1.03 tff(2151,plain,
% 0.76/1.03 ((~![U: $i] : (hskp29 | hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp14 | c0_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c3_1(a31)),
% 0.76/1.03 inference(modus_ponens,[status(thm)],[2150, 2149])).
% 0.76/1.03 tff(2152,plain,
% 0.76/1.03 (hskp29 | hskp14 | c3_1(a31)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2151, 72, 2145, 2144, 306])).
% 0.76/1.03 tff(2153,plain,
% 0.76/1.03 (hskp29),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2152, 1814, 2143])).
% 0.76/1.03 tff(2154,plain,
% 0.76/1.03 ($false),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2075, 1922, 1923, 1307, 2153, 1941])).
% 0.76/1.03 tff(2155,plain,(hskp1 | hskp24 | c3_1(a31) | (~c2_1(a31)) | c0_1(a31) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/1.03 tff(2156,plain,
% 0.76/1.03 (hskp1),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2155, 2142, 1307, 2135, 2127, 122])).
% 0.76/1.03 tff(2157,plain,
% 0.76/1.03 (~c2_1(a2)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[551, 2156])).
% 0.76/1.03 tff(2158,plain,
% 0.76/1.03 (c3_1(a2)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[559, 2156])).
% 0.76/1.03 tff(2159,plain,
% 0.76/1.03 (c0_1(a2)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[567, 2156])).
% 0.76/1.03 tff(2160,plain,
% 0.76/1.03 (~c1_1(a2)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[1990, 72, 1765, 1781, 2159, 2158, 2157, 527, 1794])).
% 0.76/1.03 tff(2161,plain,
% 0.76/1.03 (((~hskp16) | (~c1_1(a31))) <=> ((~hskp16) | (~c1_1(a31)))),
% 0.76/1.03 inference(rewrite,[status(thm)],[])).
% 0.76/1.03 tff(2162,plain,
% 0.76/1.03 (((~c1_1(a31)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a31)))),
% 0.76/1.03 inference(rewrite,[status(thm)],[])).
% 0.76/1.03 tff(2163,axiom,((~c1_1(a31)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.76/1.03 tff(2164,plain,
% 0.76/1.03 ((~hskp16) | (~c1_1(a31))),
% 0.76/1.03 inference(modus_ponens,[status(thm)],[2163, 2162])).
% 0.76/1.03 tff(2165,plain,
% 0.76/1.03 ((~hskp16) | (~c1_1(a31))),
% 0.76/1.03 inference(modus_ponens,[status(thm)],[2164, 2161])).
% 0.76/1.03 tff(2166,plain,
% 0.76/1.03 (~c1_1(a31)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2165, 2121])).
% 0.76/1.03 tff(2167,plain,
% 0.76/1.03 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c0_1(a31) | c1_1(a31) | (~ndr1_0) | c3_1(a31))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c0_1(a31) | c1_1(a31) | (~ndr1_0) | c3_1(a31))),
% 0.76/1.03 inference(rewrite,[status(thm)],[])).
% 0.76/1.03 tff(2168,plain,
% 0.76/1.03 ((hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | c0_1(a31)) <=> (hskp4 | c0_1(a31) | c1_1(a31) | (~ndr1_0) | c3_1(a31))),
% 0.76/1.03 inference(rewrite,[status(thm)],[])).
% 0.76/1.03 tff(2169,plain,
% 0.76/1.03 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | c0_1(a31))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c0_1(a31) | c1_1(a31) | (~ndr1_0) | c3_1(a31)))),
% 0.76/1.03 inference(monotonicity,[status(thm)],[2168])).
% 0.76/1.03 tff(2170,plain,
% 0.76/1.03 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | c0_1(a31))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c0_1(a31) | c1_1(a31) | (~ndr1_0) | c3_1(a31))),
% 0.76/1.03 inference(transitivity,[status(thm)],[2169, 2167])).
% 0.76/1.03 tff(2171,plain,
% 0.76/1.03 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a31) | c1_1(a31) | c0_1(a31))),
% 0.76/1.03 inference(quant_inst,[status(thm)],[])).
% 0.76/1.03 tff(2172,plain,
% 0.76/1.03 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c0_1(a31) | c1_1(a31) | (~ndr1_0) | c3_1(a31)),
% 0.76/1.03 inference(modus_ponens,[status(thm)],[2171, 2170])).
% 0.76/1.03 tff(2173,plain,
% 0.76/1.03 (hskp4 | c3_1(a31)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2172, 72, 2127, 2166, 101])).
% 0.76/1.03 tff(2174,plain,
% 0.76/1.03 (hskp4),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2173, 2142])).
% 0.76/1.03 tff(2175,plain,
% 0.76/1.03 (~c1_1(a5)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[149, 2174])).
% 0.76/1.03 tff(2176,plain,
% 0.76/1.03 (c3_1(a5)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[180, 2174])).
% 0.76/1.03 tff(2177,plain,
% 0.76/1.03 (c2_1(a5)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[188, 2174])).
% 0.76/1.03 tff(2178,plain,
% 0.76/1.03 ($false),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[610, 1, 72, 2177, 2176, 2158, 2175, 2157, 111, 2160])).
% 0.76/1.03 tff(2179,plain,(hskp22 | hskp24 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.76/1.03 tff(2180,plain,
% 0.76/1.03 (hskp22),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2179, 1307, 122])).
% 0.76/1.03 tff(2181,plain,
% 0.76/1.03 (~c3_1(a43)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[616, 2180])).
% 0.76/1.03 tff(2182,plain,
% 0.76/1.03 (~c1_1(a43)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[622, 2180])).
% 0.76/1.03 tff(2183,plain,
% 0.76/1.03 (c2_1(a43)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[630, 2180])).
% 0.76/1.03 tff(2184,assumption,(~c1_1(a2)), introduced(assumption)).
% 0.76/1.03 tff(2185,assumption,(~c2_1(a2)), introduced(assumption)).
% 0.76/1.03 tff(2186,assumption,(c0_1(a2)), introduced(assumption)).
% 0.76/1.03 tff(2187,plain,
% 0.76/1.03 (hskp21 | hskp0 | c1_1(a2)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[1128, 72, 2186, 2185, 1122])).
% 0.76/1.03 tff(2188,plain,
% 0.76/1.03 (hskp21),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2187, 528, 2184])).
% 0.76/1.03 tff(2189,plain,
% 0.76/1.03 (~c0_1(a43)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[1568, 2188, 1564, 1479, 1478])).
% 0.76/1.03 tff(2190,plain,
% 0.76/1.03 (hskp5 | hskp0 | c0_1(a43)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[1997, 72, 1478, 1564, 1077])).
% 0.76/1.03 tff(2191,plain,
% 0.76/1.03 (hskp5),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[2190, 2189, 528])).
% 0.76/1.03 tff(2192,plain,
% 0.76/1.03 (~c3_1(a6)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[1034, 2191])).
% 0.76/1.03 tff(2193,plain,
% 0.76/1.03 (~c0_1(a42)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[1135, 2188])).
% 0.76/1.03 tff(2194,plain,
% 0.76/1.03 (c2_1(a6)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[255, 2191])).
% 0.76/1.03 tff(2195,plain,
% 0.76/1.03 (c0_1(a6)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[247, 2191])).
% 0.76/1.03 tff(2196,plain,
% 0.76/1.03 (c3_1(a42)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[1143, 2188])).
% 0.76/1.03 tff(2197,plain,
% 0.76/1.03 (c2_1(a42)),
% 0.76/1.03 inference(unit_resolution,[status(thm)],[1151, 2188])).
% 0.76/1.03 tff(2198,plain,
% 0.76/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a42) | c3_1(a6) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a6)) | (~c0_1(a6)) | (~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)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a42) | c3_1(a6) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a6)) | (~c0_1(a6)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2199,plain,
% 0.86/1.03 (((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42))) <=> (c0_1(a42) | c3_1(a6) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a6)) | (~c0_1(a6)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2200,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a42) | (~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)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a42) | c3_1(a6) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a6)) | (~c0_1(a6)) | (~c2_1(a42)) | (~c3_1(a42))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2199])).
% 0.86/1.03 tff(2201,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a42) | (~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)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a42) | c3_1(a6) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a6)) | (~c0_1(a6)) | (~c2_1(a42)) | (~c3_1(a42)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2200, 2198])).
% 0.86/1.03 tff(2202,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a6) | (~c2_1(a6)) | (~c0_1(a6)) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | c0_1(a42) | (~c2_1(a42)) | (~c3_1(a42)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2203,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a42) | c3_1(a6) | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c0_1(a33)) | (~c2_1(a6)) | (~c0_1(a6)) | (~c2_1(a42)) | (~c3_1(a42))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2202, 2201])).
% 0.86/1.03 tff(2204,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2203, 72, 1785, 1784, 2197, 2196, 2195, 2194, 2193, 2192, 91, 1805])).
% 0.86/1.03 tff(2205,plain,(hskp0 | (~c0_1(a33)) | (~c2_1(a33)) | c1_1(a33) | (~c2_1(a43)) | c1_1(a43) | c3_1(a43) | c1_1(a2) | (~c0_1(a2)) | c2_1(a2)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(2206,plain,
% 0.86/1.03 (hskp0),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2205, 2183, 1781, 1794, 1765, 2182, 2181, 2114, 2112, 2111])).
% 0.86/1.03 tff(2207,plain,
% 0.86/1.03 (~c0_1(a1)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[645, 2206])).
% 0.86/1.03 tff(2208,plain,
% 0.86/1.03 (c2_1(a1)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[661, 2206])).
% 0.86/1.03 tff(2209,plain,
% 0.86/1.03 (c1_1(a1)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[653, 2206])).
% 0.86/1.03 tff(2210,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[708, 72, 2183, 2112, 2113, 2209, 2208, 2182, 2181, 2111, 2207, 121])).
% 0.86/1.03 tff(2211,plain,(hskp24 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(2212,plain,
% 0.86/1.03 (hskp24),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2211, 122])).
% 0.86/1.03 tff(2213,plain,
% 0.86/1.03 (~c1_1(a58)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1355, 2212])).
% 0.86/1.03 tff(2214,plain,
% 0.86/1.03 (c3_1(a58)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1334, 2212])).
% 0.86/1.03 tff(2215,plain,
% 0.86/1.03 (c0_1(a58)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1342, 2212])).
% 0.86/1.03 tff(2216,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a58) | c3_1(a12) | (~ndr1_0) | (~c0_1(a12)) | (~c1_1(a12)) | (~c0_1(a58)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a58) | c3_1(a12) | (~ndr1_0) | (~c0_1(a12)) | (~c1_1(a12)) | (~c0_1(a58)) | (~c3_1(a58)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2217,plain,
% 0.86/1.03 ((hskp16 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58))) <=> (hskp16 | c1_1(a58) | c3_1(a12) | (~ndr1_0) | (~c0_1(a12)) | (~c1_1(a12)) | (~c0_1(a58)) | (~c3_1(a58)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2218,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a58) | c3_1(a12) | (~ndr1_0) | (~c0_1(a12)) | (~c1_1(a12)) | (~c0_1(a58)) | (~c3_1(a58))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2217])).
% 0.86/1.03 tff(2219,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a58) | c3_1(a12) | (~ndr1_0) | (~c0_1(a12)) | (~c1_1(a12)) | (~c0_1(a58)) | (~c3_1(a58)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2218, 2216])).
% 0.86/1.03 tff(2220,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a12) | (~c1_1(a12)) | (~c0_1(a12)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2221,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a58) | c3_1(a12) | (~ndr1_0) | (~c0_1(a12)) | (~c1_1(a12)) | (~c0_1(a58)) | (~c3_1(a58))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2220, 2219])).
% 0.86/1.03 tff(2222,plain,
% 0.86/1.03 (hskp16 | (~c0_1(a12))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2221, 72, 2215, 2214, 1923, 2213, 1941, 1940])).
% 0.86/1.03 tff(2223,plain,
% 0.86/1.03 (hskp16),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2222, 1930])).
% 0.86/1.03 tff(2224,plain,
% 0.86/1.03 (~c1_1(a31)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2165, 2223])).
% 0.86/1.03 tff(2225,plain,
% 0.86/1.03 (~c0_1(a31)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2126, 2223])).
% 0.86/1.03 tff(2226,plain,
% 0.86/1.03 (((~hskp17) | (~c0_1(a32))) <=> ((~hskp17) | (~c0_1(a32)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2227,plain,
% 0.86/1.03 (((~c0_1(a32)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a32)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2228,axiom,((~c0_1(a32)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.86/1.03 tff(2229,plain,
% 0.86/1.03 ((~hskp17) | (~c0_1(a32))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2228, 2227])).
% 0.86/1.03 tff(2230,plain,
% 0.86/1.03 ((~hskp17) | (~c0_1(a32))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2229, 2226])).
% 0.86/1.03 tff(2231,plain,
% 0.86/1.03 (~c0_1(a32)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2230, 1877])).
% 0.86/1.03 tff(2232,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a36) | c3_1(a36) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a36) | c3_1(a36) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a36)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2233,plain,
% 0.86/1.03 ((hskp22 | (~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c1_1(a12)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36))) <=> (hskp22 | c2_1(a36) | c3_1(a36) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a36)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2234,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c1_1(a12)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a36) | c3_1(a36) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a36))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2233])).
% 0.86/1.03 tff(2235,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c1_1(a12)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a36) | c3_1(a36) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a36)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2234, 2232])).
% 0.86/1.03 tff(2236,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a12) | c2_1(a12) | (~c1_1(a12)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2237,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a36) | c3_1(a36) | c2_1(a12) | c3_1(a12) | (~ndr1_0) | (~c1_1(a12)) | (~c0_1(a36))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 0.86/1.03 tff(2238,plain,
% 0.86/1.03 (hskp22 | (~c0_1(a36))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2237, 72, 1923, 1851, 1870, 1922, 1941, 12])).
% 0.86/1.03 tff(2239,plain,
% 0.86/1.03 (hskp22),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2238, 1859])).
% 0.86/1.03 tff(2240,plain,
% 0.86/1.03 (~c3_1(a43)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[616, 2239])).
% 0.86/1.03 tff(2241,plain,
% 0.86/1.03 (~c1_1(a43)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[622, 2239])).
% 0.86/1.03 tff(2242,plain,
% 0.86/1.03 (c2_1(a31)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2134, 2223])).
% 0.86/1.03 tff(2243,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a31) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c1_1(a32) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a31) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c1_1(a32) | (~c0_1(a43)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2244,plain,
% 0.86/1.03 (((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c1_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a31) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c1_1(a32) | (~c0_1(a43)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2245,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c1_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a31) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c1_1(a32) | (~c0_1(a43))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2244])).
% 0.86/1.03 tff(2246,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c1_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a31) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c1_1(a32) | (~c0_1(a43)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2245, 2243])).
% 0.86/1.03 tff(2247,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c1_1(a31) | c0_1(a31) | (~c2_1(a31)) | c2_1(a32) | c1_1(a32) | c0_1(a32))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2248,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a31) | c1_1(a31) | (~ndr1_0) | (~c2_1(a31)) | c1_1(a32) | (~c0_1(a43))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2247, 2246])).
% 0.86/1.03 tff(2249,plain,
% 0.86/1.03 (~c0_1(a43)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2248, 72, 2242, 2241, 2240, 2231, 1883, 2225, 2224, 1908, 1898])).
% 0.86/1.03 tff(2250,plain,
% 0.86/1.03 (c2_1(a43)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[630, 2239])).
% 0.86/1.03 tff(2251,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a43) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)) | (~c2_1(a43)) | c0_1(a43))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)) | (~c2_1(a43)) | c0_1(a43))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2252,plain,
% 0.86/1.03 (((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c1_1(a43) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)) | (~c2_1(a43)) | c0_1(a43))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2253,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a43) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)) | (~c2_1(a43)) | c0_1(a43)))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2252])).
% 0.86/1.03 tff(2254,plain,
% 0.86/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)) | (~c2_1(a43)) | c0_1(a43))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2253, 2251])).
% 0.86/1.03 tff(2255,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2256,plain,
% 0.86/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)) | (~c2_1(a43)) | c0_1(a43)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2255, 2254])).
% 0.86/1.03 tff(2257,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2256, 72, 2250, 2241, 1852, 1870, 2231, 1883, 1908, 2249, 1859, 1898])).
% 0.86/1.03 tff(2258,plain,(hskp1 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(2259,plain,
% 0.86/1.03 (hskp1),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2258, 122])).
% 0.86/1.03 tff(2260,plain,
% 0.86/1.03 (c0_1(a2)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[567, 2259])).
% 0.86/1.03 tff(2261,plain,
% 0.86/1.03 (~c2_1(a2)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[551, 2259])).
% 0.86/1.03 tff(2262,plain,
% 0.86/1.03 (c3_1(a2)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[559, 2259])).
% 0.86/1.03 tff(2263,plain,
% 0.86/1.03 (~c1_1(a2)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1990, 72, 1765, 1781, 2260, 2262, 2261, 527, 1794])).
% 0.86/1.03 tff(2264,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a2) | (~c3_1(a2)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2265,plain,
% 0.86/1.03 ((hskp22 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2))) <=> (hskp22 | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a2) | (~c3_1(a2)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2266,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a2) | (~c3_1(a2))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2265])).
% 0.86/1.03 tff(2267,plain,
% 0.86/1.03 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a2) | (~c3_1(a2)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2266, 2264])).
% 0.86/1.03 tff(2268,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a33) | (~c2_1(a33)) | (~c3_1(a33)) | c2_1(a2) | c1_1(a2) | (~c3_1(a2)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2269,plain,
% 0.86/1.03 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c2_1(a2) | (~ndr1_0) | c1_1(a33) | (~c3_1(a33)) | (~c2_1(a33)) | c1_1(a2) | (~c3_1(a2))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2268, 2267])).
% 0.86/1.03 tff(2270,plain,
% 0.86/1.03 (hskp22),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2269, 72, 1781, 1773, 2262, 2261, 111, 1794, 2263])).
% 0.86/1.03 tff(2271,plain,
% 0.86/1.03 (~c3_1(a43)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[616, 2270])).
% 0.86/1.03 tff(2272,plain,
% 0.86/1.03 (~c1_1(a43)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[622, 2270])).
% 0.86/1.03 tff(2273,plain,
% 0.86/1.03 (c2_1(a43)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[630, 2270])).
% 0.86/1.03 tff(2274,plain,
% 0.86/1.03 (hskp0),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2205, 2273, 1781, 1794, 2261, 2272, 2271, 2263, 2260, 1765])).
% 0.86/1.03 tff(2275,plain,
% 0.86/1.03 (~c0_1(a1)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[645, 2274])).
% 0.86/1.03 tff(2276,plain,
% 0.86/1.03 (c2_1(a1)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[661, 2274])).
% 0.86/1.03 tff(2277,plain,
% 0.86/1.03 (c1_1(a1)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[653, 2274])).
% 0.86/1.03 tff(2278,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[708, 72, 2273, 2260, 2262, 2277, 2276, 2272, 2271, 2261, 2275, 121])).
% 0.86/1.03 tff(2279,plain,(hskp18), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(2280,plain,
% 0.86/1.03 (((~hskp18) | (~c2_1(a34))) <=> ((~hskp18) | (~c2_1(a34)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2281,plain,
% 0.86/1.04 (((~c2_1(a34)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a34)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2282,axiom,((~c2_1(a34)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.86/1.04 tff(2283,plain,
% 0.86/1.04 ((~hskp18) | (~c2_1(a34))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2282, 2281])).
% 0.86/1.04 tff(2284,plain,
% 0.86/1.04 ((~hskp18) | (~c2_1(a34))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2283, 2280])).
% 0.86/1.04 tff(2285,plain,
% 0.86/1.04 (~c2_1(a34)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2284, 2279])).
% 0.86/1.04 tff(2286,plain,
% 0.86/1.04 (((~hskp18) | (~c1_1(a34))) <=> ((~hskp18) | (~c1_1(a34)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2287,plain,
% 0.86/1.04 (((~c1_1(a34)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a34)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2288,axiom,((~c1_1(a34)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.86/1.04 tff(2289,plain,
% 0.86/1.04 ((~hskp18) | (~c1_1(a34))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2288, 2287])).
% 0.86/1.04 tff(2290,plain,
% 0.86/1.04 ((~hskp18) | (~c1_1(a34))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2289, 2286])).
% 0.86/1.04 tff(2291,plain,
% 0.86/1.04 (~c1_1(a34)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2290, 2279])).
% 0.86/1.04 tff(2292,plain,
% 0.86/1.04 (hskp19),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2031, 1, 1307])).
% 0.86/1.04 tff(2293,plain,
% 0.86/1.04 (~c3_1(a36)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1187, 2292])).
% 0.86/1.04 tff(2294,plain,
% 0.86/1.04 (~c1_1(a36)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1199, 2292])).
% 0.86/1.04 tff(2295,plain,
% 0.86/1.04 (((~hskp18) | c3_1(a34)) <=> ((~hskp18) | c3_1(a34))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2296,axiom,((~hskp18) | c3_1(a34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.86/1.04 tff(2297,plain,
% 0.86/1.04 ((~hskp18) | c3_1(a34)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2296, 2295])).
% 0.86/1.04 tff(2298,plain,
% 0.86/1.04 ((~hskp18) | c3_1(a34)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2297, 2295])).
% 0.86/1.04 tff(2299,plain,
% 0.86/1.04 ((~hskp18) | c3_1(a34)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2298, 2295])).
% 0.86/1.04 tff(2300,plain,
% 0.86/1.04 ((~hskp18) | c3_1(a34)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2299, 2295])).
% 0.86/1.04 tff(2301,plain,
% 0.86/1.04 ((~hskp18) | c3_1(a34)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2300, 2295])).
% 0.86/1.04 tff(2302,plain,
% 0.86/1.04 (c3_1(a34)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2301, 2279])).
% 0.86/1.04 tff(2303,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a34)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2304,plain,
% 0.86/1.04 ((hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34))) <=> (hskp22 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a34)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2305,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a34))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2304])).
% 0.86/1.04 tff(2306,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a34)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2305, 2303])).
% 0.86/1.04 tff(2307,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c3_1(a5)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2308,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c3_1(a5)) | (~c3_1(a34))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2307, 2306])).
% 0.86/1.04 tff(2309,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2308, 1, 72, 2302, 189, 181, 2291, 2285, 150, 111])).
% 0.86/1.04 tff(2310,plain,((~hskp4) | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(2311,plain,
% 0.86/1.04 (~hskp4),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2310, 1])).
% 0.86/1.04 tff(2312,plain,
% 0.86/1.04 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | c0_1(a36))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | c0_1(a36))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2313,plain,
% 0.86/1.04 ((hskp4 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c0_1(a36)) <=> (hskp4 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | c0_1(a36))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2314,plain,
% 0.86/1.04 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c0_1(a36))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | c0_1(a36)))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2313])).
% 0.86/1.04 tff(2315,plain,
% 0.86/1.04 (((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c0_1(a36))) <=> ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | c0_1(a36))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2314, 2312])).
% 0.86/1.04 tff(2316,plain,
% 0.86/1.04 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | (~ndr1_0) | c3_1(a36) | c1_1(a36) | c0_1(a36))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2317,plain,
% 0.86/1.04 ((~![U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | c1_1(a36) | c3_1(a36) | (~ndr1_0) | c0_1(a36)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 0.86/1.04 tff(2318,plain,
% 0.86/1.04 (c0_1(a36)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2317, 72, 2311, 2294, 2293, 101])).
% 0.86/1.04 tff(2319,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a34)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2320,plain,
% 0.86/1.04 ((hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34))) <=> (hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a34)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2321,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a34))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2320])).
% 0.86/1.04 tff(2322,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a34)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2321, 2319])).
% 0.86/1.04 tff(2323,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2324,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c3_1(a34))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2323, 2322])).
% 0.86/1.04 tff(2325,plain,
% 0.86/1.04 (hskp0),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2324, 72, 2302, 38, 30, 2291, 2285, 22, 585])).
% 0.86/1.04 tff(2326,plain,
% 0.86/1.04 (~c0_1(a1)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[645, 2325])).
% 0.86/1.04 tff(2327,plain,
% 0.86/1.04 (~c2_1(a36)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1193, 2292])).
% 0.86/1.04 tff(2328,plain,
% 0.86/1.04 (hskp17),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1876, 72, 2294, 2327, 2293, 1869, 2318])).
% 0.86/1.04 tff(2329,plain,
% 0.86/1.04 (~c2_1(a32)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1882, 2328])).
% 0.86/1.04 tff(2330,plain,
% 0.86/1.04 (~c0_1(a32)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2230, 2328])).
% 0.86/1.04 tff(2331,plain,
% 0.86/1.04 (c2_1(a1)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[661, 2325])).
% 0.86/1.04 tff(2332,plain,
% 0.86/1.04 (c1_1(a1)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[653, 2325])).
% 0.86/1.04 tff(2333,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a36)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a36)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2334,plain,
% 0.86/1.04 (((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32))) <=> (c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a36)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2335,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a36))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2334])).
% 0.86/1.04 tff(2336,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a36)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2335, 2333])).
% 0.86/1.04 tff(2337,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a36) | c1_1(a36) | (~c0_1(a36)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2338,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a36))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2337, 2336])).
% 0.86/1.04 tff(2339,plain,
% 0.86/1.04 (~c1_1(a32)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2338, 72, 2332, 2331, 2294, 2293, 2330, 2329, 2326, 1918, 2318])).
% 0.86/1.04 tff(2340,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a36) | c2_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a36) | c2_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2341,plain,
% 0.86/1.04 (((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c1_1(a36) | c2_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2342,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a36) | c2_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2341])).
% 0.86/1.04 tff(2343,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a36) | c2_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2342, 2340])).
% 0.86/1.04 tff(2344,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a32) | c1_1(a32) | c0_1(a32))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2345,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a36) | c2_1(a36) | c3_1(a36) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a36))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2344, 2343])).
% 0.86/1.04 tff(2346,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2345, 72, 2294, 2327, 2293, 2330, 2329, 881, 2318, 2339])).
% 0.86/1.04 tff(2347,plain,(hskp22 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(2348,plain,
% 0.86/1.04 (hskp22),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2347, 1307])).
% 0.86/1.04 tff(2349,plain,
% 0.86/1.04 (c2_1(a43)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[630, 2348])).
% 0.86/1.04 tff(2350,plain,
% 0.86/1.04 (~c3_1(a43)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[616, 2348])).
% 0.86/1.04 tff(2351,plain,
% 0.86/1.04 (~c1_1(a43)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[622, 2348])).
% 0.86/1.04 tff(2352,assumption,(hskp1), introduced(assumption)).
% 0.86/1.04 tff(2353,plain,
% 0.86/1.04 (c3_1(a2)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[559, 2352])).
% 0.86/1.04 tff(2354,plain,
% 0.86/1.04 (~c2_1(a2)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[551, 2352])).
% 0.86/1.04 tff(2355,plain,
% 0.86/1.04 (c0_1(a2)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[567, 2352])).
% 0.86/1.04 tff(2356,assumption,(c3_1(a2)), introduced(assumption)).
% 0.86/1.04 tff(2357,plain,
% 0.86/1.04 (~hskp21),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1568, 1477, 1478, 1479, 1564])).
% 0.86/1.04 tff(2358,plain,
% 0.86/1.04 ((~c1_1(a2)) | (~c0_1(a43))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1577, 72, 1478, 2186, 2356, 1564, 2185, 527])).
% 0.86/1.04 tff(2359,plain,
% 0.86/1.04 (~c1_1(a2)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2358, 1477])).
% 0.86/1.04 tff(2360,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2187, 2359, 2357, 528])).
% 0.86/1.04 tff(2361,plain,((~c0_1(a43)) | hskp0 | (~c0_1(a2)) | c2_1(a2) | (~c2_1(a43)) | (~c3_1(a2)) | c1_1(a43) | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(2362,plain,
% 0.86/1.04 (~c0_1(a43)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2361, 528, 2186, 2185, 1478, 2356, 1564, 1479])).
% 0.86/1.04 tff(2363,plain,
% 0.86/1.04 (hskp5),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2190, 2362, 528])).
% 0.86/1.04 tff(2364,plain,
% 0.86/1.04 (~c3_1(a6)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1034, 2363])).
% 0.86/1.04 tff(2365,plain,
% 0.86/1.04 (c0_1(a6)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[247, 2363])).
% 0.86/1.04 tff(2366,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | (~c1_1(a6)) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | (~c1_1(a6)) | (~c3_1(a34)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2367,plain,
% 0.86/1.04 ((hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34))) <=> (hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | (~c1_1(a6)) | (~c3_1(a34)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2368,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | (~c1_1(a6)) | (~c3_1(a34))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2367])).
% 0.86/1.04 tff(2369,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | (~c1_1(a6)) | (~c3_1(a34)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2368, 2366])).
% 0.86/1.04 tff(2370,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a6) | (~c1_1(a6)) | (~c0_1(a6)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2371,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | (~c1_1(a6)) | (~c3_1(a34))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2370, 2369])).
% 0.86/1.04 tff(2372,plain,
% 0.86/1.04 (~c1_1(a6)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2371, 72, 528, 2302, 2365, 2291, 2285, 2364, 585])).
% 0.86/1.04 tff(2373,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a43) | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | c1_1(a6) | c0_1(a34) | (~c2_1(a43)) | c0_1(a43))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | c1_1(a6) | c0_1(a34) | (~c2_1(a43)) | c0_1(a43))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2374,plain,
% 0.86/1.04 (((~ndr1_0) | c3_1(a6) | c1_1(a6) | (~c0_1(a6)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34)) <=> (c1_1(a43) | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | c1_1(a6) | c0_1(a34) | (~c2_1(a43)) | c0_1(a43))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2375,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a6) | c1_1(a6) | (~c0_1(a6)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a43) | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | c1_1(a6) | c0_1(a34) | (~c2_1(a43)) | c0_1(a43)))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2374])).
% 0.86/1.04 tff(2376,plain,
% 0.86/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a6) | c1_1(a6) | (~c0_1(a6)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | c1_1(a6) | c0_1(a34) | (~c2_1(a43)) | c0_1(a43))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2375, 2373])).
% 0.86/1.04 tff(2377,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a6) | c1_1(a6) | (~c0_1(a6)) | c1_1(a43) | c0_1(a43) | (~c2_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2378,plain,
% 0.86/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a43) | c1_1(a34) | c2_1(a34) | c3_1(a6) | (~ndr1_0) | (~c0_1(a6)) | c1_1(a6) | c0_1(a34) | (~c2_1(a43)) | c0_1(a43)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2377, 2376])).
% 0.86/1.04 tff(2379,plain,
% 0.86/1.04 (c1_1(a6) | c0_1(a34)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2378, 72, 1478, 2365, 1564, 2291, 2285, 2364, 1908, 2362])).
% 0.86/1.04 tff(2380,plain,
% 0.86/1.04 (c0_1(a34)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2379, 2372])).
% 0.86/1.04 tff(2381,plain,
% 0.86/1.04 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c0_1(a34)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c0_1(a34)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2382,plain,
% 0.86/1.04 ((hskp21 | hskp0 | (~ndr1_0) | c1_1(a34) | c2_1(a34) | (~c0_1(a34))) <=> (hskp21 | hskp0 | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c0_1(a34)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2383,plain,
% 0.86/1.04 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a34) | c2_1(a34) | (~c0_1(a34)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c0_1(a34))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2382])).
% 0.86/1.04 tff(2384,plain,
% 0.86/1.04 (((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a34) | c2_1(a34) | (~c0_1(a34)))) <=> ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c0_1(a34)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2383, 2381])).
% 0.86/1.04 tff(2385,plain,
% 0.86/1.04 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp21 | hskp0 | (~ndr1_0) | c1_1(a34) | c2_1(a34) | (~c0_1(a34)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2386,plain,
% 0.86/1.04 ((~![U: $i] : (hskp21 | hskp0 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp21 | hskp0 | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c0_1(a34))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 0.86/1.04 tff(2387,plain,
% 0.86/1.04 (hskp21 | hskp0 | (~c0_1(a34))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2386, 72, 2291, 2285, 1122])).
% 0.86/1.04 tff(2388,plain,
% 0.86/1.04 (hskp21),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2387, 2380, 528])).
% 0.86/1.04 tff(2389,plain,
% 0.86/1.04 (~c0_1(a42)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1135, 2388])).
% 0.86/1.04 tff(2390,plain,
% 0.86/1.04 (c2_1(a6)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[255, 2363])).
% 0.86/1.04 tff(2391,plain,
% 0.86/1.04 (c3_1(a42)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1143, 2388])).
% 0.86/1.04 tff(2392,plain,
% 0.86/1.04 (c2_1(a42)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1151, 2388])).
% 0.86/1.04 tff(2393,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2019, 72, 2392, 2391, 2365, 2390, 2389, 2364, 91, 2372])).
% 0.86/1.04 tff(2394,plain,(hskp0 | (~c2_1(a43)) | c1_1(a43) | (~c0_1(a2)) | c2_1(a2) | (~c3_1(a2)) | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(2395,plain,
% 0.86/1.04 (hskp0),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2394, 2355, 1564, 1478, 2354, 2353, 1479])).
% 0.86/1.04 tff(2396,plain,
% 0.86/1.04 (~c0_1(a1)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[645, 2395])).
% 0.86/1.04 tff(2397,plain,
% 0.86/1.04 (c2_1(a1)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[661, 2395])).
% 0.86/1.04 tff(2398,plain,
% 0.86/1.04 (c1_1(a1)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[653, 2395])).
% 0.86/1.04 tff(2399,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[708, 72, 1478, 2355, 2353, 2398, 2397, 1564, 1479, 2354, 2396, 121])).
% 0.86/1.04 tff(2400,plain,((~hskp1) | (~c2_1(a43)) | c1_1(a43) | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(2401,plain,
% 0.86/1.04 (~hskp1),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2400, 2349, 2351, 2350])).
% 0.86/1.04 tff(2402,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a43) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a43)) | (~c0_1(a43)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a43) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2403,plain,
% 0.86/1.04 ((hskp1 | (~ndr1_0) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34)) <=> (hskp1 | c1_1(a43) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2404,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a43) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a43)) | (~c0_1(a43))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2403])).
% 0.86/1.04 tff(2405,plain,
% 0.86/1.04 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a43) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a43)) | (~c0_1(a43)))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2404, 2402])).
% 0.86/1.04 tff(2406,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a43) | (~c2_1(a43)) | (~c0_1(a43)) | c2_1(a34) | c1_1(a34) | c0_1(a34))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2407,plain,
% 0.86/1.04 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a43) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a43)) | (~c0_1(a43))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 0.86/1.05 tff(2408,plain,
% 0.86/1.05 (hskp1 | c0_1(a34) | (~c0_1(a43))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2407, 72, 1478, 1564, 2291, 2285, 674])).
% 0.86/1.05 tff(2409,plain,
% 0.86/1.05 (c0_1(a34)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2408, 1477, 1397])).
% 0.86/1.05 tff(2410,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2387, 2409, 2357, 528])).
% 0.86/1.05 tff(2411,plain,((~c0_1(a43)) | hskp0 | hskp1 | (~c2_1(a43)) | c1_1(a43) | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(2412,plain,
% 0.86/1.05 (~c0_1(a43)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2411, 528, 1397, 1478, 1564, 1479])).
% 0.86/1.05 tff(2413,plain,
% 0.86/1.05 (hskp4),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2043, 2412])).
% 0.86/1.05 tff(2414,plain,
% 0.86/1.05 (~c1_1(a5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[149, 2413])).
% 0.86/1.05 tff(2415,plain,
% 0.86/1.05 (c3_1(a5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[180, 2413])).
% 0.86/1.05 tff(2416,plain,
% 0.86/1.05 (c2_1(a5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[188, 2413])).
% 0.86/1.05 tff(2417,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[544, 72, 1397, 528, 2416, 2415, 2414, 538])).
% 0.86/1.05 tff(2418,plain,(hskp0 | hskp1 | c1_1(a43) | c3_1(a43) | (~c2_1(a43))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(2419,plain,
% 0.86/1.05 (hskp0),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2418, 2401, 2351, 2350, 2349])).
% 0.86/1.05 tff(2420,plain,
% 0.86/1.05 (~c0_1(a1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[645, 2419])).
% 0.86/1.05 tff(2421,plain,
% 0.86/1.05 (c1_1(a1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[653, 2419])).
% 0.86/1.05 tff(2422,plain,
% 0.86/1.05 (c2_1(a1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[661, 2419])).
% 0.86/1.05 tff(2423,plain,
% 0.86/1.05 (hskp4),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2047, 2422, 1307, 2350, 2349, 2351, 2421, 2420])).
% 0.86/1.05 tff(2424,plain,
% 0.86/1.05 (c2_1(a5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[188, 2423])).
% 0.86/1.05 tff(2425,plain,
% 0.86/1.05 (c3_1(a5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[180, 2423])).
% 0.86/1.05 tff(2426,plain,
% 0.86/1.05 (~c1_1(a5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[149, 2423])).
% 0.86/1.05 tff(2427,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c2_1(a34) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a34)) | (~c0_1(a34)) | (~c2_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a34) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a34)) | (~c0_1(a34)) | (~c2_1(a43)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2428,plain,
% 0.86/1.05 (((~ndr1_0) | c2_1(a34) | (~c3_1(a34)) | (~c0_1(a34)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1))) <=> (c1_1(a43) | c3_1(a43) | c2_1(a34) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a34)) | (~c0_1(a34)) | (~c2_1(a43)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2429,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a34) | (~c3_1(a34)) | (~c0_1(a34)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c2_1(a34) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a34)) | (~c0_1(a34)) | (~c2_1(a43))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2428])).
% 0.86/1.05 tff(2430,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a34) | (~c3_1(a34)) | (~c0_1(a34)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a34) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a34)) | (~c0_1(a34)) | (~c2_1(a43)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2429, 2427])).
% 0.86/1.05 tff(2431,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a34) | (~c3_1(a34)) | (~c0_1(a34)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2432,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c2_1(a34) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c3_1(a34)) | (~c0_1(a34)) | (~c2_1(a43))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2431, 2430])).
% 0.86/1.05 tff(2433,plain,
% 0.86/1.05 (~c0_1(a34)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2432, 72, 2349, 2302, 2421, 2422, 2351, 2350, 2285, 2420, 121])).
% 0.86/1.05 tff(2434,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a34))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2435,plain,
% 0.86/1.05 ((hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a34) | c1_1(a34) | c0_1(a34)) <=> (hskp1 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a34))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2436,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a34)))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2435])).
% 0.86/1.05 tff(2437,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a34))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2436, 2434])).
% 0.86/1.05 tff(2438,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a5) | (~c2_1(a5)) | (~c0_1(a5)) | c2_1(a34) | c1_1(a34) | c0_1(a34))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2439,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a34) | c2_1(a34) | c1_1(a5) | (~ndr1_0) | (~c2_1(a5)) | (~c0_1(a5)) | c0_1(a34)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2438, 2437])).
% 0.86/1.05 tff(2440,plain,
% 0.86/1.05 ((~c0_1(a5)) | c0_1(a34)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2439, 72, 2401, 2424, 2291, 2285, 2426, 674])).
% 0.86/1.05 tff(2441,plain,
% 0.86/1.05 (~c0_1(a5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2440, 2433])).
% 0.86/1.05 tff(2442,assumption,(hskp2), introduced(assumption)).
% 0.86/1.05 tff(2443,plain,
% 0.86/1.05 (~c1_1(a3)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[156, 2442])).
% 0.86/1.05 tff(2444,plain,
% 0.86/1.05 (c0_1(a3)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[172, 2442])).
% 0.86/1.05 tff(2445,plain,
% 0.86/1.05 (c2_1(a3)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[164, 2442])).
% 0.86/1.05 tff(2446,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1221, 2445, 2444, 232, 190, 218, 2443, 233])).
% 0.86/1.05 tff(2447,plain,((~hskp2) | (~c3_1(a5)) | c1_1(a5) | c0_1(a5) | (~c2_1(a5))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(2448,plain,
% 0.86/1.05 (~hskp2),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2447, 2441, 2426, 2425, 2424])).
% 0.86/1.05 tff(2449,plain,
% 0.86/1.05 ((hskp24 | hskp23 | hskp2) <=> (hskp24 | hskp23 | hskp2)),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2450,plain,
% 0.86/1.05 (((hskp2 | hskp24) | hskp23) <=> (hskp24 | hskp23 | hskp2)),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2451,axiom,((hskp2 | hskp24) | hskp23), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.86/1.05 tff(2452,plain,
% 0.86/1.05 (hskp24 | hskp23 | hskp2),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2451, 2450])).
% 0.86/1.05 tff(2453,plain,
% 0.86/1.05 (hskp24 | hskp23 | hskp2),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2452, 2449])).
% 0.86/1.05 tff(2454,plain,
% 0.86/1.05 (hskp24 | hskp23 | hskp2),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2453, 2449])).
% 0.86/1.05 tff(2455,plain,
% 0.86/1.05 (hskp24 | hskp23 | hskp2),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2454, 2449])).
% 0.86/1.05 tff(2456,plain,
% 0.86/1.05 (hskp24 | hskp23 | hskp2),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2455, 2449])).
% 0.86/1.05 tff(2457,plain,
% 0.86/1.05 (hskp23),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2456, 2448, 1307])).
% 0.86/1.05 tff(2458,plain,
% 0.86/1.05 (((~hskp23) | (~c2_1(a52))) <=> ((~hskp23) | (~c2_1(a52)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2459,plain,
% 0.86/1.05 (((~c2_1(a52)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a52)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2460,axiom,((~c2_1(a52)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.86/1.05 tff(2461,plain,
% 0.86/1.05 ((~hskp23) | (~c2_1(a52))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2460, 2459])).
% 0.86/1.05 tff(2462,plain,
% 0.86/1.05 ((~hskp23) | (~c2_1(a52))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2461, 2458])).
% 0.86/1.05 tff(2463,plain,
% 0.86/1.05 (~c2_1(a52)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2462, 2457])).
% 0.86/1.05 tff(2464,plain,
% 0.86/1.05 (((~hskp23) | c0_1(a52)) <=> ((~hskp23) | c0_1(a52))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2465,axiom,((~hskp23) | c0_1(a52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.86/1.05 tff(2466,plain,
% 0.86/1.05 ((~hskp23) | c0_1(a52)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2465, 2464])).
% 0.86/1.05 tff(2467,plain,
% 0.86/1.05 ((~hskp23) | c0_1(a52)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2466, 2464])).
% 0.86/1.05 tff(2468,plain,
% 0.86/1.05 ((~hskp23) | c0_1(a52)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2467, 2464])).
% 0.86/1.05 tff(2469,plain,
% 0.86/1.05 ((~hskp23) | c0_1(a52)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2468, 2464])).
% 0.86/1.05 tff(2470,plain,
% 0.86/1.05 ((~hskp23) | c0_1(a52)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2469, 2464])).
% 0.86/1.05 tff(2471,plain,
% 0.86/1.05 (c0_1(a52)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2470, 2457])).
% 0.86/1.05 tff(2472,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a52) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | (~c3_1(a52)) | (~c0_1(a52)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a52) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | (~c3_1(a52)) | (~c0_1(a52)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2473,plain,
% 0.86/1.05 (((~ndr1_0) | c2_1(a52) | (~c3_1(a52)) | (~c0_1(a52)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1))) <=> (c2_1(a52) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | (~c3_1(a52)) | (~c0_1(a52)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2474,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a52) | (~c3_1(a52)) | (~c0_1(a52)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a52) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | (~c3_1(a52)) | (~c0_1(a52))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2473])).
% 0.86/1.05 tff(2475,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a52) | (~c3_1(a52)) | (~c0_1(a52)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a52) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | (~c3_1(a52)) | (~c0_1(a52)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2474, 2472])).
% 0.86/1.05 tff(2476,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a52) | (~c3_1(a52)) | (~c0_1(a52)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2477,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a52) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | (~c3_1(a52)) | (~c0_1(a52))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2476, 2475])).
% 0.86/1.05 tff(2478,plain,
% 0.86/1.05 (~c3_1(a52)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2477, 72, 2471, 2349, 2421, 2422, 2463, 2351, 2350, 2420, 121])).
% 0.86/1.05 tff(2479,plain,
% 0.86/1.05 (hskp0),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2418, 1397, 2351, 2350, 2349])).
% 0.86/1.05 tff(2480,plain,
% 0.86/1.05 (~c0_1(a1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[645, 2479])).
% 0.86/1.05 tff(2481,plain,
% 0.86/1.05 (c1_1(a1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[653, 2479])).
% 0.86/1.05 tff(2482,plain,
% 0.86/1.05 (c2_1(a1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[661, 2479])).
% 0.86/1.05 tff(2483,plain,
% 0.86/1.05 (hskp4),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2047, 2482, 1307, 2350, 2349, 2351, 2481, 2480])).
% 0.86/1.05 tff(2484,plain,
% 0.86/1.05 (c2_1(a5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[188, 2483])).
% 0.86/1.05 tff(2485,plain,
% 0.86/1.05 (~c0_1(a34)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2432, 72, 2349, 2302, 2481, 2482, 2351, 2350, 2285, 2480, 121])).
% 0.86/1.05 tff(2486,plain,
% 0.86/1.05 (~c1_1(a5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[149, 2483])).
% 0.86/1.05 tff(2487,plain,
% 0.86/1.05 ((~c0_1(a5)) | c0_1(a34)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2439, 72, 1397, 2484, 2291, 2285, 2486, 674])).
% 0.86/1.05 tff(2488,plain,
% 0.86/1.05 (~c0_1(a5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2487, 2485])).
% 0.86/1.05 tff(2489,plain,
% 0.86/1.05 (c3_1(a5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[180, 2483])).
% 0.86/1.05 tff(2490,plain,
% 0.86/1.05 (~hskp2),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2447, 2489, 2486, 2488, 2484])).
% 0.86/1.05 tff(2491,plain,
% 0.86/1.05 (hskp23),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2456, 2490, 1307])).
% 0.86/1.05 tff(2492,plain,
% 0.86/1.05 (~c2_1(a52)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2462, 2491])).
% 0.86/1.05 tff(2493,plain,
% 0.86/1.05 (((~hskp23) | (~c1_1(a52))) <=> ((~hskp23) | (~c1_1(a52)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2494,plain,
% 0.86/1.05 (((~c1_1(a52)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a52)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2495,axiom,((~c1_1(a52)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.86/1.05 tff(2496,plain,
% 0.86/1.05 ((~hskp23) | (~c1_1(a52))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2495, 2494])).
% 0.86/1.05 tff(2497,plain,
% 0.86/1.05 ((~hskp23) | (~c1_1(a52))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2496, 2493])).
% 0.86/1.05 tff(2498,plain,
% 0.86/1.05 (~c1_1(a52)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2497, 2491])).
% 0.86/1.05 tff(2499,plain,
% 0.86/1.05 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | c1_1(a52) | c2_1(a52) | (~ndr1_0) | c3_1(a52))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp19 | hskp1 | c1_1(a52) | c2_1(a52) | (~ndr1_0) | c3_1(a52))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2500,plain,
% 0.86/1.05 ((hskp19 | hskp1 | (~ndr1_0) | c3_1(a52) | c1_1(a52) | c2_1(a52)) <=> (hskp19 | hskp1 | c1_1(a52) | c2_1(a52) | (~ndr1_0) | c3_1(a52))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2501,plain,
% 0.86/1.05 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | (~ndr1_0) | c3_1(a52) | c1_1(a52) | c2_1(a52))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | c1_1(a52) | c2_1(a52) | (~ndr1_0) | c3_1(a52)))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2500])).
% 0.86/1.05 tff(2502,plain,
% 0.86/1.05 (((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | (~ndr1_0) | c3_1(a52) | c1_1(a52) | c2_1(a52))) <=> ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp19 | hskp1 | c1_1(a52) | c2_1(a52) | (~ndr1_0) | c3_1(a52))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2501, 2499])).
% 0.86/1.05 tff(2503,plain,
% 0.86/1.05 ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp19 | hskp1 | (~ndr1_0) | c3_1(a52) | c1_1(a52) | c2_1(a52))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2504,plain,
% 0.86/1.05 ((~![U: $i] : (hskp19 | hskp1 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp19 | hskp1 | c1_1(a52) | c2_1(a52) | (~ndr1_0) | c3_1(a52)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2503, 2502])).
% 0.86/1.05 tff(2505,plain,
% 0.86/1.05 (c3_1(a52)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2504, 72, 1319, 1397, 2498, 2492, 1435])).
% 0.86/1.05 tff(2506,plain,
% 0.86/1.05 (c0_1(a52)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2470, 2491])).
% 0.86/1.05 tff(2507,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2477, 72, 2506, 2349, 2481, 2482, 2492, 2351, 2350, 2480, 121, 2505])).
% 0.86/1.05 tff(2508,plain,(hskp1 | hskp19 | hskp24), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(2509,plain,
% 0.86/1.05 (hskp19),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2508, 2401, 1307])).
% 0.86/1.05 tff(2510,plain,
% 0.86/1.05 (~c3_1(a36)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1187, 2509])).
% 0.86/1.05 tff(2511,plain,
% 0.86/1.05 (~c2_1(a36)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1193, 2509])).
% 0.86/1.05 tff(2512,plain,
% 0.86/1.05 (~c1_1(a36)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1199, 2509])).
% 0.86/1.05 tff(2513,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a36) | c2_1(a36) | c3_1(a36) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c0_1(a36)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a36) | c2_1(a36) | c3_1(a36) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c0_1(a36)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2514,plain,
% 0.86/1.05 (((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a34) | c1_1(a34) | c0_1(a34)) <=> (c1_1(a36) | c2_1(a36) | c3_1(a36) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c0_1(a36)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2515,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a36) | c2_1(a36) | c3_1(a36) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c0_1(a36))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2514])).
% 0.86/1.05 tff(2516,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a36) | c2_1(a36) | c3_1(a36) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c0_1(a36)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2515, 2513])).
% 0.86/1.05 tff(2517,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)) | c2_1(a36) | c1_1(a36) | (~c0_1(a36)) | c2_1(a34) | c1_1(a34) | c0_1(a34))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2518,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a36) | c2_1(a36) | c3_1(a36) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c0_1(a36))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2517, 2516])).
% 0.86/1.05 tff(2519,plain,
% 0.86/1.05 (c0_1(a34) | (~c0_1(a36))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2518, 72, 2512, 2511, 2510, 2291, 2285, 881])).
% 0.86/1.05 tff(2520,plain,
% 0.86/1.05 (~c0_1(a36)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2519, 2433])).
% 0.86/1.05 tff(2521,plain,
% 0.86/1.05 (~c1_1(a52)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2497, 2457])).
% 0.86/1.05 tff(2522,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a52) | c2_1(a52) | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c0_1(a36) | c3_1(a52) | (~c0_1(a52)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a52) | c2_1(a52) | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c0_1(a36) | c3_1(a52) | (~c0_1(a52)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2523,plain,
% 0.86/1.05 (((~ndr1_0) | c3_1(a52) | c2_1(a52) | (~c0_1(a52)) | c2_1(a52) | c1_1(a52) | (~c0_1(a52)) | c2_1(a36) | c1_1(a36) | c0_1(a36)) <=> (c1_1(a52) | c2_1(a52) | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c0_1(a36) | c3_1(a52) | (~c0_1(a52)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2524,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a52) | c2_1(a52) | (~c0_1(a52)) | c2_1(a52) | c1_1(a52) | (~c0_1(a52)) | c2_1(a36) | c1_1(a36) | c0_1(a36))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a52) | c2_1(a52) | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c0_1(a36) | c3_1(a52) | (~c0_1(a52))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2523])).
% 0.86/1.05 tff(2525,plain,
% 0.86/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a52) | c2_1(a52) | (~c0_1(a52)) | c2_1(a52) | c1_1(a52) | (~c0_1(a52)) | c2_1(a36) | c1_1(a36) | c0_1(a36))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a52) | c2_1(a52) | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c0_1(a36) | c3_1(a52) | (~c0_1(a52)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2524, 2522])).
% 0.86/1.05 tff(2526,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a52) | c2_1(a52) | (~c0_1(a52)) | c2_1(a52) | c1_1(a52) | (~c0_1(a52)) | c2_1(a36) | c1_1(a36) | c0_1(a36))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2527,plain,
% 0.86/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a52) | c2_1(a52) | c1_1(a36) | c2_1(a36) | (~ndr1_0) | c0_1(a36) | c3_1(a52) | (~c0_1(a52))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2526, 2525])).
% 0.86/1.05 tff(2528,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2527, 72, 2471, 2521, 2463, 2512, 2511, 881, 2520, 2478])).
% 0.86/1.05 tff(2529,plain,(hskp24), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(2530,plain,
% 0.86/1.05 (~c1_1(a58)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1355, 2529])).
% 0.86/1.05 tff(2531,plain,
% 0.86/1.05 (c3_1(a58)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1334, 2529])).
% 0.86/1.05 tff(2532,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c3_1(a34)) | (~c2_1(a58)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c3_1(a34)) | (~c2_1(a58)) | (~c3_1(a58)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2533,plain,
% 0.86/1.05 ((hskp22 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34))) <=> (hskp22 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c3_1(a34)) | (~c2_1(a58)) | (~c3_1(a58)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2534,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c3_1(a34)) | (~c2_1(a58)) | (~c3_1(a58))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2533])).
% 0.86/1.05 tff(2535,plain,
% 0.86/1.05 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c3_1(a34)) | (~c2_1(a58)) | (~c3_1(a58)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2534, 2532])).
% 0.86/1.05 tff(2536,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c3_1(a58)) | c2_1(a34) | c1_1(a34) | (~c3_1(a34)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2537,plain,
% 0.86/1.05 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | (~c3_1(a34)) | (~c2_1(a58)) | (~c3_1(a58))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 0.86/1.05 tff(2538,plain,
% 0.86/1.05 (hskp22 | (~c2_1(a58))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2537, 72, 2531, 2302, 2530, 2291, 2285, 111])).
% 0.86/1.05 tff(2539,plain,
% 0.86/1.05 (~c2_1(a58)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2538, 1])).
% 0.86/1.05 tff(2540,plain,
% 0.86/1.05 (c0_1(a58)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1342, 2529])).
% 0.86/1.05 tff(2541,plain,
% 0.86/1.05 (hskp22 | hskp19 | c2_1(a58)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1349, 72, 2540, 2531, 1318])).
% 0.86/1.05 tff(2542,plain,
% 0.86/1.05 (hskp19),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2541, 1, 2539])).
% 0.86/1.05 tff(2543,plain,
% 0.86/1.05 (~c3_1(a36)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1187, 2542])).
% 0.86/1.05 tff(2544,plain,
% 0.86/1.05 (~c1_1(a36)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1199, 2542])).
% 0.86/1.05 tff(2545,plain,
% 0.86/1.05 (c0_1(a36)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2317, 72, 2311, 2544, 2543, 101])).
% 0.86/1.05 tff(2546,plain,
% 0.86/1.05 (^[U: $i] : refl((hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(2547,plain,
% 0.86/1.05 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[2546])).
% 0.86/1.05 tff(2548,plain,
% 0.86/1.05 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2549,plain,
% 0.86/1.05 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp4) <=> ((hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp4))), rewrite(((hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp4) <=> (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp4) <=> (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(2550,plain,
% 0.86/1.05 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp4) <=> ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[2549])).
% 0.86/1.05 tff(2551,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp2) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.86/1.05 tff(2552,plain,
% 0.86/1.05 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2551, 2550])).
% 0.86/1.05 tff(2553,plain,
% 0.86/1.05 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2552, 2548])).
% 0.86/1.05 tff(2554,plain,(
% 0.86/1.05 ![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.86/1.05 inference(skolemize,[status(sab)],[2553])).
% 0.86/1.05 tff(2555,plain,
% 0.86/1.05 (![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2554, 2547])).
% 0.86/1.05 tff(2556,plain,
% 0.86/1.05 (~c2_1(a36)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1193, 2542])).
% 0.86/1.05 tff(2557,plain,
% 0.86/1.05 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp4 | hskp2 | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp4 | hskp2 | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2558,plain,
% 0.86/1.05 ((hskp4 | hskp2 | (~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36))) <=> (hskp4 | hskp2 | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2559,plain,
% 0.86/1.05 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp4 | hskp2 | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2558])).
% 0.86/1.05 tff(2560,plain,
% 0.86/1.05 (((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)))) <=> ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp4 | hskp2 | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2559, 2557])).
% 0.86/1.05 tff(2561,plain,
% 0.86/1.05 ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp4 | hskp2 | (~ndr1_0) | c3_1(a36) | c2_1(a36) | (~c0_1(a36)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2562,plain,
% 0.86/1.05 ((~![U: $i] : (hskp4 | hskp2 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp4 | hskp2 | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2561, 2560])).
% 0.86/1.05 tff(2563,plain,
% 0.86/1.05 (hskp2),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2562, 72, 2311, 2556, 2543, 2555, 2545])).
% 0.86/1.06 tff(2564,plain,
% 0.86/1.06 (~c1_1(a3)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[156, 2563])).
% 0.86/1.06 tff(2565,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c0_1(a58)) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c0_1(a58)) | (~c3_1(a58)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2566,plain,
% 0.86/1.06 ((hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58))) <=> (hskp16 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c0_1(a58)) | (~c3_1(a58)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2567,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c0_1(a58)) | (~c3_1(a58))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2566])).
% 0.86/1.06 tff(2568,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c0_1(a58)) | (~c3_1(a58)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2567, 2565])).
% 0.86/1.06 tff(2569,plain,
% 0.86/1.06 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c1_1(a58) | (~c3_1(a58)) | (~c0_1(a58)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(2570,plain,
% 0.86/1.06 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | (~c0_1(a58)) | (~c3_1(a58))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 0.86/1.06 tff(2571,plain,
% 0.86/1.06 (hskp16),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2570, 72, 2540, 2531, 38, 30, 2530, 22, 1940])).
% 0.86/1.06 tff(2572,plain,
% 0.86/1.06 (~c0_1(a31)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2126, 2571])).
% 0.86/1.06 tff(2573,plain,
% 0.86/1.06 (c2_1(a3)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[164, 2563])).
% 0.86/1.06 tff(2574,plain,
% 0.86/1.06 (c0_1(a3)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[172, 2563])).
% 0.86/1.06 tff(2575,plain,
% 0.86/1.06 (c2_1(a31)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2134, 2571])).
% 0.86/1.06 tff(2576,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a31) | c3_1(a19) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a31) | c3_1(a19) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2577,plain,
% 0.86/1.06 (((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31))) <=> (c0_1(a31) | c3_1(a19) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2578,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c0_1(a31) | c3_1(a19) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2577])).
% 0.86/1.06 tff(2579,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a31) | c3_1(a19) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2578, 2576])).
% 0.86/1.06 tff(2580,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a19) | (~c2_1(a19)) | (~c0_1(a19)) | c1_1(a3) | (~c2_1(a3)) | (~c0_1(a3)) | c0_1(a31) | (~c2_1(a31)) | (~c3_1(a31)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(2581,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c0_1(a31) | c3_1(a19) | c1_1(a3) | (~ndr1_0) | (~c2_1(a3)) | (~c0_1(a3)) | (~c2_1(a19)) | (~c0_1(a19)) | (~c2_1(a31)) | (~c3_1(a31))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 0.86/1.06 tff(2582,plain,
% 0.86/1.06 (~c3_1(a31)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2581, 72, 2575, 38, 2574, 2573, 2572, 22, 2564, 91, 81])).
% 0.86/1.06 tff(2583,plain,
% 0.86/1.06 (~c1_1(a31)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2165, 2571])).
% 0.86/1.06 tff(2584,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2172, 72, 2311, 2572, 2583, 101, 2582])).
% 0.86/1.06 tff(2585,plain,(hskp22), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(2586,plain,
% 0.86/1.06 (~c1_1(a43)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[622, 2585])).
% 0.86/1.06 tff(2587,plain,
% 0.86/1.06 (~c3_1(a43)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[616, 2585])).
% 0.86/1.06 tff(2588,assumption,(~c2_1(a43)), introduced(assumption)).
% 0.86/1.06 tff(2589,plain,
% 0.86/1.06 (~hskp22),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[630, 2588])).
% 0.86/1.06 tff(2590,plain,
% 0.86/1.06 (~hskp4),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2310, 2589])).
% 0.86/1.06 tff(2591,plain,
% 0.86/1.06 (hskp19),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1672, 2590, 2529, 2589])).
% 0.86/1.06 tff(2592,plain,
% 0.86/1.06 (~c3_1(a36)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1187, 2591])).
% 0.86/1.06 tff(2593,plain,
% 0.86/1.06 (~c1_1(a36)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1199, 2591])).
% 0.86/1.06 tff(2594,plain,
% 0.86/1.06 (c0_1(a36)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2317, 72, 2590, 2593, 2592, 101])).
% 0.86/1.06 tff(2595,plain,
% 0.86/1.06 (~c2_1(a36)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1193, 2591])).
% 0.86/1.06 tff(2596,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a43) | (~c1_1(a43)) | c3_1(a43) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a43) | (~c1_1(a43)) | c3_1(a43) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2597,plain,
% 0.86/1.06 ((hskp22 | (~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36))) <=> (hskp22 | c2_1(a43) | (~c1_1(a43)) | c3_1(a43) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2598,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | c2_1(a43) | (~c1_1(a43)) | c3_1(a43) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2597])).
% 0.86/1.06 tff(2599,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a43) | (~c1_1(a43)) | c3_1(a43) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2598, 2596])).
% 0.86/1.06 tff(2600,plain,
% 0.86/1.06 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c1_1(a43)) | c2_1(a36) | c3_1(a36) | (~c0_1(a36)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(2601,plain,
% 0.86/1.06 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp22 | c2_1(a43) | (~c1_1(a43)) | c3_1(a43) | c2_1(a36) | c3_1(a36) | (~ndr1_0) | (~c0_1(a36))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2600, 2599])).
% 0.86/1.06 tff(2602,plain,
% 0.86/1.06 (~c1_1(a43)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2601, 2589, 72, 2588, 1479, 2595, 2592, 12, 2594])).
% 0.86/1.06 tff(2603,plain,
% 0.86/1.06 (hskp4 | c1_1(a43) | c0_1(a43)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1474, 72, 1479, 101])).
% 0.86/1.06 tff(2604,plain,
% 0.86/1.06 (c0_1(a43)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2603, 2602, 2590])).
% 0.86/1.06 tff(2605,plain,
% 0.86/1.06 (~c2_1(a58)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2538, 2589])).
% 0.86/1.06 tff(2606,plain,
% 0.86/1.06 (hskp11),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[15, 2589])).
% 0.86/1.06 tff(2607,plain,
% 0.86/1.06 (~c3_1(a19)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[21, 2606])).
% 0.86/1.06 tff(2608,plain,
% 0.86/1.06 (c1_1(a19)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[29, 2606])).
% 0.86/1.06 tff(2609,plain,
% 0.86/1.06 (c0_1(a19)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[37, 2606])).
% 0.86/1.06 tff(2610,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | c2_1(a58) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | c2_1(a58) | (~c3_1(a58)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2611,plain,
% 0.86/1.06 ((hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58))) <=> (hskp0 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | c2_1(a58) | (~c3_1(a58)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2612,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | c2_1(a58) | (~c3_1(a58))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2611])).
% 0.86/1.06 tff(2613,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | c2_1(a58) | (~c3_1(a58)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2612, 2610])).
% 0.86/1.06 tff(2614,plain,
% 0.86/1.06 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | c3_1(a19) | (~c1_1(a19)) | (~c0_1(a19)) | c2_1(a58) | c1_1(a58) | (~c3_1(a58)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(2615,plain,
% 0.86/1.06 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a58) | c3_1(a19) | (~ndr1_0) | (~c0_1(a19)) | (~c1_1(a19)) | c2_1(a58) | (~c3_1(a58))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2614, 2613])).
% 0.86/1.06 tff(2616,plain,
% 0.86/1.06 (hskp0),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2615, 72, 2531, 2609, 2608, 2530, 2607, 585, 2605])).
% 0.86/1.06 tff(2617,plain,
% 0.86/1.06 (~c0_1(a1)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[645, 2616])).
% 0.86/1.06 tff(2618,plain,
% 0.86/1.06 (hskp17),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1876, 72, 2593, 2595, 2592, 1869, 2594])).
% 0.86/1.06 tff(2619,plain,
% 0.86/1.06 (~c2_1(a32)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1882, 2618])).
% 0.86/1.06 tff(2620,plain,
% 0.86/1.06 (~c0_1(a32)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2230, 2618])).
% 0.86/1.06 tff(2621,plain,
% 0.86/1.06 (c2_1(a1)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[661, 2616])).
% 0.86/1.06 tff(2622,plain,
% 0.86/1.06 (c1_1(a1)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[653, 2616])).
% 0.86/1.06 tff(2623,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a43)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2624,plain,
% 0.86/1.06 (((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32))) <=> (c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a43)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2625,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a43))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2624])).
% 0.86/1.06 tff(2626,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a43)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2625, 2623])).
% 0.86/1.06 tff(2627,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a43) | c1_1(a43) | (~c0_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)) | c2_1(a32) | c0_1(a32) | (~c1_1(a32)))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(2628,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c1_1(a32)) | (~c0_1(a43))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2627, 2626])).
% 0.86/1.06 tff(2629,plain,
% 0.86/1.06 (~c1_1(a32)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2628, 72, 2622, 2621, 2602, 1479, 2620, 2619, 2617, 1918, 2604])).
% 0.86/1.06 tff(2630,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a43) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a43)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a43) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a43)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2631,plain,
% 0.86/1.06 (((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c2_1(a43) | c1_1(a43) | (~c0_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32)) <=> (c2_1(a43) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a43)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2632,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c2_1(a43) | c1_1(a43) | (~c0_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a43) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a43))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2631])).
% 0.86/1.06 tff(2633,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c2_1(a43) | c1_1(a43) | (~c0_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a43) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a43)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2632, 2630])).
% 0.86/1.06 tff(2634,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a43) | c2_1(a43) | (~c0_1(a43)) | c2_1(a43) | c1_1(a43) | (~c0_1(a43)) | c2_1(a32) | c1_1(a32) | c0_1(a32))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(2635,plain,
% 0.86/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a43) | c1_1(a43) | c3_1(a43) | c0_1(a32) | c2_1(a32) | (~ndr1_0) | c1_1(a32) | (~c0_1(a43))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2634, 2633])).
% 0.86/1.06 tff(2636,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2635, 72, 2588, 2602, 1479, 2620, 2619, 881, 2604, 2629])).
% 0.86/1.06 tff(2637,plain,(c2_1(a43) | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(2638,plain,
% 0.86/1.06 (c2_1(a43)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2637, 1479])).
% 0.86/1.06 tff(2639,plain,
% 0.86/1.06 (~hskp1),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2400, 1564, 2638, 1479])).
% 0.86/1.06 tff(2640,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2418, 2639, 1564, 528, 1479, 2638])).
% 0.86/1.06 tff(2641,plain,(c1_1(a43) | hskp0 | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(2642,plain,
% 0.86/1.06 (c1_1(a43)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2641, 528, 1479])).
% 0.86/1.06 tff(2643,plain,
% 0.86/1.06 (~hskp22),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[622, 2642])).
% 0.86/1.06 tff(2644,plain,
% 0.86/1.06 (~c2_1(a58)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2538, 2643])).
% 0.86/1.06 tff(2645,plain,
% 0.86/1.06 (hskp11),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[15, 2643])).
% 0.86/1.06 tff(2646,plain,
% 0.86/1.06 (~c3_1(a19)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[21, 2645])).
% 0.86/1.06 tff(2647,plain,
% 0.86/1.06 (c1_1(a19)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[29, 2645])).
% 0.86/1.06 tff(2648,plain,
% 0.86/1.06 (c0_1(a19)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[37, 2645])).
% 0.86/1.06 tff(2649,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2615, 72, 528, 2531, 2648, 2647, 2530, 2646, 585, 2644])).
% 0.86/1.06 tff(2650,plain,(hskp0 | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(2651,plain,
% 0.86/1.06 (hskp0),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2650, 1479])).
% 0.86/1.06 tff(2652,plain,
% 0.86/1.06 (~c0_1(a1)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[645, 2651])).
% 0.86/1.06 tff(2653,plain,
% 0.86/1.06 (c2_1(a1)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[661, 2651])).
% 0.86/1.06 tff(2654,plain,
% 0.86/1.06 (c1_1(a1)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[653, 2651])).
% 0.86/1.06 tff(2655,plain,
% 0.86/1.06 (~c0_1(a34)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2432, 72, 2638, 2302, 2654, 2653, 1564, 1479, 2285, 2652, 121])).
% 0.86/1.06 tff(2656,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a58)) | (~c0_1(a58)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a58)) | (~c0_1(a58)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2657,plain,
% 0.86/1.06 ((hskp1 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a34) | c1_1(a34) | c0_1(a34)) <=> (hskp1 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a58)) | (~c0_1(a58)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2658,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a58)) | (~c0_1(a58))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2657])).
% 0.86/1.06 tff(2659,plain,
% 0.86/1.06 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a34) | c1_1(a34) | c0_1(a34))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a58)) | (~c0_1(a58)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2658, 2656])).
% 0.86/1.06 tff(2660,plain,
% 0.86/1.06 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c1_1(a58) | (~c2_1(a58)) | (~c0_1(a58)) | c2_1(a34) | c1_1(a34) | c0_1(a34))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(2661,plain,
% 0.86/1.06 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c1_1(a58) | c1_1(a34) | c2_1(a34) | (~ndr1_0) | c0_1(a34) | (~c2_1(a58)) | (~c0_1(a58))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2660, 2659])).
% 0.86/1.06 tff(2662,plain,
% 0.86/1.06 (hskp1 | c0_1(a34) | (~c2_1(a58))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2661, 72, 2540, 2530, 2291, 2285, 674])).
% 0.86/1.06 tff(2663,plain,
% 0.86/1.06 (~c2_1(a58)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2662, 2655, 2639])).
% 0.86/1.06 tff(2664,plain,
% 0.86/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2665,plain,
% 0.86/1.06 (((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1))) <=> (c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(2666,plain,
% 0.86/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[2665])).
% 0.86/1.07 tff(2667,plain,
% 0.86/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[2666, 2664])).
% 0.86/1.07 tff(2668,plain,
% 0.86/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a58) | (~c3_1(a58)) | (~c0_1(a58)) | c1_1(a43) | c3_1(a43) | (~c2_1(a43)) | c0_1(a1) | (~c1_1(a1)) | (~c2_1(a1)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(2669,plain,
% 0.86/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a43) | c3_1(a43) | c0_1(a1) | (~ndr1_0) | (~c2_1(a1)) | (~c1_1(a1)) | (~c2_1(a43)) | c2_1(a58) | (~c0_1(a58)) | (~c3_1(a58))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[2668, 2667])).
% 0.86/1.07 tff(2670,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2669, 72, 2540, 2531, 2638, 2654, 2653, 1564, 1479, 2652, 121, 2663])).
% 0.86/1.07 tff(2671,plain,(c1_1(a43) | c3_1(a43)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(2672,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2671, 2587, 2586])).
% 0.86/1.07 % SZS output end Proof
% 0.86/1.07 % E exiting
%------------------------------------------------------------------------------