%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN462-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:39:12 AM UTC 2025
% Result : Unsatisfiable 0.59s 0.81s
% Output : Proof 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN462-1 : TPTP v9.0.0. Released v2.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:36:18 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.59/0.81 % SZS status Unsatisfiable
% 0.59/0.81 % SZS output start Proof
% 0.59/0.81 tff(c2_1_type, type, (
% 0.59/0.81 c2_1: $i > $o)).
% 0.59/0.81 tff(a272_type, type, (
% 0.59/0.81 a272: $i)).
% 0.59/0.81 tff(c0_1_type, type, (
% 0.59/0.81 c0_1: $i > $o)).
% 0.59/0.81 tff(hskp5_type, type, (
% 0.59/0.81 hskp5: $o)).
% 0.59/0.81 tff(c3_1_type, type, (
% 0.59/0.81 c3_1: $i > $o)).
% 0.59/0.81 tff(a293_type, type, (
% 0.59/0.81 a293: $i)).
% 0.59/0.81 tff(hskp23_type, type, (
% 0.59/0.81 hskp23: $o)).
% 0.59/0.81 tff(a287_type, type, (
% 0.59/0.81 a287: $i)).
% 0.59/0.81 tff(a313_type, type, (
% 0.59/0.81 a313: $i)).
% 0.59/0.81 tff(c1_1_type, type, (
% 0.59/0.81 c1_1: $i > $o)).
% 0.59/0.81 tff(ndr1_0_type, type, (
% 0.59/0.81 ndr1_0: $o)).
% 0.59/0.81 tff(hskp2_type, type, (
% 0.59/0.81 hskp2: $o)).
% 0.59/0.81 tff(a269_type, type, (
% 0.59/0.81 a269: $i)).
% 0.59/0.81 tff(a275_type, type, (
% 0.59/0.81 a275: $i)).
% 0.59/0.81 tff(hskp8_type, type, (
% 0.59/0.81 hskp8: $o)).
% 0.59/0.81 tff(a274_type, type, (
% 0.59/0.81 a274: $i)).
% 0.59/0.81 tff(hskp7_type, type, (
% 0.59/0.81 hskp7: $o)).
% 0.59/0.81 tff(a278_type, type, (
% 0.59/0.81 a278: $i)).
% 0.59/0.81 tff(hskp28_type, type, (
% 0.59/0.81 hskp28: $o)).
% 0.59/0.81 tff(hskp16_type, type, (
% 0.59/0.81 hskp16: $o)).
% 0.59/0.81 tff(a270_type, type, (
% 0.59/0.81 a270: $i)).
% 0.59/0.81 tff(hskp3_type, type, (
% 0.59/0.81 hskp3: $o)).
% 0.59/0.81 tff(a280_type, type, (
% 0.59/0.81 a280: $i)).
% 0.59/0.81 tff(hskp9_type, type, (
% 0.59/0.81 hskp9: $o)).
% 0.59/0.81 tff(a298_type, type, (
% 0.59/0.81 a298: $i)).
% 0.59/0.81 tff(hskp18_type, type, (
% 0.59/0.81 hskp18: $o)).
% 0.59/0.81 tff(hskp4_type, type, (
% 0.59/0.81 hskp4: $o)).
% 0.59/0.81 tff(a271_type, type, (
% 0.59/0.81 a271: $i)).
% 0.59/0.81 tff(hskp14_type, type, (
% 0.59/0.81 hskp14: $o)).
% 0.59/0.81 tff(hskp30_type, type, (
% 0.59/0.81 hskp30: $o)).
% 0.59/0.81 tff(a282_type, type, (
% 0.59/0.81 a282: $i)).
% 0.59/0.81 tff(hskp11_type, type, (
% 0.59/0.81 hskp11: $o)).
% 0.59/0.81 tff(a337_type, type, (
% 0.59/0.81 a337: $i)).
% 0.59/0.81 tff(hskp6_type, type, (
% 0.59/0.81 hskp6: $o)).
% 0.59/0.81 tff(a276_type, type, (
% 0.59/0.81 a276: $i)).
% 0.59/0.81 tff(hskp27_type, type, (
% 0.59/0.81 hskp27: $o)).
% 0.59/0.81 tff(a295_type, type, (
% 0.59/0.81 a295: $i)).
% 0.59/0.81 tff(hskp17_type, type, (
% 0.59/0.81 hskp17: $o)).
% 0.59/0.81 tff(a273_type, type, (
% 0.59/0.81 a273: $i)).
% 0.59/0.81 tff(a267_type, type, (
% 0.59/0.81 a267: $i)).
% 0.59/0.81 tff(hskp0_type, type, (
% 0.59/0.81 hskp0: $o)).
% 0.59/0.81 tff(a352_type, type, (
% 0.59/0.81 a352: $i)).
% 0.59/0.81 tff(hskp25_type, type, (
% 0.59/0.81 hskp25: $o)).
% 0.59/0.81 tff(hskp12_type, type, (
% 0.59/0.81 hskp12: $o)).
% 0.59/0.81 tff(a284_type, type, (
% 0.59/0.81 a284: $i)).
% 0.59/0.81 tff(a268_type, type, (
% 0.59/0.81 a268: $i)).
% 0.59/0.81 tff(hskp1_type, type, (
% 0.59/0.81 hskp1: $o)).
% 0.59/0.81 tff(a307_type, type, (
% 0.59/0.81 a307: $i)).
% 0.59/0.81 tff(hskp21_type, type, (
% 0.59/0.81 hskp21: $o)).
% 0.59/0.81 tff(1,plain,
% 0.59/0.81 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.59/0.81 inference(bind,[status(th)],[])).
% 0.59/0.81 tff(2,plain,
% 0.59/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.59/0.81 inference(quant_intro,[status(thm)],[1])).
% 0.59/0.81 tff(3,plain,
% 0.59/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.59/0.81 inference(rewrite,[status(thm)],[])).
% 0.59/0.81 tff(4,plain,
% 0.59/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c0_1(V))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c0_1(V)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_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)) <=> ((~ndr1_0) | c2_1(U) | c0_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(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | 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(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | 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(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | 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(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.59/0.81 inference(bind,[status(th)],[])).
% 0.59/0.81 tff(5,plain,
% 0.59/0.81 (![V: $i, U: $i] : ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.59/0.81 inference(quant_intro,[status(thm)],[4])).
% 0.59/0.81 tff(6,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 0.59/0.81 tff(7,plain,
% 0.59/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.59/0.81 tff(8,plain,
% 0.59/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.59/0.81 tff(9,plain,(
% 0.59/0.81 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.59/0.81 inference(skolemize,[status(sab)],[8])).
% 0.59/0.81 tff(10,plain,
% 0.59/0.81 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.59/0.81 tff(11,assumption,(hskp23), introduced(assumption)).
% 0.59/0.81 tff(12,plain,
% 0.59/0.81 (((~hskp23) | (~c3_1(a313))) <=> ((~hskp23) | (~c3_1(a313)))),
% 0.59/0.81 inference(rewrite,[status(thm)],[])).
% 0.59/0.81 tff(13,plain,
% 0.59/0.81 (((~c3_1(a313)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a313)))),
% 0.59/0.81 inference(rewrite,[status(thm)],[])).
% 0.59/0.81 tff(14,axiom,((~c3_1(a313)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 0.59/0.81 tff(15,plain,
% 0.59/0.81 ((~hskp23) | (~c3_1(a313))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.59/0.81 tff(16,plain,
% 0.59/0.81 ((~hskp23) | (~c3_1(a313))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.59/0.81 tff(17,plain,
% 0.59/0.81 (~c3_1(a313)),
% 0.59/0.81 inference(unit_resolution,[status(thm)],[16, 11])).
% 0.59/0.81 tff(18,plain,
% 0.59/0.81 (((~hskp23) | (~c2_1(a313))) <=> ((~hskp23) | (~c2_1(a313)))),
% 0.59/0.81 inference(rewrite,[status(thm)],[])).
% 0.59/0.81 tff(19,plain,
% 0.59/0.81 (((~c2_1(a313)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a313)))),
% 0.59/0.81 inference(rewrite,[status(thm)],[])).
% 0.59/0.81 tff(20,axiom,((~c2_1(a313)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.59/0.81 tff(21,plain,
% 0.59/0.81 ((~hskp23) | (~c2_1(a313))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.59/0.81 tff(22,plain,
% 0.59/0.81 ((~hskp23) | (~c2_1(a313))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.59/0.81 tff(23,plain,
% 0.59/0.81 (~c2_1(a313)),
% 0.59/0.81 inference(unit_resolution,[status(thm)],[22, 11])).
% 0.59/0.81 tff(24,plain,
% 0.59/0.81 (((~hskp23) | (~c1_1(a313))) <=> ((~hskp23) | (~c1_1(a313)))),
% 0.59/0.81 inference(rewrite,[status(thm)],[])).
% 0.59/0.81 tff(25,plain,
% 0.59/0.81 (((~c1_1(a313)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a313)))),
% 0.59/0.81 inference(rewrite,[status(thm)],[])).
% 0.59/0.81 tff(26,axiom,((~c1_1(a313)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.59/0.81 tff(27,plain,
% 0.59/0.81 ((~hskp23) | (~c1_1(a313))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.59/0.81 tff(28,plain,
% 0.59/0.81 ((~hskp23) | (~c1_1(a313))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.59/0.81 tff(29,plain,
% 0.59/0.81 (~c1_1(a313)),
% 0.59/0.81 inference(unit_resolution,[status(thm)],[28, 11])).
% 0.59/0.81 tff(30,assumption,(~c2_1(a269)), introduced(assumption)).
% 0.59/0.81 tff(31,assumption,(~hskp23), introduced(assumption)).
% 0.59/0.81 tff(32,assumption,(~hskp8), introduced(assumption)).
% 0.59/0.81 tff(33,plain,
% 0.59/0.81 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.59/0.81 inference(bind,[status(th)],[])).
% 0.59/0.81 tff(34,plain,
% 0.59/0.81 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.81 inference(quant_intro,[status(thm)],[33])).
% 0.59/0.81 tff(35,plain,
% 0.59/0.81 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.81 inference(rewrite,[status(thm)],[])).
% 0.59/0.81 tff(36,plain,
% 0.59/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp23) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp23))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.59/0.81 inference(bind,[status(th)],[])).
% 0.59/0.81 tff(37,plain,
% 0.59/0.81 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.81 inference(quant_intro,[status(thm)],[36])).
% 0.59/0.81 tff(38,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.59/0.81 tff(39,plain,
% 0.59/0.81 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.59/0.81 tff(40,plain,
% 0.59/0.81 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.59/0.81 tff(41,plain,(
% 0.59/0.81 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.81 inference(skolemize,[status(sab)],[40])).
% 0.59/0.81 tff(42,plain,
% 0.59/0.81 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.81 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.59/0.81 tff(43,assumption,(~hskp16), introduced(assumption)).
% 0.59/0.81 tff(44,plain,
% 0.59/0.81 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))))),
% 0.59/0.81 inference(bind,[status(th)],[])).
% 0.59/0.81 tff(45,plain,
% 0.59/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.59/0.81 inference(quant_intro,[status(thm)],[44])).
% 0.59/0.81 tff(46,plain,
% 0.59/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.59/0.81 inference(rewrite,[status(thm)],[])).
% 0.59/0.81 tff(47,plain,
% 0.59/0.81 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))))),
% 0.59/0.82 inference(bind,[status(th)],[])).
% 0.59/0.82 tff(48,plain,
% 0.59/0.82 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.59/0.82 inference(quant_intro,[status(thm)],[47])).
% 0.59/0.82 tff(49,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c1_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 0.59/0.82 tff(50,plain,
% 0.59/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.59/0.82 tff(51,plain,
% 0.59/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.59/0.82 tff(52,plain,(
% 0.59/0.82 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.59/0.82 inference(skolemize,[status(sab)],[51])).
% 0.59/0.82 tff(53,plain,
% 0.59/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.59/0.82 tff(54,assumption,(~hskp2), introduced(assumption)).
% 0.59/0.82 tff(55,assumption,(~hskp18), introduced(assumption)).
% 0.59/0.82 tff(56,plain,
% 0.59/0.82 ((hskp18 | hskp16 | hskp7) <=> (hskp18 | hskp16 | hskp7)),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(57,plain,
% 0.59/0.82 (((hskp16 | hskp7) | hskp18) <=> (hskp18 | hskp16 | hskp7)),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(58,axiom,((hskp16 | hskp7) | hskp18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 0.59/0.82 tff(59,plain,
% 0.59/0.82 (hskp18 | hskp16 | hskp7),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.59/0.82 tff(60,plain,
% 0.59/0.82 (hskp18 | hskp16 | hskp7),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[59, 56])).
% 0.59/0.82 tff(61,plain,
% 0.59/0.82 (hskp18 | hskp16 | hskp7),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.59/0.82 tff(62,plain,
% 0.59/0.82 (hskp18 | hskp16 | hskp7),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[61, 56])).
% 0.59/0.82 tff(63,plain,
% 0.59/0.82 (hskp18 | hskp16 | hskp7),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[62, 56])).
% 0.59/0.82 tff(64,plain,
% 0.59/0.82 (hskp7),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[63, 55, 43])).
% 0.59/0.82 tff(65,plain,
% 0.59/0.82 (((~hskp7) | (~c3_1(a274))) <=> ((~hskp7) | (~c3_1(a274)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(66,plain,
% 0.59/0.82 (((~c3_1(a274)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a274)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(67,axiom,((~c3_1(a274)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.59/0.82 tff(68,plain,
% 0.59/0.82 ((~hskp7) | (~c3_1(a274))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.59/0.82 tff(69,plain,
% 0.59/0.82 ((~hskp7) | (~c3_1(a274))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.59/0.82 tff(70,plain,
% 0.59/0.82 (~c3_1(a274)),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[69, 64])).
% 0.59/0.82 tff(71,plain,
% 0.59/0.82 (((~hskp7) | c1_1(a274)) <=> ((~hskp7) | c1_1(a274))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(72,axiom,((~hskp7) | c1_1(a274)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.59/0.82 tff(73,plain,
% 0.59/0.82 ((~hskp7) | c1_1(a274)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.59/0.82 tff(74,plain,
% 0.59/0.82 ((~hskp7) | c1_1(a274)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[73, 71])).
% 0.59/0.82 tff(75,plain,
% 0.59/0.82 ((~hskp7) | c1_1(a274)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[74, 71])).
% 0.59/0.82 tff(76,plain,
% 0.59/0.82 ((~hskp7) | c1_1(a274)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.59/0.82 tff(77,plain,
% 0.59/0.82 ((~hskp7) | c1_1(a274)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[76, 71])).
% 0.59/0.82 tff(78,plain,
% 0.59/0.82 (c1_1(a274)),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[77, 64])).
% 0.59/0.82 tff(79,assumption,(hskp4), introduced(assumption)).
% 0.59/0.82 tff(80,plain,
% 0.59/0.82 (((~hskp4) | (~c3_1(a271))) <=> ((~hskp4) | (~c3_1(a271)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(81,plain,
% 0.59/0.82 (((~c3_1(a271)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a271)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(82,axiom,((~c3_1(a271)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.59/0.82 tff(83,plain,
% 0.59/0.82 ((~hskp4) | (~c3_1(a271))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.59/0.82 tff(84,plain,
% 0.59/0.82 ((~hskp4) | (~c3_1(a271))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.59/0.82 tff(85,plain,
% 0.59/0.82 (~c3_1(a271)),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[84, 79])).
% 0.59/0.82 tff(86,plain,
% 0.59/0.82 (((~hskp4) | (~c1_1(a271))) <=> ((~hskp4) | (~c1_1(a271)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(87,plain,
% 0.59/0.82 (((~c1_1(a271)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a271)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(88,axiom,((~c1_1(a271)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.59/0.82 tff(89,plain,
% 0.59/0.82 ((~hskp4) | (~c1_1(a271))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.59/0.82 tff(90,plain,
% 0.59/0.82 ((~hskp4) | (~c1_1(a271))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[89, 86])).
% 0.59/0.82 tff(91,plain,
% 0.59/0.82 (~c1_1(a271)),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[90, 79])).
% 0.59/0.82 tff(92,plain,
% 0.59/0.82 (((~hskp4) | (~c0_1(a271))) <=> ((~hskp4) | (~c0_1(a271)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(93,plain,
% 0.59/0.82 (((~c0_1(a271)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a271)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(94,axiom,((~c0_1(a271)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.59/0.82 tff(95,plain,
% 0.59/0.82 ((~hskp4) | (~c0_1(a271))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.59/0.82 tff(96,plain,
% 0.59/0.82 ((~hskp4) | (~c0_1(a271))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[95, 92])).
% 0.59/0.82 tff(97,plain,
% 0.59/0.82 (~c0_1(a271)),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[96, 79])).
% 0.59/0.82 tff(98,plain,
% 0.59/0.82 (^[U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.59/0.82 inference(bind,[status(th)],[])).
% 0.59/0.82 tff(99,plain,
% 0.59/0.82 (![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.59/0.82 inference(quant_intro,[status(thm)],[98])).
% 0.59/0.82 tff(100,plain,
% 0.59/0.82 (![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(101,plain,
% 0.59/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.59/0.82 inference(bind,[status(th)],[])).
% 0.59/0.82 tff(102,plain,
% 0.59/0.82 (![U: $i] : (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8) <=> ![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.59/0.82 inference(quant_intro,[status(thm)],[101])).
% 0.59/0.82 tff(103,axiom,(![U: $i] : (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.59/0.82 tff(104,plain,
% 0.59/0.82 (![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.59/0.82 tff(105,plain,
% 0.59/0.82 (![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.59/0.82 tff(106,plain,(
% 0.59/0.82 ![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.59/0.82 inference(skolemize,[status(sab)],[105])).
% 0.59/0.82 tff(107,plain,
% 0.59/0.82 (![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.59/0.82 tff(108,assumption,(~c3_1(a271)), introduced(assumption)).
% 0.59/0.82 tff(109,assumption,(~c1_1(a271)), introduced(assumption)).
% 0.59/0.82 tff(110,assumption,(~c0_1(a271)), introduced(assumption)).
% 0.59/0.82 tff(111,assumption,(~c2_1(a271)), introduced(assumption)).
% 0.59/0.82 tff(112,assumption,(~ndr1_0), introduced(assumption)).
% 0.59/0.82 tff(113,plain,
% 0.59/0.82 ((ndr1_0 | (~hskp5)) <=> (ndr1_0 | (~hskp5))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(114,plain,
% 0.59/0.82 (((~hskp5) | ndr1_0) <=> (ndr1_0 | (~hskp5))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(115,axiom,((~hskp5) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause26')).
% 0.59/0.82 tff(116,plain,
% 0.59/0.82 (ndr1_0 | (~hskp5)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.59/0.82 tff(117,plain,
% 0.59/0.82 (ndr1_0 | (~hskp5)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[116, 113])).
% 0.59/0.82 tff(118,plain,
% 0.59/0.82 (~hskp5),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[117, 112])).
% 0.59/0.82 tff(119,plain,
% 0.59/0.82 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(120,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.59/0.82 tff(121,plain,
% 0.59/0.82 ((~hskp30) | ndr1_0),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.59/0.82 tff(122,plain,
% 0.59/0.82 ((~hskp30) | ndr1_0),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[121, 119])).
% 0.59/0.82 tff(123,plain,
% 0.59/0.82 ((~hskp30) | ndr1_0),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[122, 119])).
% 0.59/0.82 tff(124,plain,
% 0.59/0.82 ((~hskp30) | ndr1_0),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.59/0.82 tff(125,plain,
% 0.59/0.82 ((~hskp30) | ndr1_0),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[124, 119])).
% 0.59/0.82 tff(126,plain,
% 0.59/0.82 (~hskp30),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[125, 112])).
% 0.59/0.82 tff(127,plain,
% 0.59/0.82 ((ndr1_0 | (~hskp16)) <=> (ndr1_0 | (~hskp16))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(128,plain,
% 0.59/0.82 (((~hskp16) | ndr1_0) <=> (ndr1_0 | (~hskp16))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(129,axiom,((~hskp16) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause15')).
% 0.59/0.82 tff(130,plain,
% 0.59/0.82 (ndr1_0 | (~hskp16)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.59/0.82 tff(131,plain,
% 0.59/0.82 (ndr1_0 | (~hskp16)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[130, 127])).
% 0.59/0.82 tff(132,plain,
% 0.59/0.82 (~hskp16),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[131, 112])).
% 0.59/0.82 tff(133,plain,
% 0.59/0.82 ((hskp30 | hskp16 | hskp5) <=> (hskp30 | hskp16 | hskp5)),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(134,plain,
% 0.59/0.82 (((hskp16 | hskp30) | hskp5) <=> (hskp30 | hskp16 | hskp5)),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(135,axiom,((hskp16 | hskp30) | hskp5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 0.59/0.82 tff(136,plain,
% 0.59/0.82 (hskp30 | hskp16 | hskp5),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.59/0.82 tff(137,plain,
% 0.59/0.82 (hskp30 | hskp16 | hskp5),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[136, 133])).
% 0.59/0.82 tff(138,plain,
% 0.59/0.82 (hskp30 | hskp16 | hskp5),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.59/0.82 tff(139,plain,
% 0.59/0.82 (hskp30 | hskp16 | hskp5),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[138, 133])).
% 0.59/0.82 tff(140,plain,
% 0.59/0.82 (hskp30 | hskp16 | hskp5),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[139, 133])).
% 0.59/0.82 tff(141,plain,
% 0.59/0.82 ($false),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[140, 132, 126, 118])).
% 0.59/0.82 tff(142,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.59/0.82 tff(143,plain,
% 0.59/0.82 (((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | c1_1(a271) | (~c3_1(a271)) | (~ndr1_0) | c2_1(a271))) <=> ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp8 | c1_1(a271) | (~c3_1(a271)) | (~ndr1_0) | c2_1(a271))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(144,plain,
% 0.59/0.82 ((hskp8 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | (~c3_1(a271))) <=> (hskp8 | c1_1(a271) | (~c3_1(a271)) | (~ndr1_0) | c2_1(a271))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(145,plain,
% 0.59/0.82 (((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | (~c3_1(a271)))) <=> ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | c1_1(a271) | (~c3_1(a271)) | (~ndr1_0) | c2_1(a271)))),
% 0.59/0.82 inference(monotonicity,[status(thm)],[144])).
% 0.59/0.82 tff(146,plain,
% 0.59/0.82 (((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | (~c3_1(a271)))) <=> ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp8 | c1_1(a271) | (~c3_1(a271)) | (~ndr1_0) | c2_1(a271))),
% 0.59/0.82 inference(transitivity,[status(thm)],[145, 143])).
% 0.59/0.82 tff(147,plain,
% 0.59/0.82 ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | (~ndr1_0) | c2_1(a271) | c1_1(a271) | (~c3_1(a271)))),
% 0.59/0.82 inference(quant_inst,[status(thm)],[])).
% 0.59/0.82 tff(148,plain,
% 0.59/0.82 ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp8 | c1_1(a271) | (~c3_1(a271)) | (~ndr1_0) | c2_1(a271)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.59/0.82 tff(149,plain,
% 0.59/0.82 ((~c3_1(a271)) | c2_1(a271)),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[148, 142, 32, 109, 107])).
% 0.59/0.82 tff(150,plain,
% 0.59/0.82 (~c3_1(a271)),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[149, 111])).
% 0.59/0.82 tff(151,plain,
% 0.59/0.82 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0) | c2_1(a271))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0) | c2_1(a271))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(152,plain,
% 0.59/0.82 ((hskp2 | (~ndr1_0) | c2_1(a271) | c0_1(a271) | c3_1(a271) | c3_1(a271) | c1_1(a271) | c0_1(a271)) <=> (hskp2 | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0) | c2_1(a271))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(153,plain,
% 0.59/0.82 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a271) | c0_1(a271) | c3_1(a271) | c3_1(a271) | c1_1(a271) | c0_1(a271))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0) | c2_1(a271)))),
% 0.59/0.82 inference(monotonicity,[status(thm)],[152])).
% 0.59/0.82 tff(154,plain,
% 0.59/0.82 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a271) | c0_1(a271) | c3_1(a271) | c3_1(a271) | c1_1(a271) | c0_1(a271))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0) | c2_1(a271))),
% 0.59/0.82 inference(transitivity,[status(thm)],[153, 151])).
% 0.59/0.82 tff(155,plain,
% 0.59/0.82 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a271) | c0_1(a271) | c3_1(a271) | c3_1(a271) | c1_1(a271) | c0_1(a271))),
% 0.59/0.82 inference(quant_inst,[status(thm)],[])).
% 0.59/0.82 tff(156,plain,
% 0.59/0.82 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0) | c2_1(a271)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.59/0.82 tff(157,plain,
% 0.59/0.82 ($false),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[156, 142, 54, 110, 109, 150, 10, 111])).
% 0.59/0.82 tff(158,plain,(c2_1(a271) | hskp2 | c0_1(a271) | c1_1(a271) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.59/0.82 tff(159,plain,
% 0.59/0.82 (c2_1(a271)),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[158, 32, 110, 109, 54])).
% 0.59/0.82 tff(160,plain,
% 0.59/0.82 (^[U: $i] : refl((hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.59/0.82 inference(bind,[status(th)],[])).
% 0.59/0.82 tff(161,plain,
% 0.59/0.82 (![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.82 inference(quant_intro,[status(thm)],[160])).
% 0.59/0.82 tff(162,plain,
% 0.59/0.82 (![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(163,plain,
% 0.59/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.59/0.82 inference(bind,[status(th)],[])).
% 0.59/0.82 tff(164,plain,
% 0.59/0.82 (![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14) <=> ![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.82 inference(quant_intro,[status(thm)],[163])).
% 0.59/0.82 tff(165,axiom,(![U: $i] : (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 0.59/0.82 tff(166,plain,
% 0.59/0.82 (![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.59/0.82 tff(167,plain,
% 0.59/0.82 (![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.59/0.82 tff(168,plain,(
% 0.59/0.82 ![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.82 inference(skolemize,[status(sab)],[167])).
% 0.59/0.82 tff(169,plain,
% 0.59/0.82 (![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.59/0.82 tff(170,plain,
% 0.59/0.82 (((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | c0_1(a271) | c3_1(a271) | (~ndr1_0) | (~c2_1(a271)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | c0_1(a271) | c3_1(a271) | (~ndr1_0) | (~c2_1(a271)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(171,plain,
% 0.59/0.82 ((hskp14 | (~ndr1_0) | c0_1(a271) | c3_1(a271) | (~c2_1(a271))) <=> (hskp14 | c0_1(a271) | c3_1(a271) | (~ndr1_0) | (~c2_1(a271)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(172,plain,
% 0.59/0.82 (((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | (~ndr1_0) | c0_1(a271) | c3_1(a271) | (~c2_1(a271)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | c0_1(a271) | c3_1(a271) | (~ndr1_0) | (~c2_1(a271))))),
% 0.59/0.82 inference(monotonicity,[status(thm)],[171])).
% 0.59/0.82 tff(173,plain,
% 0.59/0.82 (((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | (~ndr1_0) | c0_1(a271) | c3_1(a271) | (~c2_1(a271)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | c0_1(a271) | c3_1(a271) | (~ndr1_0) | (~c2_1(a271)))),
% 0.59/0.82 inference(transitivity,[status(thm)],[172, 170])).
% 0.59/0.82 tff(174,plain,
% 0.59/0.82 ((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | (~ndr1_0) | c0_1(a271) | c3_1(a271) | (~c2_1(a271)))),
% 0.59/0.82 inference(quant_inst,[status(thm)],[])).
% 0.59/0.82 tff(175,plain,
% 0.59/0.82 ((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | c0_1(a271) | c3_1(a271) | (~ndr1_0) | (~c2_1(a271))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.59/0.82 tff(176,plain,
% 0.59/0.82 (hskp14 | (~c2_1(a271))),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[175, 142, 110, 108, 169])).
% 0.59/0.82 tff(177,plain,
% 0.59/0.82 (hskp14),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[176, 159])).
% 0.59/0.82 tff(178,plain,
% 0.59/0.82 (((~hskp14) | (~c2_1(a287))) <=> ((~hskp14) | (~c2_1(a287)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(179,plain,
% 0.59/0.82 (((~c2_1(a287)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a287)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(180,axiom,((~c2_1(a287)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.59/0.82 tff(181,plain,
% 0.59/0.82 ((~hskp14) | (~c2_1(a287))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.59/0.82 tff(182,plain,
% 0.59/0.82 ((~hskp14) | (~c2_1(a287))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[181, 178])).
% 0.59/0.82 tff(183,plain,
% 0.59/0.82 (~c2_1(a287)),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[182, 177])).
% 0.59/0.82 tff(184,plain,
% 0.59/0.82 (((~hskp14) | (~c0_1(a287))) <=> ((~hskp14) | (~c0_1(a287)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(185,plain,
% 0.59/0.82 (((~c0_1(a287)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a287)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(186,axiom,((~c0_1(a287)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.59/0.82 tff(187,plain,
% 0.59/0.82 ((~hskp14) | (~c0_1(a287))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.59/0.82 tff(188,plain,
% 0.59/0.82 ((~hskp14) | (~c0_1(a287))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[187, 184])).
% 0.59/0.82 tff(189,plain,
% 0.59/0.82 (~c0_1(a287)),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[188, 177])).
% 0.59/0.82 tff(190,plain,
% 0.59/0.82 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a287) | c2_1(a287) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0) | c3_1(a287))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a287) | c2_1(a287) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0) | c3_1(a287))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(191,plain,
% 0.59/0.82 ((hskp2 | (~ndr1_0) | c2_1(a287) | c0_1(a287) | c3_1(a287) | c3_1(a271) | c1_1(a271) | c0_1(a271)) <=> (hskp2 | c0_1(a287) | c2_1(a287) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0) | c3_1(a287))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(192,plain,
% 0.59/0.82 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a287) | c0_1(a287) | c3_1(a287) | c3_1(a271) | c1_1(a271) | c0_1(a271))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a287) | c2_1(a287) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0) | c3_1(a287)))),
% 0.59/0.82 inference(monotonicity,[status(thm)],[191])).
% 0.59/0.82 tff(193,plain,
% 0.59/0.82 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a287) | c0_1(a287) | c3_1(a287) | c3_1(a271) | c1_1(a271) | c0_1(a271))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a287) | c2_1(a287) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0) | c3_1(a287))),
% 0.59/0.82 inference(transitivity,[status(thm)],[192, 190])).
% 0.59/0.82 tff(194,plain,
% 0.59/0.82 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a287) | c0_1(a287) | c3_1(a287) | c3_1(a271) | c1_1(a271) | c0_1(a271))),
% 0.59/0.82 inference(quant_inst,[status(thm)],[])).
% 0.59/0.82 tff(195,plain,
% 0.59/0.82 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a287) | c2_1(a287) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0) | c3_1(a287)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.59/0.82 tff(196,plain,
% 0.59/0.82 (c3_1(a287)),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[195, 142, 54, 189, 183, 110, 109, 108, 10])).
% 0.59/0.82 tff(197,plain,
% 0.59/0.82 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.59/0.82 inference(bind,[status(th)],[])).
% 0.59/0.82 tff(198,plain,
% 0.59/0.82 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.82 inference(quant_intro,[status(thm)],[197])).
% 0.59/0.82 tff(199,plain,
% 0.59/0.82 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(200,plain,
% 0.59/0.82 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.59/0.82 inference(bind,[status(th)],[])).
% 0.59/0.82 tff(201,plain,
% 0.59/0.82 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.82 inference(quant_intro,[status(thm)],[200])).
% 0.59/0.82 tff(202,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 0.59/0.82 tff(203,plain,
% 0.59/0.82 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.59/0.82 tff(204,plain,
% 0.59/0.82 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.59/0.82 tff(205,plain,(
% 0.59/0.82 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.82 inference(skolemize,[status(sab)],[204])).
% 0.59/0.82 tff(206,plain,
% 0.59/0.82 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[205, 198])).
% 0.59/0.82 tff(207,plain,
% 0.59/0.82 (^[U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.59/0.82 inference(bind,[status(th)],[])).
% 0.59/0.82 tff(208,plain,
% 0.59/0.82 (![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.59/0.82 inference(quant_intro,[status(thm)],[207])).
% 0.59/0.82 tff(209,plain,
% 0.59/0.82 (![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(210,plain,
% 0.59/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.59/0.82 inference(bind,[status(th)],[])).
% 0.59/0.82 tff(211,plain,
% 0.59/0.82 (![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp9) <=> ![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.59/0.82 inference(quant_intro,[status(thm)],[210])).
% 0.59/0.82 tff(212,axiom,(![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.59/0.82 tff(213,plain,
% 0.59/0.82 (![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.59/0.82 tff(214,plain,
% 0.59/0.82 (![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.59/0.82 tff(215,plain,(
% 0.59/0.82 ![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.59/0.82 inference(skolemize,[status(sab)],[214])).
% 0.59/0.82 tff(216,plain,
% 0.59/0.82 (![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.59/0.82 tff(217,plain,
% 0.59/0.82 (((~hskp14) | c1_1(a287)) <=> ((~hskp14) | c1_1(a287))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(218,axiom,((~hskp14) | c1_1(a287)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.59/0.82 tff(219,plain,
% 0.59/0.82 ((~hskp14) | c1_1(a287)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.59/0.82 tff(220,plain,
% 0.59/0.82 ((~hskp14) | c1_1(a287)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[219, 217])).
% 0.59/0.82 tff(221,plain,
% 0.59/0.82 ((~hskp14) | c1_1(a287)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[220, 217])).
% 0.59/0.82 tff(222,plain,
% 0.59/0.82 ((~hskp14) | c1_1(a287)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.59/0.82 tff(223,plain,
% 0.59/0.82 ((~hskp14) | c1_1(a287)),
% 0.59/0.82 inference(modus_ponens,[status(thm)],[222, 217])).
% 0.59/0.82 tff(224,plain,
% 0.59/0.82 (c1_1(a287)),
% 0.59/0.82 inference(unit_resolution,[status(thm)],[223, 177])).
% 0.59/0.82 tff(225,plain,
% 0.59/0.82 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(226,plain,
% 0.59/0.82 ((hskp9 | (~ndr1_0) | c2_1(a287) | c0_1(a287) | (~c1_1(a287))) <=> (hskp9 | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)))),
% 0.59/0.82 inference(rewrite,[status(thm)],[])).
% 0.59/0.82 tff(227,plain,
% 0.59/0.82 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a287) | c0_1(a287) | (~c1_1(a287)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287))))),
% 0.59/0.82 inference(monotonicity,[status(thm)],[226])).
% 0.59/0.82 tff(228,plain,
% 0.59/0.82 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a287) | c0_1(a287) | (~c1_1(a287)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)))),
% 0.59/0.82 inference(transitivity,[status(thm)],[227, 225])).
% 0.59/0.82 tff(229,plain,
% 0.59/0.82 ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a287) | c0_1(a287) | (~c1_1(a287)))),
% 0.59/0.82 inference(quant_inst,[status(thm)],[])).
% 0.59/0.82 tff(230,plain,
% 0.59/0.82 ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.59/0.83 tff(231,plain,
% 0.59/0.83 (hskp9),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[230, 142, 224, 189, 183, 216])).
% 0.59/0.83 tff(232,plain,
% 0.59/0.83 (((~hskp9) | (~c1_1(a280))) <=> ((~hskp9) | (~c1_1(a280)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(233,plain,
% 0.59/0.83 (((~c1_1(a280)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a280)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(234,axiom,((~c1_1(a280)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.59/0.83 tff(235,plain,
% 0.59/0.83 ((~hskp9) | (~c1_1(a280))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.59/0.83 tff(236,plain,
% 0.59/0.83 ((~hskp9) | (~c1_1(a280))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[235, 232])).
% 0.59/0.83 tff(237,plain,
% 0.59/0.83 (~c1_1(a280)),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[236, 231])).
% 0.59/0.83 tff(238,plain,
% 0.59/0.83 (((~hskp9) | c3_1(a280)) <=> ((~hskp9) | c3_1(a280))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(239,axiom,((~hskp9) | c3_1(a280)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.59/0.83 tff(240,plain,
% 0.59/0.83 ((~hskp9) | c3_1(a280)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.59/0.83 tff(241,plain,
% 0.59/0.83 ((~hskp9) | c3_1(a280)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[240, 238])).
% 0.59/0.83 tff(242,plain,
% 0.59/0.83 ((~hskp9) | c3_1(a280)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[241, 238])).
% 0.59/0.83 tff(243,plain,
% 0.59/0.83 ((~hskp9) | c3_1(a280)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[242, 238])).
% 0.59/0.83 tff(244,plain,
% 0.59/0.83 ((~hskp9) | c3_1(a280)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[243, 238])).
% 0.59/0.83 tff(245,plain,
% 0.59/0.83 (c3_1(a280)),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[244, 231])).
% 0.59/0.83 tff(246,plain,
% 0.59/0.83 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a287) | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a287)) | (~c3_1(a287)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a287) | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(247,plain,
% 0.59/0.83 ((hskp16 | (~ndr1_0) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287))) <=> (hskp16 | c0_1(a287) | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(248,plain,
% 0.59/0.83 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a287) | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a287)) | (~c3_1(a287))))),
% 0.59/0.83 inference(monotonicity,[status(thm)],[247])).
% 0.59/0.83 tff(249,plain,
% 0.59/0.83 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a287) | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.59/0.83 inference(transitivity,[status(thm)],[248, 246])).
% 0.59/0.83 tff(250,plain,
% 0.59/0.83 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)))),
% 0.59/0.83 inference(quant_inst,[status(thm)],[])).
% 0.59/0.83 tff(251,plain,
% 0.59/0.83 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a287) | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a287)) | (~c3_1(a287))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.59/0.83 tff(252,plain,
% 0.59/0.83 (~c0_1(a280)),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[251, 142, 43, 224, 245, 189, 237, 206, 196])).
% 0.59/0.83 tff(253,plain,
% 0.59/0.83 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.59/0.83 inference(bind,[status(th)],[])).
% 0.59/0.83 tff(254,plain,
% 0.59/0.83 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.83 inference(quant_intro,[status(thm)],[253])).
% 0.59/0.83 tff(255,plain,
% 0.59/0.83 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(256,plain,
% 0.59/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.59/0.83 inference(bind,[status(th)],[])).
% 0.59/0.83 tff(257,plain,
% 0.59/0.83 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.83 inference(quant_intro,[status(thm)],[256])).
% 0.59/0.83 tff(258,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 0.59/0.83 tff(259,plain,
% 0.59/0.83 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.59/0.83 tff(260,plain,
% 0.59/0.83 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.59/0.83 tff(261,plain,(
% 0.59/0.83 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.83 inference(skolemize,[status(sab)],[260])).
% 0.59/0.83 tff(262,plain,
% 0.59/0.83 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[261, 254])).
% 0.59/0.83 tff(263,plain,
% 0.59/0.83 (((~hskp9) | c2_1(a280)) <=> ((~hskp9) | c2_1(a280))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(264,axiom,((~hskp9) | c2_1(a280)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.59/0.83 tff(265,plain,
% 0.59/0.83 ((~hskp9) | c2_1(a280)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.59/0.83 tff(266,plain,
% 0.59/0.83 ((~hskp9) | c2_1(a280)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[265, 263])).
% 0.59/0.83 tff(267,plain,
% 0.59/0.83 ((~hskp9) | c2_1(a280)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[266, 263])).
% 0.59/0.83 tff(268,plain,
% 0.59/0.83 ((~hskp9) | c2_1(a280)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[267, 263])).
% 0.59/0.83 tff(269,plain,
% 0.59/0.83 ((~hskp9) | c2_1(a280)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[268, 263])).
% 0.59/0.83 tff(270,plain,
% 0.59/0.83 (c2_1(a280)),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[269, 231])).
% 0.59/0.83 tff(271,plain,
% 0.59/0.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(272,plain,
% 0.59/0.83 ((hskp3 | (~ndr1_0) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280))) <=> (hskp3 | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(273,plain,
% 0.59/0.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c3_1(a280))))),
% 0.59/0.83 inference(monotonicity,[status(thm)],[272])).
% 0.59/0.83 tff(274,plain,
% 0.59/0.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.59/0.83 inference(transitivity,[status(thm)],[273, 271])).
% 0.59/0.83 tff(275,plain,
% 0.59/0.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))),
% 0.59/0.83 inference(quant_inst,[status(thm)],[])).
% 0.59/0.83 tff(276,plain,
% 0.59/0.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c3_1(a280))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.59/0.83 tff(277,plain,
% 0.59/0.83 (hskp3),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[276, 142, 270, 245, 237, 262, 252])).
% 0.59/0.83 tff(278,plain,
% 0.59/0.83 (((~hskp3) | (~c2_1(a270))) <=> ((~hskp3) | (~c2_1(a270)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(279,plain,
% 0.59/0.83 (((~c2_1(a270)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a270)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(280,axiom,((~c2_1(a270)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.59/0.83 tff(281,plain,
% 0.59/0.83 ((~hskp3) | (~c2_1(a270))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.59/0.83 tff(282,plain,
% 0.59/0.83 ((~hskp3) | (~c2_1(a270))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[281, 278])).
% 0.59/0.83 tff(283,plain,
% 0.59/0.83 (~c2_1(a270)),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[282, 277])).
% 0.59/0.83 tff(284,plain,
% 0.59/0.83 (((~hskp3) | c3_1(a270)) <=> ((~hskp3) | c3_1(a270))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(285,axiom,((~hskp3) | c3_1(a270)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.59/0.83 tff(286,plain,
% 0.59/0.83 ((~hskp3) | c3_1(a270)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.59/0.83 tff(287,plain,
% 0.59/0.83 ((~hskp3) | c3_1(a270)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[286, 284])).
% 0.59/0.83 tff(288,plain,
% 0.59/0.83 ((~hskp3) | c3_1(a270)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[287, 284])).
% 0.59/0.83 tff(289,plain,
% 0.59/0.83 ((~hskp3) | c3_1(a270)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[288, 284])).
% 0.59/0.83 tff(290,plain,
% 0.59/0.83 ((~hskp3) | c3_1(a270)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[289, 284])).
% 0.59/0.83 tff(291,plain,
% 0.59/0.83 (c3_1(a270)),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[290, 277])).
% 0.59/0.83 tff(292,plain,
% 0.59/0.83 (((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)))) <=> ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp8 | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(293,plain,
% 0.59/0.83 ((hskp8 | (~ndr1_0) | c2_1(a270) | c1_1(a270) | (~c3_1(a270))) <=> (hskp8 | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(294,plain,
% 0.59/0.83 (((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | (~ndr1_0) | c2_1(a270) | c1_1(a270) | (~c3_1(a270)))) <=> ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c3_1(a270))))),
% 0.59/0.83 inference(monotonicity,[status(thm)],[293])).
% 0.59/0.83 tff(295,plain,
% 0.59/0.83 (((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | (~ndr1_0) | c2_1(a270) | c1_1(a270) | (~c3_1(a270)))) <=> ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp8 | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)))),
% 0.59/0.83 inference(transitivity,[status(thm)],[294, 292])).
% 0.59/0.83 tff(296,plain,
% 0.59/0.83 ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | (~ndr1_0) | c2_1(a270) | c1_1(a270) | (~c3_1(a270)))),
% 0.59/0.83 inference(quant_inst,[status(thm)],[])).
% 0.59/0.83 tff(297,plain,
% 0.59/0.83 ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp8 | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c3_1(a270))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.59/0.83 tff(298,plain,
% 0.59/0.83 (c1_1(a270)),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[297, 142, 32, 291, 283, 107])).
% 0.59/0.83 tff(299,plain,
% 0.59/0.83 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.59/0.83 inference(bind,[status(th)],[])).
% 0.59/0.83 tff(300,plain,
% 0.59/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.59/0.83 inference(quant_intro,[status(thm)],[299])).
% 0.59/0.83 tff(301,plain,
% 0.59/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(302,plain,
% 0.59/0.83 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.59/0.83 inference(bind,[status(th)],[])).
% 0.59/0.83 tff(303,plain,
% 0.59/0.83 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.59/0.83 inference(quant_intro,[status(thm)],[302])).
% 0.59/0.83 tff(304,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.59/0.83 tff(305,plain,
% 0.59/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.59/0.83 tff(306,plain,
% 0.59/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[305, 301])).
% 0.59/0.83 tff(307,plain,(
% 0.59/0.83 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.59/0.83 inference(skolemize,[status(sab)],[306])).
% 0.59/0.83 tff(308,plain,
% 0.59/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[307, 300])).
% 0.59/0.83 tff(309,plain,
% 0.59/0.83 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.59/0.83 inference(bind,[status(th)],[])).
% 0.59/0.83 tff(310,plain,
% 0.59/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.59/0.83 inference(quant_intro,[status(thm)],[309])).
% 0.59/0.83 tff(311,plain,
% 0.59/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(312,plain,
% 0.59/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.59/0.83 inference(bind,[status(th)],[])).
% 0.59/0.83 tff(313,plain,
% 0.59/0.83 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.59/0.83 inference(quant_intro,[status(thm)],[312])).
% 0.59/0.83 tff(314,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 0.59/0.83 tff(315,plain,
% 0.59/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.59/0.83 tff(316,plain,
% 0.59/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[315, 311])).
% 0.59/0.83 tff(317,plain,(
% 0.59/0.83 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.59/0.83 inference(skolemize,[status(sab)],[316])).
% 0.59/0.83 tff(318,plain,
% 0.59/0.83 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[317, 310])).
% 0.59/0.83 tff(319,plain,
% 0.59/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(320,plain,
% 0.59/0.83 ((hskp11 | (~ndr1_0) | c2_1(a287) | (~c1_1(a287)) | (~c3_1(a287)) | c0_1(a287) | c2_1(a287) | (~c3_1(a287))) <=> (hskp11 | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(321,plain,
% 0.59/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a287) | (~c1_1(a287)) | (~c3_1(a287)) | c0_1(a287) | c2_1(a287) | (~c3_1(a287)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287))))),
% 0.59/0.83 inference(monotonicity,[status(thm)],[320])).
% 0.59/0.83 tff(322,plain,
% 0.59/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a287) | (~c1_1(a287)) | (~c3_1(a287)) | c0_1(a287) | c2_1(a287) | (~c3_1(a287)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.59/0.83 inference(transitivity,[status(thm)],[321, 319])).
% 0.59/0.83 tff(323,plain,
% 0.59/0.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a287) | (~c1_1(a287)) | (~c3_1(a287)) | c0_1(a287) | c2_1(a287) | (~c3_1(a287)))),
% 0.59/0.83 inference(quant_inst,[status(thm)],[])).
% 0.59/0.83 tff(324,plain,
% 0.59/0.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.59/0.83 tff(325,plain,
% 0.59/0.83 (hskp11 | (~c3_1(a287))),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[324, 142, 224, 189, 183, 318])).
% 0.59/0.83 tff(326,plain,
% 0.59/0.83 (hskp11),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[325, 196])).
% 0.59/0.83 tff(327,plain,
% 0.59/0.83 (((~hskp11) | (~c1_1(a282))) <=> ((~hskp11) | (~c1_1(a282)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(328,plain,
% 0.59/0.83 (((~c1_1(a282)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a282)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(329,axiom,((~c1_1(a282)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.59/0.83 tff(330,plain,
% 0.59/0.83 ((~hskp11) | (~c1_1(a282))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.59/0.83 tff(331,plain,
% 0.59/0.83 ((~hskp11) | (~c1_1(a282))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[330, 327])).
% 0.59/0.83 tff(332,plain,
% 0.59/0.83 (~c1_1(a282)),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[331, 326])).
% 0.59/0.83 tff(333,plain,
% 0.59/0.83 (((~hskp11) | (~c0_1(a282))) <=> ((~hskp11) | (~c0_1(a282)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(334,plain,
% 0.59/0.83 (((~c0_1(a282)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a282)))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(335,axiom,((~c0_1(a282)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 0.59/0.83 tff(336,plain,
% 0.59/0.83 ((~hskp11) | (~c0_1(a282))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.59/0.83 tff(337,plain,
% 0.59/0.83 ((~hskp11) | (~c0_1(a282))),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[336, 333])).
% 0.59/0.83 tff(338,plain,
% 0.59/0.83 (~c0_1(a282)),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[337, 326])).
% 0.59/0.83 tff(339,plain,
% 0.59/0.83 (((~hskp3) | c0_1(a270)) <=> ((~hskp3) | c0_1(a270))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(340,axiom,((~hskp3) | c0_1(a270)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.59/0.83 tff(341,plain,
% 0.59/0.83 ((~hskp3) | c0_1(a270)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.59/0.83 tff(342,plain,
% 0.59/0.83 ((~hskp3) | c0_1(a270)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[341, 339])).
% 0.59/0.83 tff(343,plain,
% 0.59/0.83 ((~hskp3) | c0_1(a270)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[342, 339])).
% 0.59/0.83 tff(344,plain,
% 0.59/0.83 ((~hskp3) | c0_1(a270)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[343, 339])).
% 0.59/0.83 tff(345,plain,
% 0.59/0.83 ((~hskp3) | c0_1(a270)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[344, 339])).
% 0.59/0.83 tff(346,plain,
% 0.59/0.83 (c0_1(a270)),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[345, 277])).
% 0.59/0.83 tff(347,plain,
% 0.59/0.83 (((~hskp11) | c2_1(a282)) <=> ((~hskp11) | c2_1(a282))),
% 0.59/0.83 inference(rewrite,[status(thm)],[])).
% 0.59/0.83 tff(348,axiom,((~hskp11) | c2_1(a282)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.59/0.83 tff(349,plain,
% 0.59/0.83 ((~hskp11) | c2_1(a282)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.59/0.83 tff(350,plain,
% 0.59/0.83 ((~hskp11) | c2_1(a282)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[349, 347])).
% 0.59/0.83 tff(351,plain,
% 0.59/0.83 ((~hskp11) | c2_1(a282)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[350, 347])).
% 0.59/0.83 tff(352,plain,
% 0.59/0.83 ((~hskp11) | c2_1(a282)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[351, 347])).
% 0.59/0.83 tff(353,plain,
% 0.59/0.83 ((~hskp11) | c2_1(a282)),
% 0.59/0.83 inference(modus_ponens,[status(thm)],[352, 347])).
% 0.59/0.83 tff(354,plain,
% 0.59/0.83 (c2_1(a282)),
% 0.59/0.83 inference(unit_resolution,[status(thm)],[353, 326])).
% 0.59/0.83 tff(355,plain,
% 0.59/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a287) | c0_1(a282) | c1_1(a282) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a282)) | (~c1_1(a287)) | (~c3_1(a287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a287) | c0_1(a282) | c1_1(a282) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a282)) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(356,plain,
% 0.59/0.84 (((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c1_1(a282) | c0_1(a282) | (~c2_1(a282))) <=> (c0_1(a287) | c0_1(a282) | c1_1(a282) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a282)) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(357,plain,
% 0.59/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c1_1(a282) | c0_1(a282) | (~c2_1(a282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a287) | c0_1(a282) | c1_1(a282) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a282)) | (~c1_1(a287)) | (~c3_1(a287))))),
% 0.59/0.84 inference(monotonicity,[status(thm)],[356])).
% 0.59/0.84 tff(358,plain,
% 0.59/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c1_1(a282) | c0_1(a282) | (~c2_1(a282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a287) | c0_1(a282) | c1_1(a282) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a282)) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.59/0.84 inference(transitivity,[status(thm)],[357, 355])).
% 0.59/0.84 tff(359,plain,
% 0.59/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c1_1(a282) | c0_1(a282) | (~c2_1(a282)))),
% 0.59/0.84 inference(quant_inst,[status(thm)],[])).
% 0.59/0.84 tff(360,plain,
% 0.59/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a287) | c0_1(a282) | c1_1(a282) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a282)) | (~c1_1(a287)) | (~c3_1(a287))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.59/0.84 tff(361,plain,
% 0.59/0.84 ($false),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[360, 142, 224, 354, 346, 189, 338, 332, 283, 308, 196, 298])).
% 0.59/0.84 tff(362,plain,(hskp8 | hskp16 | hskp2 | c0_1(a271) | c1_1(a271) | c3_1(a271)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.84 tff(363,plain,
% 0.59/0.84 (hskp8),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[362, 97, 54, 43, 91, 85])).
% 0.59/0.84 tff(364,plain,
% 0.59/0.84 (((~hskp8) | (~c3_1(a275))) <=> ((~hskp8) | (~c3_1(a275)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(365,plain,
% 0.59/0.84 (((~c3_1(a275)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a275)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(366,axiom,((~c3_1(a275)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.59/0.84 tff(367,plain,
% 0.59/0.84 ((~hskp8) | (~c3_1(a275))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.59/0.84 tff(368,plain,
% 0.59/0.84 ((~hskp8) | (~c3_1(a275))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[367, 364])).
% 0.59/0.84 tff(369,plain,
% 0.59/0.84 (~c3_1(a275)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[368, 363])).
% 0.59/0.84 tff(370,plain,
% 0.59/0.84 (((~hskp8) | (~c2_1(a275))) <=> ((~hskp8) | (~c2_1(a275)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(371,plain,
% 0.59/0.84 (((~c2_1(a275)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a275)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(372,axiom,((~c2_1(a275)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.59/0.84 tff(373,plain,
% 0.59/0.84 ((~hskp8) | (~c2_1(a275))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.59/0.84 tff(374,plain,
% 0.59/0.84 ((~hskp8) | (~c2_1(a275))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[373, 370])).
% 0.59/0.84 tff(375,plain,
% 0.59/0.84 (~c2_1(a275)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[374, 363])).
% 0.59/0.84 tff(376,plain,
% 0.59/0.84 (((~hskp8) | (~c0_1(a275))) <=> ((~hskp8) | (~c0_1(a275)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(377,plain,
% 0.59/0.84 (((~c0_1(a275)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a275)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(378,axiom,((~c0_1(a275)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.59/0.84 tff(379,plain,
% 0.59/0.84 ((~hskp8) | (~c0_1(a275))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.59/0.84 tff(380,plain,
% 0.59/0.84 ((~hskp8) | (~c0_1(a275))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[379, 376])).
% 0.59/0.84 tff(381,plain,
% 0.59/0.84 (~c0_1(a275)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[380, 363])).
% 0.59/0.84 tff(382,plain,
% 0.59/0.84 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a275) | c2_1(a275) | c3_1(a275) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a275) | c2_1(a275) | c3_1(a275) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(383,plain,
% 0.59/0.84 ((hskp2 | (~ndr1_0) | c2_1(a275) | c0_1(a275) | c3_1(a275) | c3_1(a271) | c1_1(a271) | c0_1(a271)) <=> (hskp2 | c0_1(a275) | c2_1(a275) | c3_1(a275) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(384,plain,
% 0.59/0.84 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a275) | c0_1(a275) | c3_1(a275) | c3_1(a271) | c1_1(a271) | c0_1(a271))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a275) | c2_1(a275) | c3_1(a275) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0)))),
% 0.59/0.84 inference(monotonicity,[status(thm)],[383])).
% 0.59/0.84 tff(385,plain,
% 0.59/0.84 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a275) | c0_1(a275) | c3_1(a275) | c3_1(a271) | c1_1(a271) | c0_1(a271))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a275) | c2_1(a275) | c3_1(a275) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0))),
% 0.59/0.84 inference(transitivity,[status(thm)],[384, 382])).
% 0.59/0.84 tff(386,plain,
% 0.59/0.84 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a275) | c0_1(a275) | c3_1(a275) | c3_1(a271) | c1_1(a271) | c0_1(a271))),
% 0.59/0.84 inference(quant_inst,[status(thm)],[])).
% 0.59/0.84 tff(387,plain,
% 0.59/0.84 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a275) | c2_1(a275) | c3_1(a275) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~ndr1_0)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.59/0.84 tff(388,plain,
% 0.59/0.84 ($false),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[387, 142, 54, 381, 375, 369, 97, 91, 85, 10])).
% 0.59/0.84 tff(389,plain,((~hskp4) | hskp2 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.59/0.84 tff(390,plain,
% 0.59/0.84 (~hskp4),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[389, 54, 43])).
% 0.59/0.84 tff(391,plain,
% 0.59/0.84 (((~hskp7) | c0_1(a274)) <=> ((~hskp7) | c0_1(a274))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(392,axiom,((~hskp7) | c0_1(a274)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.59/0.84 tff(393,plain,
% 0.59/0.84 ((~hskp7) | c0_1(a274)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.59/0.84 tff(394,plain,
% 0.59/0.84 ((~hskp7) | c0_1(a274)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[393, 391])).
% 0.59/0.84 tff(395,plain,
% 0.59/0.84 ((~hskp7) | c0_1(a274)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[394, 391])).
% 0.59/0.84 tff(396,plain,
% 0.59/0.84 ((~hskp7) | c0_1(a274)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[395, 391])).
% 0.59/0.84 tff(397,plain,
% 0.59/0.84 ((~hskp7) | c0_1(a274)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[396, 391])).
% 0.59/0.84 tff(398,plain,
% 0.59/0.84 (c0_1(a274)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[397, 64])).
% 0.59/0.84 tff(399,plain,
% 0.59/0.84 (^[U: $i] : refl((hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) <=> (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(400,plain,
% 0.59/0.84 (![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[399])).
% 0.59/0.84 tff(401,plain,
% 0.59/0.84 (![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(402,plain,
% 0.59/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) | hskp23) <=> ((hskp28 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) | hskp23))), rewrite(((hskp28 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U))) | hskp23) <=> (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) | hskp23) <=> (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(403,plain,
% 0.59/0.84 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) | hskp23) <=> ![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[402])).
% 0.59/0.84 tff(404,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp28) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 0.59/0.84 tff(405,plain,
% 0.59/0.84 (![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.59/0.84 tff(406,plain,
% 0.59/0.84 (![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[405, 401])).
% 0.59/0.84 tff(407,plain,(
% 0.59/0.84 ![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.84 inference(skolemize,[status(sab)],[406])).
% 0.59/0.84 tff(408,plain,
% 0.59/0.84 (![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[407, 400])).
% 0.59/0.84 tff(409,assumption,(~c3_1(a274)), introduced(assumption)).
% 0.59/0.84 tff(410,assumption,(c1_1(a274)), introduced(assumption)).
% 0.59/0.84 tff(411,assumption,(c0_1(a274)), introduced(assumption)).
% 0.59/0.84 tff(412,plain,
% 0.59/0.84 (((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | c3_1(a274) | (~ndr1_0) | (~c0_1(a274)) | (~c1_1(a274)))) <=> ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp23 | c3_1(a274) | (~ndr1_0) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(413,plain,
% 0.59/0.84 ((hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c0_1(a274))) <=> (hskp28 | hskp23 | c3_1(a274) | (~ndr1_0) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(414,plain,
% 0.59/0.84 (((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c0_1(a274)))) <=> ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | c3_1(a274) | (~ndr1_0) | (~c0_1(a274)) | (~c1_1(a274))))),
% 0.59/0.84 inference(monotonicity,[status(thm)],[413])).
% 0.59/0.84 tff(415,plain,
% 0.59/0.84 (((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c0_1(a274)))) <=> ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp23 | c3_1(a274) | (~ndr1_0) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.59/0.84 inference(transitivity,[status(thm)],[414, 412])).
% 0.59/0.84 tff(416,plain,
% 0.59/0.84 ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c0_1(a274)))),
% 0.59/0.84 inference(quant_inst,[status(thm)],[])).
% 0.59/0.84 tff(417,plain,
% 0.59/0.84 ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp23 | c3_1(a274) | (~ndr1_0) | (~c0_1(a274)) | (~c1_1(a274))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[416, 415])).
% 0.59/0.84 tff(418,plain,
% 0.59/0.84 (hskp28 | hskp23),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[417, 142, 411, 410, 409, 408])).
% 0.59/0.84 tff(419,plain,
% 0.59/0.84 (hskp28),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[418, 31])).
% 0.59/0.84 tff(420,plain,
% 0.59/0.84 (((~hskp28) | c1_1(a278)) <=> ((~hskp28) | c1_1(a278))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(421,axiom,((~hskp28) | c1_1(a278)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.59/0.84 tff(422,plain,
% 0.59/0.84 ((~hskp28) | c1_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.59/0.84 tff(423,plain,
% 0.59/0.84 ((~hskp28) | c1_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[422, 420])).
% 0.59/0.84 tff(424,plain,
% 0.59/0.84 ((~hskp28) | c1_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[423, 420])).
% 0.59/0.84 tff(425,plain,
% 0.59/0.84 ((~hskp28) | c1_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[424, 420])).
% 0.59/0.84 tff(426,plain,
% 0.59/0.84 ((~hskp28) | c1_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[425, 420])).
% 0.59/0.84 tff(427,plain,
% 0.59/0.84 (c1_1(a278)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[426, 419])).
% 0.59/0.84 tff(428,plain,
% 0.59/0.84 (((~hskp28) | c0_1(a278)) <=> ((~hskp28) | c0_1(a278))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(429,axiom,((~hskp28) | c0_1(a278)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.59/0.84 tff(430,plain,
% 0.59/0.84 ((~hskp28) | c0_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.59/0.84 tff(431,plain,
% 0.59/0.84 ((~hskp28) | c0_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[430, 428])).
% 0.59/0.84 tff(432,plain,
% 0.59/0.84 ((~hskp28) | c0_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[431, 428])).
% 0.59/0.84 tff(433,plain,
% 0.59/0.84 ((~hskp28) | c0_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[432, 428])).
% 0.59/0.84 tff(434,plain,
% 0.59/0.84 ((~hskp28) | c0_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[433, 428])).
% 0.59/0.84 tff(435,plain,
% 0.59/0.84 (c0_1(a278)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[434, 419])).
% 0.59/0.84 tff(436,plain,
% 0.59/0.84 (((~hskp28) | c3_1(a278)) <=> ((~hskp28) | c3_1(a278))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(437,axiom,((~hskp28) | c3_1(a278)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.59/0.84 tff(438,plain,
% 0.59/0.84 ((~hskp28) | c3_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.59/0.84 tff(439,plain,
% 0.59/0.84 ((~hskp28) | c3_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[438, 436])).
% 0.59/0.84 tff(440,plain,
% 0.59/0.84 ((~hskp28) | c3_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[439, 436])).
% 0.59/0.84 tff(441,plain,
% 0.59/0.84 ((~hskp28) | c3_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[440, 436])).
% 0.59/0.84 tff(442,plain,
% 0.59/0.84 ((~hskp28) | c3_1(a278)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[441, 436])).
% 0.59/0.84 tff(443,plain,
% 0.59/0.84 (c3_1(a278)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[442, 419])).
% 0.59/0.84 tff(444,assumption,(~c2_1(a278)), introduced(assumption)).
% 0.59/0.84 tff(445,assumption,(c3_1(a278)), introduced(assumption)).
% 0.59/0.84 tff(446,assumption,(c1_1(a278)), introduced(assumption)).
% 0.59/0.84 tff(447,assumption,(c0_1(a278)), introduced(assumption)).
% 0.59/0.84 tff(448,plain,
% 0.59/0.84 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a278)) | c2_1(a278) | (~c3_1(a278)) | (~c0_1(a278)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | (~ndr1_0) | (~c1_1(a278)) | c2_1(a278) | (~c3_1(a278)) | (~c0_1(a278)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(449,plain,
% 0.59/0.84 ((hskp23 | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c2_1(a278) | (~c3_1(a278)) | (~c1_1(a278))) <=> (hskp23 | (~ndr1_0) | (~c1_1(a278)) | c2_1(a278) | (~c3_1(a278)) | (~c0_1(a278)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(450,plain,
% 0.59/0.84 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c2_1(a278) | (~c3_1(a278)) | (~c1_1(a278)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a278)) | c2_1(a278) | (~c3_1(a278)) | (~c0_1(a278))))),
% 0.59/0.84 inference(monotonicity,[status(thm)],[449])).
% 0.59/0.84 tff(451,plain,
% 0.59/0.84 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c2_1(a278) | (~c3_1(a278)) | (~c1_1(a278)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | (~ndr1_0) | (~c1_1(a278)) | c2_1(a278) | (~c3_1(a278)) | (~c0_1(a278)))),
% 0.59/0.84 inference(transitivity,[status(thm)],[450, 448])).
% 0.59/0.84 tff(452,plain,
% 0.59/0.84 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c2_1(a278) | (~c3_1(a278)) | (~c1_1(a278)))),
% 0.59/0.84 inference(quant_inst,[status(thm)],[])).
% 0.59/0.84 tff(453,plain,
% 0.59/0.84 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | (~ndr1_0) | (~c1_1(a278)) | c2_1(a278) | (~c3_1(a278)) | (~c0_1(a278))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.59/0.84 tff(454,plain,
% 0.59/0.84 ($false),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[453, 142, 31, 447, 446, 445, 42, 444])).
% 0.59/0.84 tff(455,plain,(c2_1(a278) | hskp23 | (~c0_1(a278)) | (~c1_1(a278)) | (~c3_1(a278))), inference(lemma,lemma(discharge,[]))).
% 0.59/0.84 tff(456,plain,
% 0.59/0.84 (c2_1(a278)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[455, 443, 435, 427, 31])).
% 0.59/0.84 tff(457,plain,
% 0.59/0.84 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(458,plain,
% 0.59/0.84 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[457])).
% 0.59/0.84 tff(459,plain,
% 0.59/0.84 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(460,plain,
% 0.59/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(461,plain,
% 0.59/0.84 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[460])).
% 0.59/0.84 tff(462,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.59/0.84 tff(463,plain,
% 0.59/0.84 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.59/0.84 tff(464,plain,
% 0.59/0.84 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[463, 459])).
% 0.59/0.84 tff(465,plain,(
% 0.59/0.84 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(skolemize,[status(sab)],[464])).
% 0.59/0.84 tff(466,plain,
% 0.59/0.84 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[465, 458])).
% 0.59/0.84 tff(467,assumption,(~hskp4), introduced(assumption)).
% 0.59/0.84 tff(468,plain,
% 0.59/0.84 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp4 | hskp3 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(469,plain,
% 0.59/0.84 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)))),
% 0.59/0.84 inference(quant_inst,[status(thm)],[])).
% 0.59/0.84 tff(470,plain,
% 0.59/0.84 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp4 | hskp3 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.59/0.84 tff(471,plain,
% 0.59/0.84 (hskp3),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[470, 142, 467, 435, 427, 466, 456])).
% 0.59/0.84 tff(472,plain,
% 0.59/0.84 (~c2_1(a270)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[282, 471])).
% 0.59/0.84 tff(473,plain,
% 0.59/0.84 (c3_1(a270)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[290, 471])).
% 0.59/0.84 tff(474,plain,
% 0.59/0.84 (c1_1(a270)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[297, 142, 32, 473, 472, 107])).
% 0.59/0.84 tff(475,plain,
% 0.59/0.84 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(476,plain,
% 0.59/0.84 ((hskp23 | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c2_1(a270) | (~c3_1(a270)) | (~c1_1(a270))) <=> (hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(477,plain,
% 0.59/0.84 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c2_1(a270) | (~c3_1(a270)) | (~c1_1(a270)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278))))),
% 0.59/0.84 inference(monotonicity,[status(thm)],[476])).
% 0.59/0.84 tff(478,plain,
% 0.59/0.84 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c2_1(a270) | (~c3_1(a270)) | (~c1_1(a270)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)))),
% 0.59/0.84 inference(transitivity,[status(thm)],[477, 475])).
% 0.59/0.84 tff(479,plain,
% 0.59/0.84 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c2_1(a270) | (~c3_1(a270)) | (~c1_1(a270)))),
% 0.59/0.84 inference(quant_inst,[status(thm)],[])).
% 0.59/0.84 tff(480,plain,
% 0.59/0.84 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278))),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.59/0.84 tff(481,plain,
% 0.59/0.84 ($false),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[480, 142, 31, 435, 427, 443, 473, 472, 42, 474])).
% 0.59/0.84 tff(482,plain,(hskp23 | hskp8 | hskp4 | (~c0_1(a274)) | (~c1_1(a274)) | c3_1(a274)), inference(lemma,lemma(discharge,[]))).
% 0.59/0.84 tff(483,plain,
% 0.59/0.84 (hskp23),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[482, 398, 32, 390, 78, 70])).
% 0.59/0.84 tff(484,plain,
% 0.59/0.84 (~c3_1(a313)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[16, 483])).
% 0.59/0.84 tff(485,plain,
% 0.59/0.84 (~c2_1(a313)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[22, 483])).
% 0.59/0.84 tff(486,plain,
% 0.59/0.84 (~c1_1(a313)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[28, 483])).
% 0.59/0.84 tff(487,plain,
% 0.59/0.84 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~ndr1_0) | c0_1(a313))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~ndr1_0) | c0_1(a313))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(488,plain,
% 0.59/0.84 ((hskp2 | (~ndr1_0) | c2_1(a313) | c0_1(a313) | c3_1(a313) | c3_1(a313) | c1_1(a313) | c0_1(a313)) <=> (hskp2 | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~ndr1_0) | c0_1(a313))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(489,plain,
% 0.59/0.84 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a313) | c0_1(a313) | c3_1(a313) | c3_1(a313) | c1_1(a313) | c0_1(a313))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~ndr1_0) | c0_1(a313)))),
% 0.59/0.84 inference(monotonicity,[status(thm)],[488])).
% 0.59/0.84 tff(490,plain,
% 0.59/0.84 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a313) | c0_1(a313) | c3_1(a313) | c3_1(a313) | c1_1(a313) | c0_1(a313))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~ndr1_0) | c0_1(a313))),
% 0.59/0.84 inference(transitivity,[status(thm)],[489, 487])).
% 0.59/0.84 tff(491,plain,
% 0.59/0.84 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a313) | c0_1(a313) | c3_1(a313) | c3_1(a313) | c1_1(a313) | c0_1(a313))),
% 0.59/0.84 inference(quant_inst,[status(thm)],[])).
% 0.59/0.84 tff(492,plain,
% 0.59/0.84 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~ndr1_0) | c0_1(a313)),
% 0.59/0.84 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.59/0.84 tff(493,plain,
% 0.59/0.84 (c0_1(a313)),
% 0.59/0.84 inference(unit_resolution,[status(thm)],[492, 142, 54, 486, 485, 484, 10])).
% 0.59/0.84 tff(494,assumption,(c0_1(a313)), introduced(assumption)).
% 0.59/0.84 tff(495,assumption,(~c2_1(a274)), introduced(assumption)).
% 0.59/0.84 tff(496,plain,
% 0.59/0.84 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.59/0.84 inference(bind,[status(th)],[])).
% 0.59/0.84 tff(497,plain,
% 0.59/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.59/0.84 inference(quant_intro,[status(thm)],[496])).
% 0.59/0.84 tff(498,plain,
% 0.59/0.84 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.59/0.84 inference(rewrite,[status(thm)],[])).
% 0.59/0.84 tff(499,plain,
% 0.59/0.84 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(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))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c2_1(V) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.59/0.85 inference(bind,[status(th)],[])).
% 0.59/0.85 tff(500,plain,
% 0.59/0.85 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.59/0.85 inference(quant_intro,[status(thm)],[499])).
% 0.59/0.85 tff(501,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c0_1(W))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 0.59/0.85 tff(502,plain,
% 0.59/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.59/0.85 tff(503,plain,
% 0.59/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[502, 498])).
% 0.59/0.85 tff(504,plain,(
% 0.59/0.85 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.59/0.85 inference(skolemize,[status(sab)],[503])).
% 0.59/0.85 tff(505,plain,
% 0.59/0.85 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[504, 497])).
% 0.59/0.85 tff(506,assumption,(~c3_1(a313)), introduced(assumption)).
% 0.59/0.85 tff(507,assumption,(~c2_1(a313)), introduced(assumption)).
% 0.59/0.85 tff(508,assumption,(~c1_1(a313)), introduced(assumption)).
% 0.59/0.85 tff(509,plain,
% 0.59/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | (~c0_1(a313)))),
% 0.59/0.85 inference(rewrite,[status(thm)],[])).
% 0.59/0.85 tff(510,plain,
% 0.59/0.85 (((~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | c3_1(a274) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313))) <=> (c1_1(a313) | c2_1(a313) | c3_1(a313) | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | (~c0_1(a313)))),
% 0.59/0.85 inference(rewrite,[status(thm)],[])).
% 0.59/0.85 tff(511,plain,
% 0.59/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | c3_1(a274) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | (~c0_1(a313))))),
% 0.59/0.85 inference(monotonicity,[status(thm)],[510])).
% 0.59/0.85 tff(512,plain,
% 0.59/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | c3_1(a274) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | (~c0_1(a313)))),
% 0.59/0.85 inference(transitivity,[status(thm)],[511, 509])).
% 0.59/0.85 tff(513,plain,
% 0.59/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | c3_1(a274) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))),
% 0.59/0.85 inference(quant_inst,[status(thm)],[])).
% 0.59/0.85 tff(514,plain,
% 0.59/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c3_1(a274) | (~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | (~c0_1(a313))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.59/0.85 tff(515,plain,
% 0.59/0.85 ($false),
% 0.59/0.85 inference(unit_resolution,[status(thm)],[514, 142, 410, 508, 507, 506, 409, 505, 495, 494])).
% 0.59/0.85 tff(516,plain,(c2_1(a274) | (~c1_1(a274)) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c3_1(a274) | (~c0_1(a313))), inference(lemma,lemma(discharge,[]))).
% 0.59/0.85 tff(517,plain,
% 0.59/0.85 (c2_1(a274)),
% 0.59/0.85 inference(unit_resolution,[status(thm)],[516, 493, 486, 485, 484, 70, 78])).
% 0.59/0.85 tff(518,plain,
% 0.59/0.85 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.59/0.85 inference(bind,[status(th)],[])).
% 0.59/0.85 tff(519,plain,
% 0.59/0.85 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.85 inference(quant_intro,[status(thm)],[518])).
% 0.59/0.85 tff(520,plain,
% 0.59/0.85 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.85 inference(rewrite,[status(thm)],[])).
% 0.59/0.85 tff(521,plain,
% 0.59/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~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)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp18) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.59/0.85 inference(bind,[status(th)],[])).
% 0.59/0.85 tff(522,plain,
% 0.59/0.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.85 inference(quant_intro,[status(thm)],[521])).
% 0.59/0.85 tff(523,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 0.59/0.85 tff(524,plain,
% 0.59/0.85 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.59/0.85 tff(525,plain,
% 0.59/0.85 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[524, 520])).
% 0.59/0.85 tff(526,plain,(
% 0.59/0.85 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.85 inference(skolemize,[status(sab)],[525])).
% 0.59/0.85 tff(527,plain,
% 0.59/0.85 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[526, 519])).
% 0.59/0.85 tff(528,plain,
% 0.59/0.85 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a313) | c2_1(a313) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c0_1(a313)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a313) | c2_1(a313) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c0_1(a313)))),
% 0.59/0.85 inference(rewrite,[status(thm)],[])).
% 0.59/0.85 tff(529,plain,
% 0.59/0.85 ((hskp18 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a313) | c2_1(a313) | (~c0_1(a313))) <=> (hskp18 | c1_1(a313) | c2_1(a313) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c0_1(a313)))),
% 0.59/0.85 inference(rewrite,[status(thm)],[])).
% 0.59/0.85 tff(530,plain,
% 0.59/0.85 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a313) | c2_1(a313) | (~c0_1(a313)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a313) | c2_1(a313) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c0_1(a313))))),
% 0.59/0.85 inference(monotonicity,[status(thm)],[529])).
% 0.59/0.85 tff(531,plain,
% 0.59/0.85 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a313) | c2_1(a313) | (~c0_1(a313)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a313) | c2_1(a313) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c0_1(a313)))),
% 0.59/0.85 inference(transitivity,[status(thm)],[530, 528])).
% 0.59/0.85 tff(532,plain,
% 0.59/0.85 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a313) | c2_1(a313) | (~c0_1(a313)))),
% 0.59/0.85 inference(quant_inst,[status(thm)],[])).
% 0.59/0.85 tff(533,plain,
% 0.59/0.85 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a313) | c2_1(a313) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c0_1(a313))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[532, 531])).
% 0.59/0.85 tff(534,plain,
% 0.59/0.85 ((~c2_1(a274)) | (~c0_1(a313))),
% 0.59/0.85 inference(unit_resolution,[status(thm)],[533, 142, 55, 398, 78, 486, 485, 527])).
% 0.59/0.85 tff(535,plain,
% 0.59/0.85 ($false),
% 0.59/0.85 inference(unit_resolution,[status(thm)],[534, 517, 493])).
% 0.59/0.85 tff(536,plain,(hskp18 | hskp2 | hskp8 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.59/0.85 tff(537,plain,
% 0.59/0.85 (hskp18),
% 0.59/0.85 inference(unit_resolution,[status(thm)],[536, 54, 32, 43])).
% 0.59/0.85 tff(538,plain,
% 0.59/0.85 (((~hskp18) | (~c2_1(a298))) <=> ((~hskp18) | (~c2_1(a298)))),
% 0.59/0.85 inference(rewrite,[status(thm)],[])).
% 0.59/0.85 tff(539,plain,
% 0.59/0.85 (((~c2_1(a298)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a298)))),
% 0.59/0.85 inference(rewrite,[status(thm)],[])).
% 0.59/0.85 tff(540,axiom,((~c2_1(a298)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.59/0.85 tff(541,plain,
% 0.59/0.85 ((~hskp18) | (~c2_1(a298))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[540, 539])).
% 0.59/0.85 tff(542,plain,
% 0.59/0.85 ((~hskp18) | (~c2_1(a298))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[541, 538])).
% 0.59/0.85 tff(543,plain,
% 0.59/0.85 (~c2_1(a298)),
% 0.59/0.85 inference(unit_resolution,[status(thm)],[542, 537])).
% 0.59/0.85 tff(544,plain,
% 0.59/0.85 (((~hskp18) | c3_1(a298)) <=> ((~hskp18) | c3_1(a298))),
% 0.59/0.85 inference(rewrite,[status(thm)],[])).
% 0.59/0.85 tff(545,axiom,((~hskp18) | c3_1(a298)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.59/0.85 tff(546,plain,
% 0.59/0.85 ((~hskp18) | c3_1(a298)),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.59/0.85 tff(547,plain,
% 0.59/0.85 ((~hskp18) | c3_1(a298)),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[546, 544])).
% 0.59/0.85 tff(548,plain,
% 0.59/0.85 ((~hskp18) | c3_1(a298)),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[547, 544])).
% 0.59/0.85 tff(549,plain,
% 0.59/0.85 ((~hskp18) | c3_1(a298)),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[548, 544])).
% 0.59/0.85 tff(550,plain,
% 0.59/0.85 ((~hskp18) | c3_1(a298)),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[549, 544])).
% 0.59/0.85 tff(551,plain,
% 0.59/0.85 (c3_1(a298)),
% 0.59/0.85 inference(unit_resolution,[status(thm)],[550, 537])).
% 0.59/0.85 tff(552,plain,
% 0.59/0.85 (((~hskp18) | c1_1(a298)) <=> ((~hskp18) | c1_1(a298))),
% 0.59/0.85 inference(rewrite,[status(thm)],[])).
% 0.59/0.85 tff(553,axiom,((~hskp18) | c1_1(a298)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.59/0.85 tff(554,plain,
% 0.59/0.85 ((~hskp18) | c1_1(a298)),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[553, 552])).
% 0.59/0.85 tff(555,plain,
% 0.59/0.85 ((~hskp18) | c1_1(a298)),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[554, 552])).
% 0.59/0.85 tff(556,plain,
% 0.59/0.85 ((~hskp18) | c1_1(a298)),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[555, 552])).
% 0.59/0.85 tff(557,plain,
% 0.59/0.85 ((~hskp18) | c1_1(a298)),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[556, 552])).
% 0.59/0.85 tff(558,plain,
% 0.59/0.85 ((~hskp18) | c1_1(a298)),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[557, 552])).
% 0.59/0.85 tff(559,plain,
% 0.59/0.85 (c1_1(a298)),
% 0.59/0.85 inference(unit_resolution,[status(thm)],[558, 537])).
% 0.59/0.85 tff(560,assumption,(~hskp7), introduced(assumption)).
% 0.59/0.85 tff(561,plain,
% 0.59/0.85 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))),
% 0.59/0.85 inference(bind,[status(th)],[])).
% 0.59/0.85 tff(562,plain,
% 0.59/0.85 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.85 inference(quant_intro,[status(thm)],[561])).
% 0.59/0.85 tff(563,plain,
% 0.59/0.85 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.85 inference(rewrite,[status(thm)],[])).
% 0.59/0.85 tff(564,plain,
% 0.59/0.85 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp7))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) | hskp8) <=> ((hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp8))), rewrite(((hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U))) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.59/0.85 inference(bind,[status(th)],[])).
% 0.59/0.85 tff(565,plain,
% 0.59/0.85 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) | hskp8) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.85 inference(quant_intro,[status(thm)],[564])).
% 0.59/0.85 tff(566,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp7) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.59/0.85 tff(567,plain,
% 0.59/0.85 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[566, 565])).
% 0.59/0.85 tff(568,plain,
% 0.59/0.85 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[567, 563])).
% 0.59/0.85 tff(569,plain,(
% 0.59/0.85 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.85 inference(skolemize,[status(sab)],[568])).
% 0.59/0.85 tff(570,plain,
% 0.59/0.85 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[569, 562])).
% 0.59/0.85 tff(571,plain,
% 0.59/0.85 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.59/0.85 inference(bind,[status(th)],[])).
% 0.59/0.85 tff(572,plain,
% 0.59/0.85 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.85 inference(quant_intro,[status(thm)],[571])).
% 0.59/0.85 tff(573,plain,
% 0.59/0.85 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.85 inference(rewrite,[status(thm)],[])).
% 0.59/0.85 tff(574,plain,
% 0.59/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~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) | c1_1(U) | c3_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) | c3_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) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_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) | c1_1(U) | c3_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) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_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) | c1_1(U) | c3_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)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_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)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.59/0.85 inference(bind,[status(th)],[])).
% 0.59/0.85 tff(575,plain,
% 0.59/0.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.85 inference(quant_intro,[status(thm)],[574])).
% 0.59/0.85 tff(576,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 0.59/0.85 tff(577,plain,
% 0.59/0.85 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[576, 575])).
% 0.59/0.85 tff(578,plain,
% 0.59/0.85 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[577, 573])).
% 0.59/0.85 tff(579,plain,(
% 0.59/0.85 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.85 inference(skolemize,[status(sab)],[578])).
% 0.59/0.85 tff(580,plain,
% 0.59/0.85 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.59/0.85 inference(modus_ponens,[status(thm)],[579, 572])).
% 0.59/0.85 tff(581,assumption,(~hskp30), introduced(assumption)).
% 0.59/0.85 tff(582,plain,
% 0.59/0.85 (hskp5),
% 0.59/0.85 inference(unit_resolution,[status(thm)],[140, 581, 43])).
% 0.59/0.85 tff(583,plain,
% 0.59/0.85 (((~hskp5) | (~c3_1(a272))) <=> ((~hskp5) | (~c3_1(a272)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(584,plain,
% 0.69/0.85 (((~c3_1(a272)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a272)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(585,axiom,((~c3_1(a272)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.69/0.85 tff(586,plain,
% 0.69/0.85 ((~hskp5) | (~c3_1(a272))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.69/0.85 tff(587,plain,
% 0.69/0.85 ((~hskp5) | (~c3_1(a272))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[586, 583])).
% 0.69/0.85 tff(588,plain,
% 0.69/0.85 (~c3_1(a272)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[587, 582])).
% 0.69/0.85 tff(589,plain,
% 0.69/0.85 (((~hskp5) | (~c1_1(a272))) <=> ((~hskp5) | (~c1_1(a272)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(590,plain,
% 0.69/0.85 (((~c1_1(a272)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a272)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(591,axiom,((~c1_1(a272)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.69/0.85 tff(592,plain,
% 0.69/0.85 ((~hskp5) | (~c1_1(a272))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.69/0.85 tff(593,plain,
% 0.69/0.85 ((~hskp5) | (~c1_1(a272))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[592, 589])).
% 0.69/0.85 tff(594,plain,
% 0.69/0.85 (~c1_1(a272)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[593, 582])).
% 0.69/0.85 tff(595,plain,
% 0.69/0.85 (((~hskp5) | c0_1(a272)) <=> ((~hskp5) | c0_1(a272))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(596,axiom,((~hskp5) | c0_1(a272)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.69/0.85 tff(597,plain,
% 0.69/0.85 ((~hskp5) | c0_1(a272)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.69/0.85 tff(598,plain,
% 0.69/0.85 ((~hskp5) | c0_1(a272)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[597, 595])).
% 0.69/0.85 tff(599,plain,
% 0.69/0.85 ((~hskp5) | c0_1(a272)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[598, 595])).
% 0.69/0.85 tff(600,plain,
% 0.69/0.85 ((~hskp5) | c0_1(a272)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[599, 595])).
% 0.69/0.85 tff(601,plain,
% 0.69/0.85 ((~hskp5) | c0_1(a272)),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[600, 595])).
% 0.69/0.85 tff(602,plain,
% 0.69/0.85 (c0_1(a272)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[601, 582])).
% 0.69/0.85 tff(603,plain,
% 0.69/0.85 (hskp18),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[63, 560, 43])).
% 0.69/0.85 tff(604,plain,
% 0.69/0.85 (~c2_1(a298)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[542, 603])).
% 0.69/0.85 tff(605,plain,
% 0.69/0.85 (c3_1(a298)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[550, 603])).
% 0.69/0.85 tff(606,plain,
% 0.69/0.85 (c1_1(a298)),
% 0.69/0.85 inference(unit_resolution,[status(thm)],[558, 603])).
% 0.69/0.85 tff(607,assumption,(c0_1(a272)), introduced(assumption)).
% 0.69/0.85 tff(608,assumption,(~c1_1(a272)), introduced(assumption)).
% 0.69/0.85 tff(609,plain,
% 0.69/0.85 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(610,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[609])).
% 0.69/0.85 tff(611,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(612,plain,
% 0.69/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.69/0.85 inference(bind,[status(th)],[])).
% 0.69/0.85 tff(613,plain,
% 0.69/0.85 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.85 inference(quant_intro,[status(thm)],[612])).
% 0.69/0.85 tff(614,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 0.69/0.85 tff(615,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[614, 613])).
% 0.69/0.85 tff(616,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[615, 611])).
% 0.69/0.85 tff(617,plain,(
% 0.69/0.85 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.85 inference(skolemize,[status(sab)],[616])).
% 0.69/0.85 tff(618,plain,
% 0.69/0.85 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.69/0.85 inference(modus_ponens,[status(thm)],[617, 610])).
% 0.69/0.85 tff(619,assumption,(~c2_1(a298)), introduced(assumption)).
% 0.69/0.85 tff(620,assumption,(c3_1(a298)), introduced(assumption)).
% 0.69/0.85 tff(621,assumption,(c1_1(a298)), introduced(assumption)).
% 0.69/0.85 tff(622,plain,
% 0.69/0.85 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | c1_1(a313) | c2_1(a313) | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a313)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a313) | c2_1(a313) | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a313)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.85 tff(623,plain,
% 0.69/0.85 ((hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a313) | c2_1(a313) | (~c0_1(a313))) <=> (hskp7 | c1_1(a313) | c2_1(a313) | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a313)))),
% 0.69/0.85 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(624,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a313) | c2_1(a313) | (~c0_1(a313)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | c1_1(a313) | c2_1(a313) | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a313))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[623])).
% 0.69/0.86 tff(625,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a313) | c2_1(a313) | (~c0_1(a313)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a313) | c2_1(a313) | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a313)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[624, 622])).
% 0.69/0.86 tff(626,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a313) | c2_1(a313) | (~c0_1(a313)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(627,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a313) | c2_1(a313) | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a313))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.69/0.86 tff(628,plain,
% 0.69/0.86 (~c0_1(a313)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[627, 142, 560, 621, 620, 29, 23, 619, 618])).
% 0.69/0.86 tff(629,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | c2_1(a298) | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | (~c1_1(a298)) | (~c3_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c2_1(a298) | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(630,plain,
% 0.69/0.86 ((hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272))) <=> (hskp7 | c2_1(a298) | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(631,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | c2_1(a298) | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | (~c1_1(a298)) | (~c3_1(a298))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[630])).
% 0.69/0.86 tff(632,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c2_1(a298) | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[631, 629])).
% 0.69/0.86 tff(633,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(634,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c2_1(a298) | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | (~c1_1(a298)) | (~c3_1(a298))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[633, 632])).
% 0.69/0.86 tff(635,plain,
% 0.69/0.86 (c2_1(a272)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[634, 142, 560, 621, 620, 607, 619, 608, 618])).
% 0.69/0.86 tff(636,plain,
% 0.69/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(637,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[636])).
% 0.69/0.86 tff(638,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(639,plain,
% 0.69/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(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)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(640,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[639])).
% 0.69/0.86 tff(641,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 0.69/0.86 tff(642,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[641, 640])).
% 0.69/0.86 tff(643,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[642, 638])).
% 0.69/0.86 tff(644,plain,(
% 0.69/0.86 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.86 inference(skolemize,[status(sab)],[643])).
% 0.69/0.86 tff(645,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[644, 637])).
% 0.69/0.86 tff(646,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | c0_1(a313))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | c0_1(a313))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(647,plain,
% 0.69/0.86 (((~ndr1_0) | c1_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a313) | c1_1(a313) | c0_1(a313)) <=> (c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | c0_1(a313))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(648,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a313) | c1_1(a313) | c0_1(a313))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | c0_1(a313)))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[647])).
% 0.69/0.86 tff(649,plain,
% 0.69/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a313) | c1_1(a313) | c0_1(a313))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | c0_1(a313))),
% 0.69/0.86 inference(transitivity,[status(thm)],[648, 646])).
% 0.69/0.86 tff(650,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a313) | c1_1(a313) | c0_1(a313))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(651,plain,
% 0.69/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | c0_1(a313)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.69/0.86 tff(652,plain,
% 0.69/0.86 ($false),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[651, 142, 607, 29, 23, 17, 608, 645, 635, 628])).
% 0.69/0.86 tff(653,plain,((~hskp23) | (~c0_1(a272)) | c1_1(a272) | hskp7 | (~c1_1(a298)) | (~c3_1(a298)) | c2_1(a298)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.86 tff(654,plain,
% 0.69/0.86 (~hskp23),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[653, 606, 608, 607, 560, 605, 604])).
% 0.69/0.86 tff(655,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | (~c0_1(a298)) | (~c3_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | (~c0_1(a298)) | (~c3_1(a298)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(656,plain,
% 0.69/0.86 ((hskp23 | (~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a298)) | c2_1(a298) | (~c3_1(a298)) | (~c1_1(a298))) <=> (hskp23 | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | (~c0_1(a298)) | (~c3_1(a298)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(657,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a298)) | c2_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | (~c0_1(a298)) | (~c3_1(a298))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[656])).
% 0.69/0.86 tff(658,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a298)) | c2_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | (~c0_1(a298)) | (~c3_1(a298)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[657, 655])).
% 0.69/0.86 tff(659,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a298)) | c2_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(660,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | (~c0_1(a298)) | (~c3_1(a298))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[659, 658])).
% 0.69/0.86 tff(661,plain,
% 0.69/0.86 (~c0_1(a298)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[660, 142, 654, 606, 605, 604, 42])).
% 0.69/0.86 tff(662,plain,
% 0.69/0.86 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | c0_1(a298))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | c0_1(a298))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(663,plain,
% 0.69/0.86 ((hskp9 | (~ndr1_0) | c2_1(a298) | c0_1(a298) | (~c1_1(a298))) <=> (hskp9 | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | c0_1(a298))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(664,plain,
% 0.69/0.86 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a298) | c0_1(a298) | (~c1_1(a298)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | c0_1(a298)))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[663])).
% 0.69/0.86 tff(665,plain,
% 0.69/0.86 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a298) | c0_1(a298) | (~c1_1(a298)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | c0_1(a298))),
% 0.69/0.86 inference(transitivity,[status(thm)],[664, 662])).
% 0.69/0.86 tff(666,plain,
% 0.69/0.86 ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a298) | c0_1(a298) | (~c1_1(a298)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(667,plain,
% 0.69/0.86 ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c2_1(a298) | (~ndr1_0) | (~c1_1(a298)) | c0_1(a298)),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.69/0.86 tff(668,plain,
% 0.69/0.86 (hskp9),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[667, 142, 606, 604, 216, 661])).
% 0.69/0.86 tff(669,plain,
% 0.69/0.86 (~c1_1(a280)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[236, 668])).
% 0.69/0.86 tff(670,plain,
% 0.69/0.86 (c3_1(a280)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[244, 668])).
% 0.69/0.86 tff(671,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(672,plain,
% 0.69/0.86 ((hskp16 | (~ndr1_0) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298))) <=> (hskp16 | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(673,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[672])).
% 0.69/0.86 tff(674,plain,
% 0.69/0.86 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[673, 671])).
% 0.69/0.86 tff(675,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(676,plain,
% 0.69/0.86 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.69/0.86 tff(677,plain,
% 0.69/0.86 (~c0_1(a280)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[676, 142, 43, 606, 605, 670, 669, 206, 661])).
% 0.69/0.86 tff(678,plain,
% 0.69/0.86 (^[U: $i] : refl((hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(679,plain,
% 0.69/0.86 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[678])).
% 0.69/0.86 tff(680,plain,
% 0.69/0.86 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(681,plain,
% 0.69/0.86 (^[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)) | hskp7) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) | hskp8) <=> ((hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp8))), rewrite(((hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) | hskp8) <=> (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(682,plain,
% 0.69/0.86 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) | hskp8) <=> ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[681])).
% 0.69/0.86 tff(683,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp7) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.69/0.86 tff(684,plain,
% 0.69/0.86 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.69/0.86 tff(685,plain,
% 0.69/0.86 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[684, 680])).
% 0.69/0.86 tff(686,plain,(
% 0.69/0.86 ![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.69/0.86 inference(skolemize,[status(sab)],[685])).
% 0.69/0.86 tff(687,plain,
% 0.69/0.86 (![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[686, 679])).
% 0.69/0.86 tff(688,plain,
% 0.69/0.86 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c3_1(a280)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c3_1(a280)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(689,plain,
% 0.69/0.86 ((hskp8 | hskp7 | (~ndr1_0) | c1_1(a280) | c0_1(a280) | (~c3_1(a280))) <=> (hskp8 | hskp7 | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c3_1(a280)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(690,plain,
% 0.69/0.86 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c3_1(a280))))),
% 0.69/0.86 inference(monotonicity,[status(thm)],[689])).
% 0.69/0.86 tff(691,plain,
% 0.69/0.86 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c3_1(a280)))),
% 0.69/0.86 inference(transitivity,[status(thm)],[690, 688])).
% 0.69/0.86 tff(692,plain,
% 0.69/0.86 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)))),
% 0.69/0.86 inference(quant_inst,[status(thm)],[])).
% 0.69/0.86 tff(693,plain,
% 0.69/0.86 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp8 | hskp7 | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c3_1(a280))),
% 0.69/0.86 inference(modus_ponens,[status(thm)],[692, 691])).
% 0.69/0.86 tff(694,plain,
% 0.69/0.86 ($false),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[693, 142, 32, 560, 670, 669, 687, 677])).
% 0.69/0.86 tff(695,plain,(hskp7 | hskp8 | hskp16 | c1_1(a272) | (~c0_1(a272))), inference(lemma,lemma(discharge,[]))).
% 0.69/0.86 tff(696,plain,
% 0.69/0.86 (hskp7),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[695, 32, 43, 594, 602])).
% 0.69/0.86 tff(697,plain,
% 0.69/0.86 (c0_1(a274)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[397, 696])).
% 0.69/0.86 tff(698,plain,
% 0.69/0.86 (~c3_1(a274)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[69, 696])).
% 0.69/0.86 tff(699,plain,
% 0.69/0.86 (c1_1(a274)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[77, 696])).
% 0.69/0.86 tff(700,plain,
% 0.69/0.86 (~hskp23),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[653, 560, 608, 607, 606, 605, 604])).
% 0.69/0.86 tff(701,plain,
% 0.69/0.86 (hskp23 | (~c0_1(a298))),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[660, 142, 606, 605, 604, 42])).
% 0.69/0.86 tff(702,plain,
% 0.69/0.86 (~c0_1(a298)),
% 0.69/0.86 inference(unit_resolution,[status(thm)],[701, 700])).
% 0.69/0.86 tff(703,plain,
% 0.69/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(704,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[703])).
% 0.69/0.86 tff(705,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.86 inference(rewrite,[status(thm)],[])).
% 0.69/0.86 tff(706,plain,
% 0.69/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.69/0.86 inference(bind,[status(th)],[])).
% 0.69/0.86 tff(707,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.86 inference(quant_intro,[status(thm)],[706])).
% 0.69/0.86 tff(708,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 0.69/0.86 tff(709,plain,
% 0.69/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.69/0.87 tff(710,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[709, 705])).
% 0.69/0.87 tff(711,plain,(
% 0.69/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.87 inference(skolemize,[status(sab)],[710])).
% 0.69/0.87 tff(712,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[711, 704])).
% 0.69/0.87 tff(713,assumption,(~c3_1(a272)), introduced(assumption)).
% 0.69/0.87 tff(714,assumption,(~c1_1(a269)), introduced(assumption)).
% 0.69/0.87 tff(715,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | c2_1(a298) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a298)) | (~c3_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c2_1(a298) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(716,plain,
% 0.69/0.87 ((hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269))) <=> (hskp7 | c2_1(a298) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(717,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | c2_1(a298) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a298)) | (~c3_1(a298))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[716])).
% 0.69/0.87 tff(718,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c2_1(a298) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[717, 715])).
% 0.69/0.87 tff(719,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(720,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c2_1(a298) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a298)) | (~c3_1(a298))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[719, 718])).
% 0.69/0.87 tff(721,plain,
% 0.69/0.87 (~c0_1(a269)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[720, 142, 560, 621, 620, 619, 714, 30, 618])).
% 0.69/0.87 tff(722,plain,
% 0.69/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(723,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[722])).
% 0.69/0.87 tff(724,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(725,plain,
% 0.69/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(726,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_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) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[725])).
% 0.69/0.87 tff(727,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_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','clause177')).
% 0.69/0.87 tff(728,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[727, 726])).
% 0.69/0.87 tff(729,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[728, 724])).
% 0.69/0.87 tff(730,plain,(
% 0.69/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.87 inference(skolemize,[status(sab)],[729])).
% 0.69/0.87 tff(731,plain,
% 0.69/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[730, 723])).
% 0.69/0.87 tff(732,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a269) | c1_1(a272) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c2_1(a272)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a269) | c1_1(a272) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c2_1(a272)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(733,plain,
% 0.69/0.87 (((~ndr1_0) | c1_1(a272) | c3_1(a272) | (~c2_1(a272)) | c1_1(a269) | c2_1(a269) | (~c3_1(a269)) | c2_1(a269) | c1_1(a269) | c0_1(a269)) <=> (c0_1(a269) | c1_1(a272) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c2_1(a272)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(734,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a272) | c3_1(a272) | (~c2_1(a272)) | c1_1(a269) | c2_1(a269) | (~c3_1(a269)) | c2_1(a269) | c1_1(a269) | c0_1(a269))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a269) | c1_1(a272) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c2_1(a272))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[733])).
% 0.69/0.87 tff(735,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a272) | c3_1(a272) | (~c2_1(a272)) | c1_1(a269) | c2_1(a269) | (~c3_1(a269)) | c2_1(a269) | c1_1(a269) | c0_1(a269))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a269) | c1_1(a272) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c2_1(a272)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[734, 732])).
% 0.69/0.87 tff(736,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a272) | c3_1(a272) | (~c2_1(a272)) | c1_1(a269) | c2_1(a269) | (~c3_1(a269)) | c2_1(a269) | c1_1(a269) | c0_1(a269))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(737,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a269) | c1_1(a272) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c2_1(a272))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[736, 735])).
% 0.69/0.87 tff(738,plain,
% 0.69/0.87 (c0_1(a269) | (~c3_1(a269))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[737, 142, 608, 713, 714, 30, 731, 635])).
% 0.69/0.87 tff(739,plain,
% 0.69/0.87 (~c3_1(a269)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[738, 721])).
% 0.69/0.87 tff(740,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a269) | c1_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a272)) | (~c2_1(a272)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a269) | c1_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a272)) | (~c2_1(a272)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(741,plain,
% 0.69/0.87 (((~ndr1_0) | c1_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a269) | c1_1(a269) | c2_1(a269) | c2_1(a269) | c1_1(a269) | c0_1(a269)) <=> (c0_1(a269) | c1_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a272)) | (~c2_1(a272)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(742,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a269) | c1_1(a269) | c2_1(a269) | c2_1(a269) | c1_1(a269) | c0_1(a269))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a269) | c1_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a272)) | (~c2_1(a272))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[741])).
% 0.69/0.87 tff(743,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a269) | c1_1(a269) | c2_1(a269) | c2_1(a269) | c1_1(a269) | c0_1(a269))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a269) | c1_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a272)) | (~c2_1(a272)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[742, 740])).
% 0.69/0.87 tff(744,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a269) | c1_1(a269) | c2_1(a269) | c2_1(a269) | c1_1(a269) | c0_1(a269))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(745,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a269) | c1_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a272)) | (~c2_1(a272))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.69/0.87 tff(746,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[745, 142, 607, 721, 608, 714, 30, 645, 635, 739])).
% 0.69/0.87 tff(747,plain,(c1_1(a269) | (~c0_1(a272)) | c1_1(a272) | c2_1(a269) | c3_1(a272) | hskp7 | (~c1_1(a298)) | (~c3_1(a298)) | c2_1(a298)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.87 tff(748,plain,
% 0.69/0.87 (c1_1(a269)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[747, 560, 608, 30, 713, 607, 606, 605, 604])).
% 0.69/0.87 tff(749,assumption,(c1_1(a269)), introduced(assumption)).
% 0.69/0.87 tff(750,assumption,(~c0_1(a269)), introduced(assumption)).
% 0.69/0.87 tff(751,assumption,(c0_1(a280)), introduced(assumption)).
% 0.69/0.87 tff(752,plain,
% 0.69/0.87 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | c0_1(a269) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c0_1(a269) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(753,plain,
% 0.69/0.87 ((hskp9 | (~ndr1_0) | c2_1(a269) | c0_1(a269) | (~c1_1(a269))) <=> (hskp9 | c0_1(a269) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(754,plain,
% 0.69/0.87 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a269) | c0_1(a269) | (~c1_1(a269)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | c0_1(a269) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0)))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[753])).
% 0.69/0.87 tff(755,plain,
% 0.69/0.87 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a269) | c0_1(a269) | (~c1_1(a269)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c0_1(a269) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0))),
% 0.69/0.87 inference(transitivity,[status(thm)],[754, 752])).
% 0.69/0.87 tff(756,plain,
% 0.69/0.87 ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a269) | c0_1(a269) | (~c1_1(a269)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(757,plain,
% 0.69/0.87 ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c0_1(a269) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.69/0.87 tff(758,plain,
% 0.69/0.87 (hskp9 | c0_1(a269) | (~c1_1(a269))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[757, 142, 30, 216])).
% 0.69/0.87 tff(759,plain,
% 0.69/0.87 (hskp9),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[758, 750, 749])).
% 0.69/0.87 tff(760,plain,
% 0.69/0.87 (~c1_1(a280)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[236, 759])).
% 0.69/0.87 tff(761,plain,
% 0.69/0.87 (c3_1(a280)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[244, 759])).
% 0.69/0.87 tff(762,plain,
% 0.69/0.87 (c2_1(a280)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[269, 759])).
% 0.69/0.87 tff(763,plain,
% 0.69/0.87 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(764,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[763])).
% 0.69/0.87 tff(765,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(766,plain,
% 0.69/0.87 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp27) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp27))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.69/0.87 inference(bind,[status(th)],[])).
% 0.69/0.87 tff(767,plain,
% 0.69/0.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.87 inference(quant_intro,[status(thm)],[766])).
% 0.69/0.87 tff(768,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 0.69/0.87 tff(769,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[768, 767])).
% 0.69/0.87 tff(770,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[769, 765])).
% 0.69/0.87 tff(771,plain,(
% 0.69/0.87 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.87 inference(skolemize,[status(sab)],[770])).
% 0.69/0.87 tff(772,plain,
% 0.69/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[771, 764])).
% 0.69/0.87 tff(773,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | c0_1(a269) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a269) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(774,plain,
% 0.69/0.87 ((hskp27 | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a269) | c2_1(a269) | (~c1_1(a269))) <=> (hskp27 | c0_1(a269) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(775,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a269) | c2_1(a269) | (~c1_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | c0_1(a269) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[774])).
% 0.69/0.87 tff(776,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a269) | c2_1(a269) | (~c1_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a269) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[775, 773])).
% 0.69/0.87 tff(777,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a269) | c2_1(a269) | (~c1_1(a269)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(778,plain,
% 0.69/0.87 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a269) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[777, 776])).
% 0.69/0.87 tff(779,plain,
% 0.69/0.87 (hskp27 | (~c0_1(a280))),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[778, 142, 762, 761, 750, 749, 30, 772])).
% 0.69/0.87 tff(780,plain,
% 0.69/0.87 (hskp27),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[779, 751])).
% 0.69/0.87 tff(781,plain,
% 0.69/0.87 (((~hskp27) | c3_1(a276)) <=> ((~hskp27) | c3_1(a276))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(782,axiom,((~hskp27) | c3_1(a276)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.69/0.87 tff(783,plain,
% 0.69/0.87 ((~hskp27) | c3_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[782, 781])).
% 0.69/0.87 tff(784,plain,
% 0.69/0.87 ((~hskp27) | c3_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[783, 781])).
% 0.69/0.87 tff(785,plain,
% 0.69/0.87 ((~hskp27) | c3_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[784, 781])).
% 0.69/0.87 tff(786,plain,
% 0.69/0.87 ((~hskp27) | c3_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[785, 781])).
% 0.69/0.87 tff(787,plain,
% 0.69/0.87 ((~hskp27) | c3_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[786, 781])).
% 0.69/0.87 tff(788,plain,
% 0.69/0.87 (c3_1(a276)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[787, 780])).
% 0.69/0.87 tff(789,plain,
% 0.69/0.87 (((~hskp27) | c2_1(a276)) <=> ((~hskp27) | c2_1(a276))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(790,axiom,((~hskp27) | c2_1(a276)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.69/0.87 tff(791,plain,
% 0.69/0.87 ((~hskp27) | c2_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.69/0.87 tff(792,plain,
% 0.69/0.87 ((~hskp27) | c2_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[791, 789])).
% 0.69/0.87 tff(793,plain,
% 0.69/0.87 ((~hskp27) | c2_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[792, 789])).
% 0.69/0.87 tff(794,plain,
% 0.69/0.87 ((~hskp27) | c2_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[793, 789])).
% 0.69/0.87 tff(795,plain,
% 0.69/0.87 ((~hskp27) | c2_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[794, 789])).
% 0.69/0.87 tff(796,plain,
% 0.69/0.87 (c2_1(a276)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[795, 780])).
% 0.69/0.87 tff(797,plain,
% 0.69/0.87 (((~hskp27) | c1_1(a276)) <=> ((~hskp27) | c1_1(a276))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(798,axiom,((~hskp27) | c1_1(a276)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.69/0.87 tff(799,plain,
% 0.69/0.87 ((~hskp27) | c1_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[798, 797])).
% 0.69/0.87 tff(800,plain,
% 0.69/0.87 ((~hskp27) | c1_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[799, 797])).
% 0.69/0.87 tff(801,plain,
% 0.69/0.87 ((~hskp27) | c1_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[800, 797])).
% 0.69/0.87 tff(802,plain,
% 0.69/0.87 ((~hskp27) | c1_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[801, 797])).
% 0.69/0.87 tff(803,plain,
% 0.69/0.87 ((~hskp27) | c1_1(a276)),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[802, 797])).
% 0.69/0.87 tff(804,plain,
% 0.69/0.87 (c1_1(a276)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[803, 780])).
% 0.69/0.87 tff(805,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a280) | (~ndr1_0) | (~c3_1(a276)) | (~c1_1(a276)) | (~c2_1(a276)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a280) | (~ndr1_0) | (~c3_1(a276)) | (~c1_1(a276)) | (~c2_1(a276)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(806,plain,
% 0.69/0.87 (((~ndr1_0) | (~c1_1(a276)) | (~c2_1(a276)) | (~c3_1(a276)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c1_1(a280) | (~c0_1(a280)) | (~c2_1(a280))) <=> (c1_1(a280) | (~ndr1_0) | (~c3_1(a276)) | (~c1_1(a276)) | (~c2_1(a276)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(807,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a276)) | (~c2_1(a276)) | (~c3_1(a276)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c1_1(a280) | (~c0_1(a280)) | (~c2_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a280) | (~ndr1_0) | (~c3_1(a276)) | (~c1_1(a276)) | (~c2_1(a276)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280))))),
% 0.69/0.87 inference(monotonicity,[status(thm)],[806])).
% 0.69/0.87 tff(808,plain,
% 0.69/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a276)) | (~c2_1(a276)) | (~c3_1(a276)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c1_1(a280) | (~c0_1(a280)) | (~c2_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a280) | (~ndr1_0) | (~c3_1(a276)) | (~c1_1(a276)) | (~c2_1(a276)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.69/0.87 inference(transitivity,[status(thm)],[807, 805])).
% 0.69/0.87 tff(809,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a276)) | (~c2_1(a276)) | (~c3_1(a276)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c1_1(a280) | (~c0_1(a280)) | (~c2_1(a280)))),
% 0.69/0.87 inference(quant_inst,[status(thm)],[])).
% 0.69/0.87 tff(810,plain,
% 0.69/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a280) | (~ndr1_0) | (~c3_1(a276)) | (~c1_1(a276)) | (~c2_1(a276)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280))),
% 0.69/0.87 inference(modus_ponens,[status(thm)],[809, 808])).
% 0.69/0.87 tff(811,plain,
% 0.69/0.87 ($false),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[810, 142, 804, 796, 788, 762, 761, 760, 53, 751])).
% 0.69/0.87 tff(812,plain,((~c0_1(a280)) | c0_1(a269) | (~c1_1(a269)) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.87 tff(813,plain,
% 0.69/0.87 (~c0_1(a280)),
% 0.69/0.87 inference(unit_resolution,[status(thm)],[812, 750, 749, 30])).
% 0.69/0.87 tff(814,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a280) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a280) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | c0_1(a280) | (~c2_1(a280)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(815,plain,
% 0.69/0.87 ((hskp4 | (~ndr1_0) | c1_1(a272) | c3_1(a272) | (~c0_1(a272)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280))) <=> (hskp4 | c1_1(a280) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | c0_1(a280) | (~c2_1(a280)))),
% 0.69/0.87 inference(rewrite,[status(thm)],[])).
% 0.69/0.87 tff(816,plain,
% 0.69/0.87 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a272) | c3_1(a272) | (~c0_1(a272)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a280) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | c0_1(a280) | (~c2_1(a280))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[815])).
% 0.69/0.88 tff(817,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a272) | c3_1(a272) | (~c0_1(a272)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a280) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | c0_1(a280) | (~c2_1(a280)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[816, 814])).
% 0.69/0.88 tff(818,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a272) | c3_1(a272) | (~c0_1(a272)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(819,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a280) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | c0_1(a280) | (~c2_1(a280))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[818, 817])).
% 0.69/0.88 tff(820,plain,
% 0.69/0.88 (hskp4 | c0_1(a280)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[819, 142, 762, 607, 760, 608, 713, 580])).
% 0.69/0.88 tff(821,plain,
% 0.69/0.88 (hskp4),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[820, 813])).
% 0.69/0.88 tff(822,plain,
% 0.69/0.88 (~c3_1(a271)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[84, 821])).
% 0.69/0.88 tff(823,plain,
% 0.69/0.88 (~c1_1(a271)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[90, 821])).
% 0.69/0.88 tff(824,plain,
% 0.69/0.88 (~c0_1(a271)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[96, 821])).
% 0.69/0.88 tff(825,plain,
% 0.69/0.88 (hskp8 | c0_1(a280)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[693, 142, 560, 761, 760, 687])).
% 0.69/0.88 tff(826,plain,
% 0.69/0.88 (hskp8),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[825, 813])).
% 0.69/0.88 tff(827,plain,
% 0.69/0.88 (~c3_1(a275)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[368, 826])).
% 0.69/0.88 tff(828,plain,
% 0.69/0.88 (~c2_1(a275)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[374, 826])).
% 0.69/0.88 tff(829,plain,
% 0.69/0.88 (~c0_1(a275)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[380, 826])).
% 0.69/0.88 tff(830,plain,
% 0.69/0.88 (((~hskp2) | (~c1_1(a269))) <=> ((~hskp2) | (~c1_1(a269)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(831,plain,
% 0.69/0.88 (((~c1_1(a269)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a269)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(832,axiom,((~c1_1(a269)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.69/0.88 tff(833,plain,
% 0.69/0.88 ((~hskp2) | (~c1_1(a269))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[832, 831])).
% 0.69/0.88 tff(834,plain,
% 0.69/0.88 ((~hskp2) | (~c1_1(a269))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[833, 830])).
% 0.69/0.88 tff(835,plain,
% 0.69/0.88 (~hskp2),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[834, 749])).
% 0.69/0.88 tff(836,plain,
% 0.69/0.88 ($false),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[387, 142, 835, 829, 828, 827, 824, 823, 822, 10])).
% 0.69/0.88 tff(837,plain,(c0_1(a269) | (~c0_1(a272)) | c1_1(a272) | c3_1(a272) | hskp7 | (~c1_1(a269)) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.88 tff(838,plain,
% 0.69/0.88 (c0_1(a269)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[837, 560, 608, 713, 607, 748, 30])).
% 0.69/0.88 tff(839,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a298) | (~c1_1(a269)) | (~ndr1_0) | (~c0_1(a269)) | (~c3_1(a269)) | (~c1_1(a298)) | (~c3_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a298) | (~c1_1(a269)) | (~ndr1_0) | (~c0_1(a269)) | (~c3_1(a269)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(840,plain,
% 0.69/0.88 ((hskp23 | (~ndr1_0) | (~c1_1(a269)) | (~c3_1(a269)) | (~c0_1(a269)) | c2_1(a298) | (~c3_1(a298)) | (~c1_1(a298))) <=> (hskp23 | c2_1(a298) | (~c1_1(a269)) | (~ndr1_0) | (~c0_1(a269)) | (~c3_1(a269)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(841,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a269)) | (~c3_1(a269)) | (~c0_1(a269)) | c2_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a298) | (~c1_1(a269)) | (~ndr1_0) | (~c0_1(a269)) | (~c3_1(a269)) | (~c1_1(a298)) | (~c3_1(a298))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[840])).
% 0.69/0.88 tff(842,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a269)) | (~c3_1(a269)) | (~c0_1(a269)) | c2_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a298) | (~c1_1(a269)) | (~ndr1_0) | (~c0_1(a269)) | (~c3_1(a269)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[841, 839])).
% 0.69/0.88 tff(843,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a269)) | (~c3_1(a269)) | (~c0_1(a269)) | c2_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(844,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a298) | (~c1_1(a269)) | (~ndr1_0) | (~c0_1(a269)) | (~c3_1(a269)) | (~c1_1(a298)) | (~c3_1(a298))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[843, 842])).
% 0.69/0.88 tff(845,plain,
% 0.69/0.88 (hskp23 | (~c0_1(a269)) | (~c3_1(a269))),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[844, 142, 606, 605, 604, 748, 42])).
% 0.69/0.88 tff(846,plain,
% 0.69/0.88 (~c3_1(a269)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[845, 700, 838])).
% 0.69/0.88 tff(847,plain,
% 0.69/0.88 (((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~c1_1(a269)) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)))) <=> ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp23 | (~c1_1(a269)) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(848,plain,
% 0.69/0.88 ((hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a269)) | c3_1(a269) | (~c0_1(a269))) <=> (hskp28 | hskp23 | (~c1_1(a269)) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(849,plain,
% 0.69/0.88 (((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a269)) | c3_1(a269) | (~c0_1(a269)))) <=> ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~c1_1(a269)) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[848])).
% 0.69/0.88 tff(850,plain,
% 0.69/0.88 (((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a269)) | c3_1(a269) | (~c0_1(a269)))) <=> ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp23 | (~c1_1(a269)) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[849, 847])).
% 0.69/0.88 tff(851,plain,
% 0.69/0.88 ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a269)) | c3_1(a269) | (~c0_1(a269)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(852,plain,
% 0.69/0.88 ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp23 | (~c1_1(a269)) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[851, 850])).
% 0.69/0.88 tff(853,plain,
% 0.69/0.88 (hskp28 | hskp23 | c3_1(a269) | (~c0_1(a269))),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[852, 142, 748, 408])).
% 0.69/0.88 tff(854,plain,
% 0.69/0.88 (hskp28),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[853, 700, 838, 846])).
% 0.69/0.88 tff(855,plain,
% 0.69/0.88 (c3_1(a278)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[442, 854])).
% 0.69/0.88 tff(856,plain,
% 0.69/0.88 (c1_1(a278)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[426, 854])).
% 0.69/0.88 tff(857,plain,
% 0.69/0.88 (c0_1(a278)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[434, 854])).
% 0.69/0.88 tff(858,plain,
% 0.69/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a298) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a298) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(859,plain,
% 0.69/0.88 (((~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)) | c2_1(a298) | c0_1(a298) | (~c3_1(a298))) <=> (c2_1(a298) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(860,plain,
% 0.69/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)) | c2_1(a298) | c0_1(a298) | (~c3_1(a298)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a298) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[859])).
% 0.69/0.88 tff(861,plain,
% 0.69/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)) | c2_1(a298) | c0_1(a298) | (~c3_1(a298)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a298) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[860, 858])).
% 0.69/0.88 tff(862,plain,
% 0.69/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)) | c2_1(a298) | c0_1(a298) | (~c3_1(a298)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(863,plain,
% 0.69/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a298) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[862, 861])).
% 0.69/0.88 tff(864,plain,
% 0.69/0.88 ($false),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[863, 142, 857, 856, 855, 606, 605, 604, 712, 702])).
% 0.69/0.88 tff(865,plain,(hskp7 | c1_1(a272) | (~c0_1(a272)) | c3_1(a272) | c2_1(a269) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.69/0.88 tff(866,plain,
% 0.69/0.88 (hskp7),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[865, 30, 602, 588, 594, 43])).
% 0.69/0.88 tff(867,plain,
% 0.69/0.88 (c0_1(a274)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[397, 866])).
% 0.69/0.88 tff(868,plain,
% 0.69/0.88 (~c3_1(a274)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[69, 866])).
% 0.69/0.88 tff(869,plain,
% 0.69/0.88 (c1_1(a274)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[77, 866])).
% 0.69/0.88 tff(870,assumption,(~c3_1(a269)), introduced(assumption)).
% 0.69/0.88 tff(871,plain,
% 0.69/0.88 (((~hskp2) | c0_1(a269)) <=> ((~hskp2) | c0_1(a269))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(872,axiom,((~hskp2) | c0_1(a269)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.69/0.88 tff(873,plain,
% 0.69/0.88 ((~hskp2) | c0_1(a269)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[872, 871])).
% 0.69/0.88 tff(874,plain,
% 0.69/0.88 ((~hskp2) | c0_1(a269)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[873, 871])).
% 0.69/0.88 tff(875,plain,
% 0.69/0.88 ((~hskp2) | c0_1(a269)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[874, 871])).
% 0.69/0.88 tff(876,plain,
% 0.69/0.88 ((~hskp2) | c0_1(a269)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[875, 871])).
% 0.69/0.88 tff(877,plain,
% 0.69/0.88 ((~hskp2) | c0_1(a269)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[876, 871])).
% 0.69/0.88 tff(878,plain,
% 0.69/0.88 (~hskp2),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[877, 750])).
% 0.69/0.88 tff(879,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a269) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a269) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(880,plain,
% 0.69/0.88 ((hskp2 | (~ndr1_0) | c2_1(a269) | c0_1(a269) | c3_1(a269) | c3_1(a269) | c1_1(a269) | c0_1(a269)) <=> (hskp2 | c0_1(a269) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(881,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a269) | c0_1(a269) | c3_1(a269) | c3_1(a269) | c1_1(a269) | c0_1(a269))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a269) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269)))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[880])).
% 0.69/0.88 tff(882,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a269) | c0_1(a269) | c3_1(a269) | c3_1(a269) | c1_1(a269) | c0_1(a269))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a269) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269))),
% 0.69/0.88 inference(transitivity,[status(thm)],[881, 879])).
% 0.69/0.88 tff(883,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a269) | c0_1(a269) | c3_1(a269) | c3_1(a269) | c1_1(a269) | c0_1(a269))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(884,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a269) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[883, 882])).
% 0.69/0.88 tff(885,plain,
% 0.69/0.88 ($false),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[884, 142, 878, 750, 714, 30, 10, 870])).
% 0.69/0.88 tff(886,plain,(c3_1(a269) | c0_1(a269) | c1_1(a269) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.88 tff(887,plain,
% 0.69/0.88 (c3_1(a269)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[886, 714, 750, 30])).
% 0.69/0.88 tff(888,plain,
% 0.69/0.88 (((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)))) <=> ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp8 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(889,plain,
% 0.69/0.88 ((hskp8 | (~ndr1_0) | c2_1(a269) | c1_1(a269) | (~c3_1(a269))) <=> (hskp8 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(890,plain,
% 0.69/0.88 (((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | (~ndr1_0) | c2_1(a269) | c1_1(a269) | (~c3_1(a269)))) <=> ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[889])).
% 0.69/0.88 tff(891,plain,
% 0.69/0.88 (((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | (~ndr1_0) | c2_1(a269) | c1_1(a269) | (~c3_1(a269)))) <=> ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp8 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[890, 888])).
% 0.69/0.88 tff(892,plain,
% 0.69/0.88 ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | (~ndr1_0) | c2_1(a269) | c1_1(a269) | (~c3_1(a269)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(893,plain,
% 0.69/0.88 ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp8 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.69/0.88 tff(894,plain,
% 0.69/0.88 (hskp8 | c1_1(a269) | (~c3_1(a269))),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[893, 142, 30, 107])).
% 0.69/0.88 tff(895,plain,
% 0.69/0.88 (hskp8),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[894, 887, 714])).
% 0.69/0.88 tff(896,plain,
% 0.69/0.88 (~c3_1(a275)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[368, 895])).
% 0.69/0.88 tff(897,plain,
% 0.69/0.88 (~c2_1(a275)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[374, 895])).
% 0.69/0.88 tff(898,plain,
% 0.69/0.88 (~c0_1(a275)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[380, 895])).
% 0.69/0.88 tff(899,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a275) | c2_1(a275) | c3_1(a275) | (~ndr1_0) | c1_1(a275))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a275) | c2_1(a275) | c3_1(a275) | (~ndr1_0) | c1_1(a275))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(900,plain,
% 0.69/0.88 ((hskp2 | (~ndr1_0) | c2_1(a275) | c0_1(a275) | c3_1(a275) | c3_1(a275) | c1_1(a275) | c0_1(a275)) <=> (hskp2 | c0_1(a275) | c2_1(a275) | c3_1(a275) | (~ndr1_0) | c1_1(a275))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(901,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a275) | c0_1(a275) | c3_1(a275) | c3_1(a275) | c1_1(a275) | c0_1(a275))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a275) | c2_1(a275) | c3_1(a275) | (~ndr1_0) | c1_1(a275)))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[900])).
% 0.69/0.88 tff(902,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a275) | c0_1(a275) | c3_1(a275) | c3_1(a275) | c1_1(a275) | c0_1(a275))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a275) | c2_1(a275) | c3_1(a275) | (~ndr1_0) | c1_1(a275))),
% 0.69/0.88 inference(transitivity,[status(thm)],[901, 899])).
% 0.69/0.88 tff(903,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a275) | c0_1(a275) | c3_1(a275) | c3_1(a275) | c1_1(a275) | c0_1(a275))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(904,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a275) | c2_1(a275) | c3_1(a275) | (~ndr1_0) | c1_1(a275)),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[903, 902])).
% 0.69/0.88 tff(905,plain,
% 0.69/0.88 (c1_1(a275)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[904, 142, 878, 898, 897, 896, 10])).
% 0.69/0.88 tff(906,assumption,(c2_1(a272)), introduced(assumption)).
% 0.69/0.88 tff(907,plain,
% 0.69/0.88 ((~c3_1(a269)) | (~c2_1(a272))),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[737, 142, 750, 608, 713, 714, 30, 731])).
% 0.69/0.88 tff(908,plain,
% 0.69/0.88 (~c3_1(a269)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[907, 906])).
% 0.69/0.88 tff(909,plain,
% 0.69/0.88 ($false),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[745, 142, 607, 750, 608, 714, 30, 645, 906, 908])).
% 0.69/0.88 tff(910,plain,((~c2_1(a272)) | (~c0_1(a272)) | c0_1(a269) | c1_1(a272) | c1_1(a269) | c2_1(a269) | c3_1(a272)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.88 tff(911,plain,
% 0.69/0.88 (~c2_1(a272)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[910, 714, 750, 608, 607, 30, 713])).
% 0.69/0.88 tff(912,assumption,(~c2_1(a272)), introduced(assumption)).
% 0.69/0.88 tff(913,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a272) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c2_1(a272) | (~c0_1(a272)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a272) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c2_1(a272) | (~c0_1(a272)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(914,plain,
% 0.69/0.88 ((hskp18 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272))) <=> (hskp18 | c1_1(a272) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c2_1(a272) | (~c0_1(a272)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(915,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a272) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c2_1(a272) | (~c0_1(a272))))),
% 0.69/0.88 inference(monotonicity,[status(thm)],[914])).
% 0.69/0.88 tff(916,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a272) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c2_1(a272) | (~c0_1(a272)))),
% 0.69/0.88 inference(transitivity,[status(thm)],[915, 913])).
% 0.69/0.88 tff(917,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272)))),
% 0.69/0.88 inference(quant_inst,[status(thm)],[])).
% 0.69/0.88 tff(918,plain,
% 0.69/0.88 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a272) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c2_1(a272) | (~c0_1(a272))),
% 0.69/0.88 inference(modus_ponens,[status(thm)],[917, 916])).
% 0.69/0.88 tff(919,plain,
% 0.69/0.88 (hskp18),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[918, 142, 435, 427, 607, 608, 527, 912, 456])).
% 0.69/0.88 tff(920,plain,
% 0.69/0.88 (~c2_1(a298)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[542, 919])).
% 0.69/0.88 tff(921,plain,
% 0.69/0.88 (c3_1(a298)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[550, 919])).
% 0.69/0.88 tff(922,plain,
% 0.69/0.88 (c1_1(a298)),
% 0.69/0.88 inference(unit_resolution,[status(thm)],[558, 919])).
% 0.69/0.88 tff(923,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a298) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a298)) | (~c3_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a298) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(924,plain,
% 0.69/0.88 ((hskp23 | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c2_1(a298) | (~c3_1(a298)) | (~c1_1(a298))) <=> (hskp23 | c2_1(a298) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.69/0.88 inference(rewrite,[status(thm)],[])).
% 0.69/0.88 tff(925,plain,
% 0.69/0.88 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c2_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a298) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a298)) | (~c3_1(a298))))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[924])).
% 0.72/0.88 tff(926,plain,
% 0.72/0.88 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c2_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a298) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.72/0.88 inference(transitivity,[status(thm)],[925, 923])).
% 0.72/0.88 tff(927,plain,
% 0.72/0.88 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c2_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(928,plain,
% 0.72/0.88 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a298) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a298)) | (~c3_1(a298))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[927, 926])).
% 0.72/0.88 tff(929,plain,
% 0.72/0.88 ($false),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[928, 142, 31, 435, 427, 443, 922, 921, 920, 42])).
% 0.72/0.88 tff(930,plain,(hskp23 | (~c0_1(a272)) | c1_1(a272) | c2_1(a272) | (~c0_1(a274)) | (~c1_1(a274)) | c3_1(a274)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.88 tff(931,plain,
% 0.72/0.88 (hskp23),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[930, 911, 608, 607, 411, 410, 409])).
% 0.72/0.88 tff(932,plain,
% 0.72/0.88 (~c3_1(a313)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[16, 931])).
% 0.72/0.88 tff(933,plain,
% 0.72/0.88 (~c2_1(a313)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[22, 931])).
% 0.72/0.88 tff(934,plain,
% 0.72/0.88 (~c1_1(a313)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[28, 931])).
% 0.72/0.88 tff(935,plain,
% 0.72/0.88 (c0_1(a313)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[492, 142, 878, 934, 933, 932, 10])).
% 0.72/0.88 tff(936,plain,
% 0.72/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a275) | c3_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a275) | c3_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c0_1(a313)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(937,plain,
% 0.72/0.88 (((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313))) <=> (c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a275) | c3_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c0_1(a313)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(938,plain,
% 0.72/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a275) | c3_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c0_1(a313))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[937])).
% 0.72/0.89 tff(939,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a275) | c3_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c0_1(a313)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[938, 936])).
% 0.72/0.89 tff(940,plain,
% 0.72/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(941,plain,
% 0.72/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a275) | c3_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c0_1(a313))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.72/0.89 tff(942,plain,
% 0.72/0.89 ($false),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[941, 142, 934, 933, 932, 897, 896, 505, 935, 905])).
% 0.72/0.89 tff(943,plain,(c1_1(a269) | c2_1(a269) | c0_1(a269) | c1_1(a272) | (~c0_1(a272)) | (~c0_1(a274)) | (~c1_1(a274)) | c3_1(a274) | c3_1(a272)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.89 tff(944,plain,
% 0.72/0.89 (c1_1(a269)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[943, 750, 30, 608, 607, 411, 410, 409, 713])).
% 0.72/0.89 tff(945,plain,
% 0.72/0.89 (~c0_1(a280)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[812, 944, 750, 30])).
% 0.72/0.89 tff(946,plain,
% 0.72/0.89 (hskp9),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[758, 944, 750])).
% 0.72/0.89 tff(947,plain,
% 0.72/0.89 (~c1_1(a280)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[236, 946])).
% 0.72/0.89 tff(948,plain,
% 0.72/0.89 (c2_1(a280)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[269, 946])).
% 0.72/0.89 tff(949,plain,
% 0.72/0.89 (hskp4),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[819, 142, 948, 607, 947, 608, 713, 580, 945])).
% 0.72/0.89 tff(950,plain,
% 0.72/0.89 (~c3_1(a271)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[84, 949])).
% 0.72/0.89 tff(951,plain,
% 0.72/0.89 (~c1_1(a271)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[90, 949])).
% 0.72/0.89 tff(952,plain,
% 0.72/0.89 (~c0_1(a271)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[96, 949])).
% 0.72/0.89 tff(953,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a269) | c0_1(a271) | c1_1(a271) | c3_1(a271) | c2_1(a269) | (~ndr1_0) | c3_1(a269))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a269) | c0_1(a271) | c1_1(a271) | c3_1(a271) | c2_1(a269) | (~ndr1_0) | c3_1(a269))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(954,plain,
% 0.72/0.89 ((hskp2 | (~ndr1_0) | c2_1(a269) | c0_1(a269) | c3_1(a269) | c3_1(a271) | c1_1(a271) | c0_1(a271)) <=> (hskp2 | c0_1(a269) | c0_1(a271) | c1_1(a271) | c3_1(a271) | c2_1(a269) | (~ndr1_0) | c3_1(a269))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(955,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a269) | c0_1(a269) | c3_1(a269) | c3_1(a271) | c1_1(a271) | c0_1(a271))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a269) | c0_1(a271) | c1_1(a271) | c3_1(a271) | c2_1(a269) | (~ndr1_0) | c3_1(a269)))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[954])).
% 0.72/0.89 tff(956,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a269) | c0_1(a269) | c3_1(a269) | c3_1(a271) | c1_1(a271) | c0_1(a271))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a269) | c0_1(a271) | c1_1(a271) | c3_1(a271) | c2_1(a269) | (~ndr1_0) | c3_1(a269))),
% 0.72/0.89 inference(transitivity,[status(thm)],[955, 953])).
% 0.72/0.89 tff(957,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a269) | c0_1(a269) | c3_1(a269) | c3_1(a271) | c1_1(a271) | c0_1(a271))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(958,plain,
% 0.72/0.89 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a269) | c0_1(a271) | c1_1(a271) | c3_1(a271) | c2_1(a269) | (~ndr1_0) | c3_1(a269)),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[957, 956])).
% 0.72/0.89 tff(959,plain,
% 0.72/0.89 (c3_1(a269)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[958, 142, 878, 750, 952, 951, 950, 30, 10])).
% 0.72/0.89 tff(960,plain,
% 0.72/0.89 (c3_1(a280)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[244, 946])).
% 0.72/0.89 tff(961,plain,
% 0.72/0.89 (hskp3),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[276, 142, 948, 960, 947, 262, 945])).
% 0.72/0.89 tff(962,plain,
% 0.72/0.89 (~c2_1(a270)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[282, 961])).
% 0.72/0.89 tff(963,plain,
% 0.72/0.89 (c0_1(a270)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[345, 961])).
% 0.72/0.89 tff(964,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a269) | c1_1(a280) | c2_1(a270) | (~c1_1(a269)) | (~ndr1_0) | (~c3_1(a269)) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a269) | c1_1(a280) | c2_1(a270) | (~c1_1(a269)) | (~ndr1_0) | (~c3_1(a269)) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a280) | (~c2_1(a280)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(965,plain,
% 0.72/0.89 (((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a269) | (~c3_1(a269)) | (~c1_1(a269)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280))) <=> (c0_1(a269) | c1_1(a280) | c2_1(a270) | (~c1_1(a269)) | (~ndr1_0) | (~c3_1(a269)) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a280) | (~c2_1(a280)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(966,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a269) | (~c3_1(a269)) | (~c1_1(a269)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a269) | c1_1(a280) | c2_1(a270) | (~c1_1(a269)) | (~ndr1_0) | (~c3_1(a269)) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a280) | (~c2_1(a280))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[965])).
% 0.72/0.89 tff(967,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a269) | (~c3_1(a269)) | (~c1_1(a269)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a269) | c1_1(a280) | c2_1(a270) | (~c1_1(a269)) | (~ndr1_0) | (~c3_1(a269)) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a280) | (~c2_1(a280)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[966, 964])).
% 0.72/0.89 tff(968,plain,
% 0.72/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a269) | (~c3_1(a269)) | (~c1_1(a269)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(969,plain,
% 0.72/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a269) | c1_1(a280) | c2_1(a270) | (~c1_1(a269)) | (~ndr1_0) | (~c3_1(a269)) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a280) | (~c2_1(a280))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[968, 967])).
% 0.72/0.89 tff(970,plain,
% 0.72/0.89 (~c1_1(a270)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[969, 142, 948, 963, 750, 947, 962, 944, 308, 959, 945])).
% 0.72/0.89 tff(971,plain,
% 0.72/0.89 (c3_1(a270)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[290, 961])).
% 0.72/0.89 tff(972,plain,
% 0.72/0.89 (hskp8 | c1_1(a270)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[297, 142, 971, 962, 107])).
% 0.72/0.89 tff(973,plain,
% 0.72/0.89 (hskp8),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[972, 970])).
% 0.72/0.89 tff(974,plain,
% 0.72/0.89 (~c3_1(a275)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[368, 973])).
% 0.72/0.89 tff(975,plain,
% 0.72/0.89 (~c2_1(a275)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[374, 973])).
% 0.72/0.89 tff(976,plain,
% 0.72/0.89 (~c0_1(a275)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[380, 973])).
% 0.72/0.89 tff(977,plain,
% 0.72/0.89 (c1_1(a275)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[904, 142, 878, 976, 975, 974, 10])).
% 0.72/0.89 tff(978,plain,
% 0.72/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(979,plain,
% 0.72/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[978])).
% 0.72/0.89 tff(980,plain,
% 0.72/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(981,plain,
% 0.72/0.89 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(982,plain,
% 0.72/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[981])).
% 0.72/0.89 tff(983,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 0.72/0.89 tff(984,plain,
% 0.72/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[983, 982])).
% 0.72/0.89 tff(985,plain,
% 0.72/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[984, 980])).
% 0.72/0.89 tff(986,plain,(
% 0.72/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[985])).
% 0.72/0.89 tff(987,plain,
% 0.72/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[986, 979])).
% 0.72/0.89 tff(988,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a275) | c3_1(a275) | c3_1(a274) | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c3_1(a270)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c1_1(a275)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a275) | c3_1(a275) | c3_1(a274) | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c3_1(a270)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c1_1(a275)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(989,plain,
% 0.72/0.89 (((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c0_1(a274)) | c1_1(a270) | (~c3_1(a270)) | (~c0_1(a270)) | c0_1(a275) | c3_1(a275) | (~c1_1(a275))) <=> (c0_1(a275) | c3_1(a275) | c3_1(a274) | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c3_1(a270)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c1_1(a275)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(990,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c0_1(a274)) | c1_1(a270) | (~c3_1(a270)) | (~c0_1(a270)) | c0_1(a275) | c3_1(a275) | (~c1_1(a275)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a275) | c3_1(a275) | c3_1(a274) | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c3_1(a270)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c1_1(a275))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[989])).
% 0.72/0.89 tff(991,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c0_1(a274)) | c1_1(a270) | (~c3_1(a270)) | (~c0_1(a270)) | c0_1(a275) | c3_1(a275) | (~c1_1(a275)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a275) | c3_1(a275) | c3_1(a274) | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c3_1(a270)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c1_1(a275)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[990, 988])).
% 0.72/0.89 tff(992,plain,
% 0.72/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c0_1(a274)) | c1_1(a270) | (~c3_1(a270)) | (~c0_1(a270)) | c0_1(a275) | c3_1(a275) | (~c1_1(a275)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(993,plain,
% 0.72/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a275) | c3_1(a275) | c3_1(a274) | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c3_1(a270)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c1_1(a275))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[992, 991])).
% 0.72/0.89 tff(994,plain,
% 0.72/0.89 ($false),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[993, 142, 411, 410, 963, 971, 976, 974, 409, 987, 970, 977])).
% 0.72/0.89 tff(995,plain,(c0_1(a269) | (~c0_1(a274)) | (~c1_1(a274)) | c3_1(a274) | c2_1(a269) | (~c0_1(a272)) | c1_1(a272) | c3_1(a272)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.89 tff(996,plain,
% 0.72/0.89 (c0_1(a269)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[995, 867, 869, 868, 30, 602, 594, 588])).
% 0.72/0.89 tff(997,assumption,(c0_1(a269)), introduced(assumption)).
% 0.72/0.89 tff(998,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a274) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a274) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(999,plain,
% 0.72/0.89 (((~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | c3_1(a274) | c3_1(a274) | c2_1(a274) | (~c0_1(a274)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269))) <=> (c3_1(a274) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1000,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | c3_1(a274) | c3_1(a274) | c2_1(a274) | (~c0_1(a274)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a274) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[999])).
% 0.72/0.89 tff(1001,plain,
% 0.72/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | c3_1(a274) | c3_1(a274) | c2_1(a274) | (~c0_1(a274)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a274) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[1000, 998])).
% 0.72/0.89 tff(1002,plain,
% 0.72/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | c3_1(a274) | c3_1(a274) | c2_1(a274) | (~c0_1(a274)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(1003,plain,
% 0.72/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a274) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 0.72/0.89 tff(1004,plain,
% 0.72/0.89 ($false),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1003, 142, 411, 410, 997, 409, 714, 30, 505, 495])).
% 0.72/0.89 tff(1005,plain,(c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274)) | (~c0_1(a269)) | c3_1(a274) | c1_1(a269) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.89 tff(1006,plain,
% 0.72/0.89 (c2_1(a274)),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[1005, 714, 869, 996, 868, 867, 30])).
% 0.72/0.89 tff(1007,plain,
% 0.72/0.89 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(1008,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[1007])).
% 0.72/0.89 tff(1009,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1010,plain,
% 0.72/0.89 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp6) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.72/0.89 inference(bind,[status(th)],[])).
% 0.72/0.89 tff(1011,plain,
% 0.72/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(quant_intro,[status(thm)],[1010])).
% 0.72/0.89 tff(1012,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 0.72/0.89 tff(1013,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 0.72/0.89 tff(1014,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1013, 1009])).
% 0.72/0.89 tff(1015,plain,(
% 0.72/0.89 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(skolemize,[status(sab)],[1014])).
% 0.72/0.89 tff(1016,plain,
% 0.72/0.89 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[1015, 1008])).
% 0.72/0.89 tff(1017,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1018,plain,
% 0.72/0.89 ((hskp18 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269))) <=> (hskp18 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.89 inference(rewrite,[status(thm)],[])).
% 0.72/0.89 tff(1019,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274))))),
% 0.72/0.89 inference(monotonicity,[status(thm)],[1018])).
% 0.72/0.89 tff(1020,plain,
% 0.72/0.89 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[1019, 1017])).
% 0.72/0.90 tff(1021,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(1022,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 0.72/0.90 tff(1023,plain,
% 0.72/0.90 (hskp18 | (~c2_1(a274))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1022, 142, 867, 869, 996, 714, 30, 527])).
% 0.72/0.90 tff(1024,plain,
% 0.72/0.90 (hskp18),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1023, 1006])).
% 0.72/0.90 tff(1025,plain,
% 0.72/0.90 (~c2_1(a298)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[542, 1024])).
% 0.72/0.90 tff(1026,plain,
% 0.72/0.90 (c3_1(a298)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[550, 1024])).
% 0.72/0.90 tff(1027,plain,
% 0.72/0.90 (c1_1(a298)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[558, 1024])).
% 0.72/0.90 tff(1028,assumption,(c2_1(a274)), introduced(assumption)).
% 0.72/0.90 tff(1029,plain,
% 0.72/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(1030,plain,
% 0.72/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[1029])).
% 0.72/0.90 tff(1031,plain,
% 0.72/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1032,plain,
% 0.72/0.90 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_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)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(1033,plain,
% 0.72/0.90 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[1032])).
% 0.72/0.90 tff(1034,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 0.72/0.90 tff(1035,plain,
% 0.72/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 0.72/0.90 tff(1036,plain,
% 0.72/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1035, 1031])).
% 0.72/0.90 tff(1037,plain,(
% 0.72/0.90 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.72/0.90 inference(skolemize,[status(sab)],[1036])).
% 0.72/0.90 tff(1038,plain,
% 0.72/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1037, 1030])).
% 0.72/0.90 tff(1039,assumption,(hskp6), introduced(assumption)).
% 0.72/0.90 tff(1040,plain,
% 0.72/0.90 (((~hskp6) | (~c0_1(a273))) <=> ((~hskp6) | (~c0_1(a273)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1041,plain,
% 0.72/0.90 (((~c0_1(a273)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a273)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1042,axiom,((~c0_1(a273)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.72/0.90 tff(1043,plain,
% 0.72/0.90 ((~hskp6) | (~c0_1(a273))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 0.72/0.90 tff(1044,plain,
% 0.72/0.90 ((~hskp6) | (~c0_1(a273))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1043, 1040])).
% 0.72/0.90 tff(1045,plain,
% 0.72/0.90 (~c0_1(a273)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1044, 1039])).
% 0.72/0.90 tff(1046,plain,
% 0.72/0.90 (((~hskp6) | c2_1(a273)) <=> ((~hskp6) | c2_1(a273))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1047,axiom,((~hskp6) | c2_1(a273)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.72/0.90 tff(1048,plain,
% 0.72/0.90 ((~hskp6) | c2_1(a273)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 0.72/0.90 tff(1049,plain,
% 0.72/0.90 ((~hskp6) | c2_1(a273)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1048, 1046])).
% 0.72/0.90 tff(1050,plain,
% 0.72/0.90 ((~hskp6) | c2_1(a273)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1049, 1046])).
% 0.72/0.90 tff(1051,plain,
% 0.72/0.90 ((~hskp6) | c2_1(a273)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1050, 1046])).
% 0.72/0.90 tff(1052,plain,
% 0.72/0.90 ((~hskp6) | c2_1(a273)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1051, 1046])).
% 0.72/0.90 tff(1053,plain,
% 0.72/0.90 (c2_1(a273)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1052, 1039])).
% 0.72/0.90 tff(1054,plain,
% 0.72/0.90 (((~hskp6) | c1_1(a273)) <=> ((~hskp6) | c1_1(a273))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1055,axiom,((~hskp6) | c1_1(a273)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.72/0.90 tff(1056,plain,
% 0.72/0.90 ((~hskp6) | c1_1(a273)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1055, 1054])).
% 0.72/0.90 tff(1057,plain,
% 0.72/0.90 ((~hskp6) | c1_1(a273)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1056, 1054])).
% 0.72/0.90 tff(1058,plain,
% 0.72/0.90 ((~hskp6) | c1_1(a273)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1057, 1054])).
% 0.72/0.90 tff(1059,plain,
% 0.72/0.90 ((~hskp6) | c1_1(a273)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1058, 1054])).
% 0.72/0.90 tff(1060,plain,
% 0.72/0.90 ((~hskp6) | c1_1(a273)),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1059, 1054])).
% 0.72/0.90 tff(1061,plain,
% 0.72/0.90 (c1_1(a273)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1060, 1039])).
% 0.72/0.90 tff(1062,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a274) | c0_1(a273) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a274) | c0_1(a273) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1063,plain,
% 0.72/0.90 (((~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a272) | c1_1(a272) | (~c0_1(a272)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273))) <=> (c3_1(a274) | c0_1(a273) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1064,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a272) | c1_1(a272) | (~c0_1(a272)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a274) | c0_1(a273) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[1063])).
% 0.72/0.90 tff(1065,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a272) | c1_1(a272) | (~c0_1(a272)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a274) | c0_1(a273) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[1064, 1062])).
% 0.72/0.90 tff(1066,plain,
% 0.72/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a272) | c1_1(a272) | (~c0_1(a272)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(1067,plain,
% 0.72/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a274) | c0_1(a273) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.72/0.90 tff(1068,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1067, 142, 411, 1061, 1053, 607, 409, 1045, 608, 713, 1038, 1028])).
% 0.72/0.90 tff(1069,plain,((~hskp6) | (~c0_1(a274)) | (~c0_1(a272)) | c3_1(a274) | c1_1(a272) | c3_1(a272) | (~c2_1(a274))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(1070,plain,
% 0.72/0.90 (~hskp6),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1069, 1006, 602, 868, 594, 588, 867])).
% 0.72/0.90 tff(1071,assumption,(~c0_1(a298)), introduced(assumption)).
% 0.72/0.90 tff(1072,plain,
% 0.72/0.90 (hskp9 | c0_1(a298)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[667, 142, 621, 619, 216])).
% 0.72/0.90 tff(1073,plain,
% 0.72/0.90 (hskp9),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1072, 1071])).
% 0.72/0.90 tff(1074,plain,
% 0.72/0.90 (~c1_1(a280)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[236, 1073])).
% 0.72/0.90 tff(1075,plain,
% 0.72/0.90 (c3_1(a280)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[244, 1073])).
% 0.72/0.90 tff(1076,plain,
% 0.72/0.90 (~c0_1(a280)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[676, 142, 43, 621, 620, 1075, 1074, 206, 1071])).
% 0.72/0.90 tff(1077,assumption,(~hskp6), introduced(assumption)).
% 0.72/0.90 tff(1078,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a280) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | c0_1(a280) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a280) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | c0_1(a280) | (~c3_1(a280)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1079,plain,
% 0.72/0.90 ((hskp6 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a280) | c0_1(a280) | (~c3_1(a280))) <=> (hskp6 | c1_1(a280) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | c0_1(a280) | (~c3_1(a280)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1080,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a280) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | c0_1(a280) | (~c3_1(a280))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[1079])).
% 0.72/0.90 tff(1081,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a280) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | c0_1(a280) | (~c3_1(a280)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[1080, 1078])).
% 0.72/0.90 tff(1082,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(1083,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a280) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | c0_1(a280) | (~c3_1(a280))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 0.72/0.90 tff(1084,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1083, 142, 1077, 1075, 411, 410, 1074, 1016, 1076, 1028])).
% 0.72/0.90 tff(1085,plain,(c0_1(a298) | hskp6 | (~c0_1(a274)) | (~c1_1(a274)) | (~c2_1(a274)) | hskp16 | (~c1_1(a298)) | (~c3_1(a298)) | c2_1(a298)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(1086,plain,
% 0.72/0.90 (c0_1(a298)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1085, 1070, 867, 869, 1006, 43, 1027, 1026, 1025])).
% 0.72/0.90 tff(1087,plain,
% 0.72/0.90 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(1088,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[1087])).
% 0.72/0.90 tff(1089,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1090,plain,
% 0.72/0.90 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp0))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.72/0.90 inference(bind,[status(th)],[])).
% 0.72/0.90 tff(1091,plain,
% 0.72/0.90 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.90 inference(quant_intro,[status(thm)],[1090])).
% 0.72/0.90 tff(1092,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.72/0.90 tff(1093,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 0.72/0.90 tff(1094,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1093, 1089])).
% 0.72/0.90 tff(1095,plain,(
% 0.72/0.90 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.90 inference(skolemize,[status(sab)],[1094])).
% 0.72/0.90 tff(1096,plain,
% 0.72/0.90 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1095, 1088])).
% 0.72/0.90 tff(1097,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1098,plain,
% 0.72/0.90 ((hskp0 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274))) <=> (hskp0 | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1099,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[1098])).
% 0.72/0.90 tff(1100,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[1099, 1097])).
% 0.72/0.90 tff(1101,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(1102,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp0 | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 0.72/0.90 tff(1103,plain,
% 0.72/0.90 (hskp0 | (~c2_1(a274))),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1102, 142, 867, 869, 868, 1096])).
% 0.72/0.90 tff(1104,plain,
% 0.72/0.90 (hskp0),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1103, 1006])).
% 0.72/0.90 tff(1105,plain,
% 0.72/0.90 (((~hskp0) | (~c3_1(a267))) <=> ((~hskp0) | (~c3_1(a267)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1106,plain,
% 0.72/0.90 (((~c3_1(a267)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a267)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1107,axiom,((~c3_1(a267)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 0.72/0.90 tff(1108,plain,
% 0.72/0.90 ((~hskp0) | (~c3_1(a267))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 0.72/0.90 tff(1109,plain,
% 0.72/0.90 ((~hskp0) | (~c3_1(a267))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1108, 1105])).
% 0.72/0.90 tff(1110,plain,
% 0.72/0.90 (~c3_1(a267)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1109, 1104])).
% 0.72/0.90 tff(1111,plain,
% 0.72/0.90 (((~hskp0) | (~c2_1(a267))) <=> ((~hskp0) | (~c2_1(a267)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1112,plain,
% 0.72/0.90 (((~c2_1(a267)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a267)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1113,axiom,((~c2_1(a267)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.72/0.90 tff(1114,plain,
% 0.72/0.90 ((~hskp0) | (~c2_1(a267))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 0.72/0.90 tff(1115,plain,
% 0.72/0.90 ((~hskp0) | (~c2_1(a267))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1114, 1111])).
% 0.72/0.90 tff(1116,plain,
% 0.72/0.90 (~c2_1(a267)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1115, 1104])).
% 0.72/0.90 tff(1117,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1118,plain,
% 0.72/0.90 ((hskp18 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269))) <=> (hskp18 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1119,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[1118])).
% 0.72/0.90 tff(1120,plain,
% 0.72/0.90 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[1119, 1117])).
% 0.72/0.90 tff(1121,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269)))),
% 0.72/0.90 inference(quant_inst,[status(thm)],[])).
% 0.72/0.90 tff(1122,plain,
% 0.72/0.90 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278))),
% 0.72/0.90 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 0.72/0.90 tff(1123,plain,
% 0.72/0.90 (hskp18),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1122, 142, 435, 427, 997, 714, 30, 527, 456])).
% 0.72/0.90 tff(1124,plain,
% 0.72/0.90 (~c2_1(a298)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[542, 1123])).
% 0.72/0.90 tff(1125,plain,
% 0.72/0.90 (c3_1(a298)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[550, 1123])).
% 0.72/0.90 tff(1126,plain,
% 0.72/0.90 (c1_1(a298)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[558, 1123])).
% 0.72/0.90 tff(1127,plain,
% 0.72/0.90 ($false),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[928, 142, 31, 435, 427, 443, 1126, 1125, 1124, 42])).
% 0.72/0.90 tff(1128,plain,(hskp23 | (~c0_1(a269)) | c1_1(a269) | c2_1(a269) | (~c0_1(a274)) | (~c1_1(a274)) | c3_1(a274)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.90 tff(1129,plain,
% 0.72/0.90 (hskp23),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[1128, 714, 996, 30, 867, 869, 868])).
% 0.72/0.90 tff(1130,plain,
% 0.72/0.90 (~c3_1(a313)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[16, 1129])).
% 0.72/0.90 tff(1131,plain,
% 0.72/0.90 (~c2_1(a313)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[22, 1129])).
% 0.72/0.90 tff(1132,plain,
% 0.72/0.90 (~c1_1(a313)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[28, 1129])).
% 0.72/0.90 tff(1133,assumption,(c0_1(a298)), introduced(assumption)).
% 0.72/0.90 tff(1134,assumption,(hskp14), introduced(assumption)).
% 0.72/0.90 tff(1135,plain,
% 0.72/0.90 (~c2_1(a287)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[182, 1134])).
% 0.72/0.90 tff(1136,plain,
% 0.72/0.90 (~c0_1(a287)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[188, 1134])).
% 0.72/0.90 tff(1137,plain,
% 0.72/0.90 (c1_1(a287)),
% 0.72/0.90 inference(unit_resolution,[status(thm)],[223, 1134])).
% 0.72/0.90 tff(1138,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)) | (~c1_1(a298)) | (~c0_1(a298)) | (~c3_1(a298)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)) | (~c1_1(a298)) | (~c0_1(a298)) | (~c3_1(a298)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1139,plain,
% 0.72/0.90 (((~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a298)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287))) <=> (c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)) | (~c1_1(a298)) | (~c0_1(a298)) | (~c3_1(a298)))),
% 0.72/0.90 inference(rewrite,[status(thm)],[])).
% 0.72/0.90 tff(1140,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a298)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)) | (~c1_1(a298)) | (~c0_1(a298)) | (~c3_1(a298))))),
% 0.72/0.90 inference(monotonicity,[status(thm)],[1139])).
% 0.72/0.90 tff(1141,plain,
% 0.72/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a298)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)) | (~c1_1(a298)) | (~c0_1(a298)) | (~c3_1(a298)))),
% 0.72/0.90 inference(transitivity,[status(thm)],[1140, 1138])).
% 0.72/0.90 tff(1142,plain,
% 0.72/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a298)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1143,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)) | (~c1_1(a298)) | (~c0_1(a298)) | (~c3_1(a298))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 0.72/0.91 tff(1144,plain,
% 0.72/0.91 (~c3_1(a287)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1143, 142, 621, 620, 1137, 1136, 1135, 712, 1133])).
% 0.72/0.91 tff(1145,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | c3_1(a287) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | c3_1(a287) | (~c0_1(a313)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1146,plain,
% 0.72/0.91 (((~ndr1_0) | c2_1(a287) | (~c1_1(a287)) | c3_1(a287) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313))) <=> (c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | c3_1(a287) | (~c0_1(a313)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1147,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a287) | (~c1_1(a287)) | c3_1(a287) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | c3_1(a287) | (~c0_1(a313))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1146])).
% 0.72/0.91 tff(1148,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a287) | (~c1_1(a287)) | c3_1(a287) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | c3_1(a287) | (~c0_1(a313)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1147, 1145])).
% 0.72/0.91 tff(1149,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a287) | (~c1_1(a287)) | c3_1(a287) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1150,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | c3_1(a287) | (~c0_1(a313))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1149, 1148])).
% 0.72/0.91 tff(1151,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1150, 142, 1137, 508, 507, 506, 1135, 505, 494, 1144])).
% 0.72/0.91 tff(1152,plain,((~hskp14) | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~c0_1(a313)) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a298))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(1153,plain,
% 0.72/0.91 (~hskp14),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1152, 1133, 507, 506, 494, 621, 620, 508])).
% 0.72/0.91 tff(1154,plain,
% 0.72/0.91 ((hskp30 | hskp17 | hskp14) <=> (hskp30 | hskp17 | hskp14)),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1155,plain,
% 0.72/0.91 (((hskp30 | hskp14) | hskp17) <=> (hskp30 | hskp17 | hskp14)),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1156,plain,
% 0.72/0.91 ((hskp30 | hskp14) <=> (hskp30 | hskp14)),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1157,plain,
% 0.72/0.91 (((hskp30 | hskp14) | hskp17) <=> ((hskp30 | hskp14) | hskp17)),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1156])).
% 0.72/0.91 tff(1158,plain,
% 0.72/0.91 (((hskp30 | hskp14) | hskp17) <=> (hskp30 | hskp17 | hskp14)),
% 0.72/0.91 inference(transitivity,[status(thm)],[1157, 1155])).
% 0.72/0.91 tff(1159,axiom,((hskp30 | hskp14) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 0.72/0.91 tff(1160,plain,
% 0.72/0.91 (hskp30 | hskp17 | hskp14),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 0.72/0.91 tff(1161,plain,
% 0.72/0.91 (hskp30 | hskp17 | hskp14),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1160, 1154])).
% 0.72/0.91 tff(1162,plain,
% 0.72/0.91 (hskp30 | hskp17 | hskp14),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1161, 1154])).
% 0.72/0.91 tff(1163,plain,
% 0.72/0.91 (hskp30 | hskp17 | hskp14),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1162, 1154])).
% 0.72/0.91 tff(1164,plain,
% 0.72/0.91 (hskp30 | hskp17 | hskp14),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1163, 1154])).
% 0.72/0.91 tff(1165,plain,
% 0.72/0.91 (hskp17),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1164, 1153, 581])).
% 0.72/0.91 tff(1166,plain,
% 0.72/0.91 (((~hskp17) | (~c1_1(a295))) <=> ((~hskp17) | (~c1_1(a295)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1167,plain,
% 0.72/0.91 (((~c1_1(a295)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a295)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1168,axiom,((~c1_1(a295)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.72/0.91 tff(1169,plain,
% 0.72/0.91 ((~hskp17) | (~c1_1(a295))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1168, 1167])).
% 0.72/0.91 tff(1170,plain,
% 0.72/0.91 ((~hskp17) | (~c1_1(a295))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1169, 1166])).
% 0.72/0.91 tff(1171,plain,
% 0.72/0.91 (~c1_1(a295)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1170, 1165])).
% 0.72/0.91 tff(1172,plain,
% 0.72/0.91 (((~hskp17) | c3_1(a295)) <=> ((~hskp17) | c3_1(a295))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1173,axiom,((~hskp17) | c3_1(a295)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.72/0.91 tff(1174,plain,
% 0.72/0.91 ((~hskp17) | c3_1(a295)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 0.72/0.91 tff(1175,plain,
% 0.72/0.91 ((~hskp17) | c3_1(a295)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1174, 1172])).
% 0.72/0.91 tff(1176,plain,
% 0.72/0.91 ((~hskp17) | c3_1(a295)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1175, 1172])).
% 0.72/0.91 tff(1177,plain,
% 0.72/0.91 ((~hskp17) | c3_1(a295)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1176, 1172])).
% 0.72/0.91 tff(1178,plain,
% 0.72/0.91 ((~hskp17) | c3_1(a295)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1177, 1172])).
% 0.72/0.91 tff(1179,plain,
% 0.72/0.91 (c3_1(a295)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1178, 1165])).
% 0.72/0.91 tff(1180,plain,
% 0.72/0.91 (((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | c1_1(a295) | (~ndr1_0) | c2_1(a295) | (~c3_1(a295)))) <=> ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp8 | c1_1(a295) | (~ndr1_0) | c2_1(a295) | (~c3_1(a295)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1181,plain,
% 0.72/0.91 ((hskp8 | (~ndr1_0) | c2_1(a295) | c1_1(a295) | (~c3_1(a295))) <=> (hskp8 | c1_1(a295) | (~ndr1_0) | c2_1(a295) | (~c3_1(a295)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1182,plain,
% 0.72/0.91 (((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | (~ndr1_0) | c2_1(a295) | c1_1(a295) | (~c3_1(a295)))) <=> ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | c1_1(a295) | (~ndr1_0) | c2_1(a295) | (~c3_1(a295))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1181])).
% 0.72/0.91 tff(1183,plain,
% 0.72/0.91 (((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | (~ndr1_0) | c2_1(a295) | c1_1(a295) | (~c3_1(a295)))) <=> ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp8 | c1_1(a295) | (~ndr1_0) | c2_1(a295) | (~c3_1(a295)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1182, 1180])).
% 0.72/0.91 tff(1184,plain,
% 0.72/0.91 ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp8 | (~ndr1_0) | c2_1(a295) | c1_1(a295) | (~c3_1(a295)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1185,plain,
% 0.72/0.91 ((~![U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp8 | c1_1(a295) | (~ndr1_0) | c2_1(a295) | (~c3_1(a295))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 0.72/0.91 tff(1186,plain,
% 0.72/0.91 (c2_1(a295)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1185, 142, 32, 1179, 1171, 107])).
% 0.72/0.91 tff(1187,plain,
% 0.72/0.91 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(1188,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[1187])).
% 0.72/0.91 tff(1189,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1190,plain,
% 0.72/0.91 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.72/0.91 inference(bind,[status(th)],[])).
% 0.72/0.91 tff(1191,plain,
% 0.72/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.72/0.91 inference(quant_intro,[status(thm)],[1190])).
% 0.72/0.91 tff(1192,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c1_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.72/0.91 tff(1193,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 0.72/0.91 tff(1194,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1193, 1189])).
% 0.72/0.91 tff(1195,plain,(
% 0.72/0.91 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.72/0.91 inference(skolemize,[status(sab)],[1194])).
% 0.72/0.91 tff(1196,plain,
% 0.72/0.91 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1195, 1188])).
% 0.72/0.91 tff(1197,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c2_1(a298) | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c3_1(a295)) | (~c1_1(a298)) | (~c0_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a298) | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c3_1(a295)) | (~c1_1(a298)) | (~c0_1(a298)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1198,plain,
% 0.72/0.91 ((hskp8 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c0_1(a298)) | c1_1(a295) | (~c2_1(a295)) | (~c3_1(a295))) <=> (hskp8 | c2_1(a298) | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c3_1(a295)) | (~c1_1(a298)) | (~c0_1(a298)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1199,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c0_1(a298)) | c1_1(a295) | (~c2_1(a295)) | (~c3_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c2_1(a298) | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c3_1(a295)) | (~c1_1(a298)) | (~c0_1(a298))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1198])).
% 0.72/0.91 tff(1200,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c0_1(a298)) | c1_1(a295) | (~c2_1(a295)) | (~c3_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a298) | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c3_1(a295)) | (~c1_1(a298)) | (~c0_1(a298)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1199, 1197])).
% 0.72/0.91 tff(1201,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c0_1(a298)) | c1_1(a295) | (~c2_1(a295)) | (~c3_1(a295)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1202,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a298) | c1_1(a295) | (~ndr1_0) | (~c2_1(a295)) | (~c3_1(a295)) | (~c1_1(a298)) | (~c0_1(a298))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 0.72/0.91 tff(1203,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1202, 142, 32, 621, 1179, 619, 1171, 1196, 1133, 1186])).
% 0.72/0.91 tff(1204,plain,((~c0_1(a298)) | hskp8 | (~c1_1(a298)) | c2_1(a298) | hskp30 | c2_1(a313) | c3_1(a313) | (~c0_1(a313)) | (~c3_1(a298)) | c1_1(a313)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(1205,plain,
% 0.72/0.91 (~c0_1(a313)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1204, 32, 621, 619, 581, 507, 506, 620, 1133, 508])).
% 0.72/0.91 tff(1206,assumption,(hskp17), introduced(assumption)).
% 0.72/0.91 tff(1207,plain,
% 0.72/0.91 (~c1_1(a295)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1170, 1206])).
% 0.72/0.91 tff(1208,plain,
% 0.72/0.91 (c3_1(a295)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1178, 1206])).
% 0.72/0.91 tff(1209,plain,
% 0.72/0.91 (c2_1(a295)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1185, 142, 32, 1208, 1207, 107])).
% 0.72/0.91 tff(1210,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1202, 142, 32, 621, 1208, 619, 1207, 1196, 1133, 1209])).
% 0.72/0.91 tff(1211,plain,((~hskp17) | hskp8 | (~c1_1(a298)) | c2_1(a298) | (~c0_1(a298))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(1212,plain,
% 0.72/0.91 (~hskp17),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1211, 1133, 621, 619, 32])).
% 0.72/0.91 tff(1213,plain,
% 0.72/0.91 (hskp14),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1164, 1212, 581])).
% 0.72/0.91 tff(1214,plain,
% 0.72/0.91 (~c2_1(a287)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[182, 1213])).
% 0.72/0.91 tff(1215,plain,
% 0.72/0.91 (~c0_1(a287)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[188, 1213])).
% 0.72/0.91 tff(1216,plain,
% 0.72/0.91 (c1_1(a287)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[223, 1213])).
% 0.72/0.91 tff(1217,plain,
% 0.72/0.91 (~c3_1(a287)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1143, 142, 621, 620, 1216, 1215, 1214, 712, 1133])).
% 0.72/0.91 tff(1218,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a287) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | c2_1(a272) | (~c0_1(a272)) | (~c1_1(a287)) | c3_1(a287))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a287) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | c2_1(a272) | (~c0_1(a272)) | (~c1_1(a287)) | c3_1(a287))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1219,plain,
% 0.72/0.91 (((~ndr1_0) | c2_1(a287) | (~c1_1(a287)) | c3_1(a287) | c3_1(a272) | c2_1(a272) | (~c0_1(a272)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269))) <=> (c2_1(a287) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | c2_1(a272) | (~c0_1(a272)) | (~c1_1(a287)) | c3_1(a287))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1220,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a287) | (~c1_1(a287)) | c3_1(a287) | c3_1(a272) | c2_1(a272) | (~c0_1(a272)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a287) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | c2_1(a272) | (~c0_1(a272)) | (~c1_1(a287)) | c3_1(a287)))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1219])).
% 0.72/0.91 tff(1221,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a287) | (~c1_1(a287)) | c3_1(a287) | c3_1(a272) | c2_1(a272) | (~c0_1(a272)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a287) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | c2_1(a272) | (~c0_1(a272)) | (~c1_1(a287)) | c3_1(a287))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1220, 1218])).
% 0.72/0.91 tff(1222,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a287) | (~c1_1(a287)) | c3_1(a287) | c3_1(a272) | c2_1(a272) | (~c0_1(a272)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1223,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a287) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | c2_1(a272) | (~c0_1(a272)) | (~c1_1(a287)) | c3_1(a287)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 0.72/0.91 tff(1224,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1223, 142, 1216, 607, 997, 1214, 713, 714, 30, 505, 912, 1217])).
% 0.72/0.91 tff(1225,plain,((~c0_1(a298)) | (~c0_1(a272)) | (~c0_1(a269)) | c3_1(a272) | c1_1(a269) | c2_1(a269) | c2_1(a272) | (~c1_1(a298)) | (~c3_1(a298)) | hskp30 | c2_1(a298) | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(1226,plain,
% 0.72/0.91 (c2_1(a272)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1225, 32, 997, 713, 714, 30, 607, 621, 620, 581, 619, 1133])).
% 0.72/0.91 tff(1227,plain,
% 0.72/0.91 ((~c2_1(a272)) | c0_1(a313)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[651, 142, 607, 508, 507, 506, 608, 645])).
% 0.72/0.91 tff(1228,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1227, 1226, 1205])).
% 0.72/0.91 tff(1229,plain,(hskp8 | (~c0_1(a272)) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a272) | (~c0_1(a269)) | c3_1(a272) | c1_1(a269) | c2_1(a269) | (~c1_1(a298)) | (~c3_1(a298)) | hskp30 | c2_1(a298) | (~c0_1(a298))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(1230,plain,
% 0.72/0.91 (hskp8),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1229, 1132, 602, 1131, 1130, 594, 996, 588, 714, 30, 1027, 1026, 581, 1025, 1086])).
% 0.72/0.91 tff(1231,plain,
% 0.72/0.91 (~c3_1(a275)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[368, 1230])).
% 0.72/0.91 tff(1232,plain,
% 0.72/0.91 (~c2_1(a275)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[374, 1230])).
% 0.72/0.91 tff(1233,plain,
% 0.72/0.91 (((~hskp0) | c0_1(a267)) <=> ((~hskp0) | c0_1(a267))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1234,axiom,((~hskp0) | c0_1(a267)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.72/0.91 tff(1235,plain,
% 0.72/0.91 ((~hskp0) | c0_1(a267)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 0.72/0.91 tff(1236,plain,
% 0.72/0.91 ((~hskp0) | c0_1(a267)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1235, 1233])).
% 0.72/0.91 tff(1237,plain,
% 0.72/0.91 ((~hskp0) | c0_1(a267)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1236, 1233])).
% 0.72/0.91 tff(1238,plain,
% 0.72/0.91 ((~hskp0) | c0_1(a267)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1237, 1233])).
% 0.72/0.91 tff(1239,plain,
% 0.72/0.91 ((~hskp0) | c0_1(a267)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1238, 1233])).
% 0.72/0.91 tff(1240,plain,
% 0.72/0.91 (c0_1(a267)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1239, 1104])).
% 0.72/0.91 tff(1241,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a275) | c3_1(a275) | c1_1(a269) | c2_1(a269) | c2_1(a267) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c0_1(a269)) | (~c1_1(a275)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a275) | c3_1(a275) | c1_1(a269) | c2_1(a269) | c2_1(a267) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c0_1(a269)) | (~c1_1(a275)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1242,plain,
% 0.72/0.91 (((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a267) | c2_1(a267) | (~c0_1(a267)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269))) <=> (c2_1(a275) | c3_1(a275) | c1_1(a269) | c2_1(a269) | c2_1(a267) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c0_1(a269)) | (~c1_1(a275)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1243,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a267) | c2_1(a267) | (~c0_1(a267)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a275) | c3_1(a275) | c1_1(a269) | c2_1(a269) | c2_1(a267) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c0_1(a269)) | (~c1_1(a275))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1242])).
% 0.72/0.91 tff(1244,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a267) | c2_1(a267) | (~c0_1(a267)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a275) | c3_1(a275) | c1_1(a269) | c2_1(a269) | c2_1(a267) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c0_1(a269)) | (~c1_1(a275)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1243, 1241])).
% 0.72/0.91 tff(1245,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a267) | c2_1(a267) | (~c0_1(a267)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1246,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a275) | c3_1(a275) | c1_1(a269) | c2_1(a269) | c2_1(a267) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c0_1(a269)) | (~c1_1(a275))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 0.72/0.91 tff(1247,plain,
% 0.72/0.91 (~c1_1(a275)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1246, 142, 996, 1240, 1232, 1231, 714, 30, 1116, 1110, 505])).
% 0.72/0.91 tff(1248,plain,
% 0.72/0.91 (~c0_1(a275)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[380, 1230])).
% 0.72/0.91 tff(1249,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c0_1(a275) | c2_1(a275) | c1_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | c1_1(a275))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c0_1(a275) | c2_1(a275) | c1_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | c1_1(a275))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1250,plain,
% 0.72/0.91 (((~ndr1_0) | c1_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a275) | c1_1(a275) | c0_1(a275)) <=> (c1_1(a313) | c2_1(a313) | c3_1(a313) | c0_1(a275) | c2_1(a275) | c1_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | c1_1(a275))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1251,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a275) | c1_1(a275) | c0_1(a275))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c0_1(a275) | c2_1(a275) | c1_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | c1_1(a275)))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1250])).
% 0.72/0.91 tff(1252,plain,
% 0.72/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a275) | c1_1(a275) | c0_1(a275))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c0_1(a275) | c2_1(a275) | c1_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | c1_1(a275))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1251, 1249])).
% 0.72/0.91 tff(1253,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a275) | c1_1(a275) | c0_1(a275))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1254,plain,
% 0.72/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c0_1(a275) | c2_1(a275) | c1_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | c1_1(a275)),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 0.72/0.91 tff(1255,plain,
% 0.72/0.91 (~c2_1(a272)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1254, 142, 602, 1132, 1131, 1130, 1248, 1232, 594, 645, 1247])).
% 0.72/0.91 tff(1256,plain,
% 0.72/0.91 ($false),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1223, 142, 1137, 607, 997, 1135, 713, 714, 30, 505, 912, 1144])).
% 0.72/0.91 tff(1257,plain,((~hskp14) | (~c0_1(a272)) | (~c0_1(a269)) | c3_1(a272) | c1_1(a269) | c2_1(a269) | c2_1(a272) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a298))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.91 tff(1258,plain,
% 0.72/0.91 (~hskp14),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1257, 714, 996, 588, 602, 30, 1255, 1027, 1026, 1086])).
% 0.72/0.91 tff(1259,plain,
% 0.72/0.91 (hskp17),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1164, 1258, 581])).
% 0.72/0.91 tff(1260,plain,
% 0.72/0.91 (~c1_1(a295)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1170, 1259])).
% 0.72/0.91 tff(1261,plain,
% 0.72/0.91 (((~hskp17) | (~c0_1(a295))) <=> ((~hskp17) | (~c0_1(a295)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1262,plain,
% 0.72/0.91 (((~c0_1(a295)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a295)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1263,axiom,((~c0_1(a295)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.72/0.91 tff(1264,plain,
% 0.72/0.91 ((~hskp17) | (~c0_1(a295))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 0.72/0.91 tff(1265,plain,
% 0.72/0.91 ((~hskp17) | (~c0_1(a295))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1264, 1261])).
% 0.72/0.91 tff(1266,plain,
% 0.72/0.91 (~c0_1(a295)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1265, 1259])).
% 0.72/0.91 tff(1267,plain,
% 0.72/0.91 (c3_1(a295)),
% 0.72/0.91 inference(unit_resolution,[status(thm)],[1178, 1259])).
% 0.72/0.91 tff(1268,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a295) | c1_1(a295) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c3_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a295) | c1_1(a295) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c3_1(a295)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1269,plain,
% 0.72/0.91 ((hskp6 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a295) | c0_1(a295) | (~c3_1(a295))) <=> (hskp6 | c0_1(a295) | c1_1(a295) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c3_1(a295)))),
% 0.72/0.91 inference(rewrite,[status(thm)],[])).
% 0.72/0.91 tff(1270,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a295) | c0_1(a295) | (~c3_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a295) | c1_1(a295) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c3_1(a295))))),
% 0.72/0.91 inference(monotonicity,[status(thm)],[1269])).
% 0.72/0.91 tff(1271,plain,
% 0.72/0.91 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a295) | c0_1(a295) | (~c3_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a295) | c1_1(a295) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c3_1(a295)))),
% 0.72/0.91 inference(transitivity,[status(thm)],[1270, 1268])).
% 0.72/0.91 tff(1272,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a295) | c0_1(a295) | (~c3_1(a295)))),
% 0.72/0.91 inference(quant_inst,[status(thm)],[])).
% 0.72/0.91 tff(1273,plain,
% 0.72/0.91 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a295) | c1_1(a295) | (~ndr1_0) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c3_1(a295))),
% 0.72/0.91 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 0.72/0.92 tff(1274,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1273, 142, 1070, 1267, 867, 869, 1266, 1260, 1016, 1006])).
% 0.72/0.92 tff(1275,plain,(c1_1(a269) | hskp30 | c2_1(a269) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(1276,plain,
% 0.72/0.92 (c1_1(a269)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1275, 30, 581, 43])).
% 0.72/0.92 tff(1277,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c1_1(a295) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a295)) | (~c3_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a295) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a295)) | (~c3_1(a295)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1278,plain,
% 0.72/0.92 ((hskp8 | (~ndr1_0) | c2_1(a269) | (~c1_1(a269)) | (~c0_1(a269)) | c1_1(a295) | (~c2_1(a295)) | (~c3_1(a295))) <=> (hskp8 | c1_1(a295) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a295)) | (~c3_1(a295)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1279,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a269) | (~c1_1(a269)) | (~c0_1(a269)) | c1_1(a295) | (~c2_1(a295)) | (~c3_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c1_1(a295) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a295)) | (~c3_1(a295))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1278])).
% 0.72/0.92 tff(1280,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a269) | (~c1_1(a269)) | (~c0_1(a269)) | c1_1(a295) | (~c2_1(a295)) | (~c3_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a295) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a295)) | (~c3_1(a295)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1279, 1277])).
% 0.72/0.92 tff(1281,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a269) | (~c1_1(a269)) | (~c0_1(a269)) | c1_1(a295) | (~c2_1(a295)) | (~c3_1(a295)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1282,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a295) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a295)) | (~c3_1(a295))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.72/0.92 tff(1283,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1282, 142, 32, 1208, 997, 1207, 749, 30, 1196, 1209])).
% 0.72/0.92 tff(1284,plain,((~hskp17) | hskp8 | (~c0_1(a269)) | (~c1_1(a269)) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(1285,plain,
% 0.72/0.92 (~hskp17),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1284, 32, 997, 749, 30])).
% 0.72/0.92 tff(1286,plain,
% 0.72/0.92 (hskp14),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1164, 1285, 581])).
% 0.72/0.92 tff(1287,plain,
% 0.72/0.92 (~c2_1(a287)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[182, 1286])).
% 0.72/0.92 tff(1288,plain,
% 0.72/0.92 (~c0_1(a287)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[188, 1286])).
% 0.72/0.92 tff(1289,plain,
% 0.72/0.92 (c1_1(a287)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[223, 1286])).
% 0.72/0.92 tff(1290,plain,
% 0.72/0.92 (hskp9),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[230, 142, 1289, 1288, 1287, 216])).
% 0.72/0.92 tff(1291,plain,
% 0.72/0.92 (~c1_1(a280)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[236, 1290])).
% 0.72/0.92 tff(1292,plain,
% 0.72/0.92 (c3_1(a280)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[244, 1290])).
% 0.72/0.92 tff(1293,plain,
% 0.72/0.92 (c2_1(a280)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[269, 1290])).
% 0.72/0.92 tff(1294,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c1_1(a280) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a280)) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a280) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1295,plain,
% 0.72/0.92 ((hskp8 | (~ndr1_0) | c2_1(a269) | (~c1_1(a269)) | (~c0_1(a269)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280))) <=> (hskp8 | c1_1(a280) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1296,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a269) | (~c1_1(a269)) | (~c0_1(a269)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c1_1(a280) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a280)) | (~c3_1(a280))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1295])).
% 0.72/0.92 tff(1297,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a269) | (~c1_1(a269)) | (~c0_1(a269)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a280) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1296, 1294])).
% 0.72/0.92 tff(1298,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a269) | (~c1_1(a269)) | (~c0_1(a269)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1299,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a280) | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c2_1(a280)) | (~c3_1(a280))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 0.72/0.92 tff(1300,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1299, 142, 32, 1293, 1292, 997, 1291, 749, 30, 1196])).
% 0.72/0.92 tff(1301,plain,(hskp8 | (~c0_1(a269)) | (~c1_1(a269)) | c2_1(a269) | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(1302,plain,
% 0.72/0.92 (hskp8),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1301, 996, 1276, 30, 581])).
% 0.72/0.92 tff(1303,plain,
% 0.72/0.92 (~c3_1(a275)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[368, 1302])).
% 0.72/0.92 tff(1304,plain,
% 0.72/0.92 (~c2_1(a275)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[374, 1302])).
% 0.72/0.92 tff(1305,plain,
% 0.72/0.92 (~c0_1(a275)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[380, 1302])).
% 0.72/0.92 tff(1306,plain,
% 0.72/0.92 (~hskp2),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[834, 1276])).
% 0.72/0.92 tff(1307,plain,
% 0.72/0.92 (c1_1(a275)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[904, 142, 1306, 1305, 1304, 1303, 10])).
% 0.72/0.92 tff(1308,plain,
% 0.72/0.92 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c1_1(a275)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c1_1(a275)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1309,plain,
% 0.72/0.92 ((hskp9 | (~ndr1_0) | c2_1(a275) | c0_1(a275) | (~c1_1(a275))) <=> (hskp9 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c1_1(a275)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1310,plain,
% 0.72/0.92 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a275) | c0_1(a275) | (~c1_1(a275)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c1_1(a275))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1309])).
% 0.72/0.92 tff(1311,plain,
% 0.72/0.92 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a275) | c0_1(a275) | (~c1_1(a275)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c1_1(a275)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1310, 1308])).
% 0.72/0.92 tff(1312,plain,
% 0.72/0.92 ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a275) | c0_1(a275) | (~c1_1(a275)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1313,plain,
% 0.72/0.92 ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c1_1(a275))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1312, 1311])).
% 0.72/0.92 tff(1314,plain,
% 0.72/0.92 (hskp9 | (~c1_1(a275))),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1313, 142, 1305, 1304, 216])).
% 0.72/0.92 tff(1315,plain,
% 0.72/0.92 (hskp9),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1314, 1307])).
% 0.72/0.92 tff(1316,plain,
% 0.72/0.92 (~c1_1(a280)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[236, 1315])).
% 0.72/0.92 tff(1317,plain,
% 0.72/0.92 (c3_1(a280)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[244, 1315])).
% 0.72/0.92 tff(1318,plain,
% 0.72/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a280) | c0_1(a275) | c3_1(a275) | c3_1(a274) | (~ndr1_0) | (~c0_1(a274)) | (~c1_1(a274)) | (~c1_1(a275)) | (~c3_1(a280)) | (~c0_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a280) | c0_1(a275) | c3_1(a275) | c3_1(a274) | (~ndr1_0) | (~c0_1(a274)) | (~c1_1(a274)) | (~c1_1(a275)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1319,plain,
% 0.72/0.92 (((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c0_1(a274)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a275) | c3_1(a275) | (~c1_1(a275))) <=> (c1_1(a280) | c0_1(a275) | c3_1(a275) | c3_1(a274) | (~ndr1_0) | (~c0_1(a274)) | (~c1_1(a274)) | (~c1_1(a275)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1320,plain,
% 0.72/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c0_1(a274)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a275) | c3_1(a275) | (~c1_1(a275)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a280) | c0_1(a275) | c3_1(a275) | c3_1(a274) | (~ndr1_0) | (~c0_1(a274)) | (~c1_1(a274)) | (~c1_1(a275)) | (~c3_1(a280)) | (~c0_1(a280))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1319])).
% 0.72/0.92 tff(1321,plain,
% 0.72/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c0_1(a274)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a275) | c3_1(a275) | (~c1_1(a275)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a280) | c0_1(a275) | c3_1(a275) | c3_1(a274) | (~ndr1_0) | (~c0_1(a274)) | (~c1_1(a274)) | (~c1_1(a275)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1320, 1318])).
% 0.72/0.92 tff(1322,plain,
% 0.72/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c0_1(a274)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a275) | c3_1(a275) | (~c1_1(a275)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1323,plain,
% 0.72/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a280) | c0_1(a275) | c3_1(a275) | c3_1(a274) | (~ndr1_0) | (~c0_1(a274)) | (~c1_1(a274)) | (~c1_1(a275)) | (~c3_1(a280)) | (~c0_1(a280))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1322, 1321])).
% 0.72/0.92 tff(1324,plain,
% 0.72/0.92 (~c0_1(a280)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1323, 142, 1317, 867, 869, 1316, 1305, 1303, 868, 987, 1307])).
% 0.72/0.92 tff(1325,plain,
% 0.72/0.92 (c2_1(a280)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[269, 1315])).
% 0.72/0.92 tff(1326,plain,
% 0.72/0.92 (hskp4),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[819, 142, 1325, 602, 1316, 594, 588, 580, 1324])).
% 0.72/0.92 tff(1327,plain,
% 0.72/0.92 (~c3_1(a271)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[84, 1326])).
% 0.72/0.92 tff(1328,plain,
% 0.72/0.92 (~c1_1(a271)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[90, 1326])).
% 0.72/0.92 tff(1329,plain,
% 0.72/0.92 (~c0_1(a271)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[96, 1326])).
% 0.72/0.92 tff(1330,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[387, 142, 1306, 1305, 1304, 1303, 1329, 1328, 1327, 10])).
% 0.72/0.92 tff(1331,plain,(c2_1(a269) | hskp30 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(1332,plain,
% 0.72/0.92 (c2_1(a269)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1331, 581, 43])).
% 0.72/0.92 tff(1333,plain,
% 0.72/0.92 (((~hskp2) | (~c2_1(a269))) <=> ((~hskp2) | (~c2_1(a269)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1334,plain,
% 0.72/0.92 (((~c2_1(a269)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a269)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1335,axiom,((~c2_1(a269)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.72/0.92 tff(1336,plain,
% 0.72/0.92 ((~hskp2) | (~c2_1(a269))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 0.72/0.92 tff(1337,plain,
% 0.72/0.92 ((~hskp2) | (~c2_1(a269))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1336, 1333])).
% 0.72/0.92 tff(1338,plain,
% 0.72/0.92 (~hskp2),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1337, 1332])).
% 0.72/0.92 tff(1339,plain,
% 0.72/0.92 (~hskp4),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[389, 1338, 43])).
% 0.72/0.92 tff(1340,plain,
% 0.72/0.92 (hskp23),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[482, 32, 1339, 697, 699, 698])).
% 0.72/0.92 tff(1341,plain,
% 0.72/0.92 (~c3_1(a313)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[16, 1340])).
% 0.72/0.92 tff(1342,plain,
% 0.72/0.92 (~c2_1(a313)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[22, 1340])).
% 0.72/0.92 tff(1343,plain,
% 0.72/0.92 (~c1_1(a313)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[28, 1340])).
% 0.72/0.92 tff(1344,plain,
% 0.72/0.92 (c0_1(a313)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[492, 142, 1338, 1343, 1342, 1341, 10])).
% 0.72/0.92 tff(1345,plain,
% 0.72/0.92 (c2_1(a274)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[516, 1344, 1343, 1342, 1341, 698, 699])).
% 0.72/0.92 tff(1346,plain,
% 0.72/0.92 (~hskp6),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1069, 1345, 602, 698, 594, 588, 697])).
% 0.72/0.92 tff(1347,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1348,plain,
% 0.72/0.92 ((hskp18 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272))) <=> (hskp18 | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1349,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1348])).
% 0.72/0.92 tff(1350,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1349, 1347])).
% 0.72/0.92 tff(1351,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c1_1(a274)) | (~c2_1(a274)) | (~c0_1(a274)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1352,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp18 | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c1_1(a274))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 0.72/0.92 tff(1353,plain,
% 0.72/0.92 (hskp18 | c2_1(a272) | (~c2_1(a274))),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1352, 142, 411, 410, 607, 608, 527])).
% 0.72/0.92 tff(1354,plain,
% 0.72/0.92 (~c2_1(a274)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1353, 912, 55])).
% 0.72/0.92 tff(1355,plain,
% 0.72/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a274) | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a274) | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1356,plain,
% 0.72/0.92 (((~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | c3_1(a274) | c3_1(a274) | c2_1(a274) | (~c0_1(a274)) | c2_1(a272) | c1_1(a272) | (~c0_1(a272))) <=> (c3_1(a274) | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1357,plain,
% 0.72/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | c3_1(a274) | c3_1(a274) | c2_1(a274) | (~c0_1(a274)) | c2_1(a272) | c1_1(a272) | (~c0_1(a272)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a274) | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1356])).
% 0.72/0.92 tff(1358,plain,
% 0.72/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | c3_1(a274) | c3_1(a274) | c2_1(a274) | (~c0_1(a274)) | c2_1(a272) | c1_1(a272) | (~c0_1(a272)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a274) | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1357, 1355])).
% 0.72/0.92 tff(1359,plain,
% 0.72/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a274) | (~c1_1(a274)) | c3_1(a274) | c3_1(a274) | c2_1(a274) | (~c0_1(a274)) | c2_1(a272) | c1_1(a272) | (~c0_1(a272)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1360,plain,
% 0.72/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a274) | c1_1(a272) | (~ndr1_0) | c2_1(a272) | (~c0_1(a272)) | c2_1(a274) | (~c0_1(a274)) | (~c1_1(a274))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 0.72/0.92 tff(1361,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1360, 142, 411, 410, 607, 409, 608, 505, 912, 1354])).
% 0.72/0.92 tff(1362,plain,(c2_1(a272) | (~c0_1(a274)) | (~c1_1(a274)) | (~c0_1(a272)) | c3_1(a274) | c1_1(a272) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(1363,plain,
% 0.72/0.92 (c2_1(a272)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1362, 55, 410, 607, 409, 608, 411])).
% 0.72/0.92 tff(1364,plain,
% 0.72/0.92 (~c0_1(a313)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[516, 507, 495, 508, 506, 409, 410])).
% 0.72/0.92 tff(1365,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[651, 142, 607, 508, 507, 506, 608, 645, 906, 1364])).
% 0.72/0.92 tff(1366,plain,(c2_1(a313) | (~c0_1(a272)) | c1_1(a313) | c3_1(a313) | c1_1(a272) | (~c2_1(a272)) | c2_1(a274) | c3_1(a274) | (~c1_1(a274))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(1367,plain,
% 0.72/0.92 (c2_1(a274)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1366, 507, 410, 1363, 608, 506, 508, 409, 607])).
% 0.72/0.92 tff(1368,plain,
% 0.72/0.92 (c2_1(a313) | (~c2_1(a274)) | (~c0_1(a313))),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[533, 142, 55, 411, 410, 508, 527])).
% 0.72/0.92 tff(1369,plain,
% 0.72/0.92 (~c0_1(a313)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1368, 1367, 507])).
% 0.72/0.92 tff(1370,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[651, 142, 607, 508, 507, 506, 608, 645, 1363, 1369])).
% 0.72/0.92 tff(1371,plain,(c2_1(a313) | (~c0_1(a272)) | c1_1(a313) | c3_1(a313) | c1_1(a272) | hskp18 | (~c0_1(a274)) | (~c1_1(a274)) | c3_1(a274)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(1372,plain,
% 0.72/0.92 (hskp18),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1371, 1342, 602, 1341, 594, 1343, 697, 699, 698])).
% 0.72/0.92 tff(1373,plain,
% 0.72/0.92 (c3_1(a298)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[550, 1372])).
% 0.72/0.92 tff(1374,plain,
% 0.72/0.92 (c1_1(a298)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[558, 1372])).
% 0.72/0.92 tff(1375,plain,
% 0.72/0.92 (~c2_1(a298)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[542, 1372])).
% 0.72/0.92 tff(1376,plain,
% 0.72/0.92 (~c0_1(a298)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1204, 1344, 1374, 1375, 581, 1342, 1341, 1343, 1373, 32])).
% 0.72/0.92 tff(1377,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1085, 1376, 1345, 697, 699, 1375, 43, 1374, 1373, 1346])).
% 0.72/0.92 tff(1378,plain,(hskp8 | hskp16 | hskp30), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(1379,plain,
% 0.72/0.92 (hskp8),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1378, 581, 43])).
% 0.72/0.92 tff(1380,plain,
% 0.72/0.92 (~c3_1(a275)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[368, 1379])).
% 0.72/0.92 tff(1381,plain,
% 0.72/0.92 (~c2_1(a275)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[374, 1379])).
% 0.72/0.92 tff(1382,plain,
% 0.72/0.92 (~c0_1(a275)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[380, 1379])).
% 0.72/0.92 tff(1383,plain,
% 0.72/0.92 (c1_1(a275)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[904, 142, 1338, 1382, 1381, 1380, 10])).
% 0.72/0.92 tff(1384,plain,
% 0.72/0.92 (hskp9 | (~c1_1(a275))),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1313, 142, 1382, 1381, 216])).
% 0.72/0.92 tff(1385,plain,
% 0.72/0.92 (hskp9),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1384, 1383])).
% 0.72/0.92 tff(1386,plain,
% 0.72/0.92 (~c1_1(a280)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[236, 1385])).
% 0.72/0.92 tff(1387,plain,
% 0.72/0.92 (c2_1(a280)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[269, 1385])).
% 0.72/0.92 tff(1388,plain,
% 0.72/0.92 (c0_1(a280)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[819, 142, 1339, 1387, 602, 1386, 594, 588, 580])).
% 0.72/0.92 tff(1389,plain,
% 0.72/0.92 (c3_1(a280)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[244, 1385])).
% 0.72/0.92 tff(1390,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1391,plain,
% 0.72/0.92 ((hskp27 | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a275) | c2_1(a275) | (~c1_1(a275))) <=> (hskp27 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1392,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a275) | c2_1(a275) | (~c1_1(a275)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1391])).
% 0.72/0.92 tff(1393,plain,
% 0.72/0.92 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a275) | c2_1(a275) | (~c1_1(a275)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.72/0.92 inference(transitivity,[status(thm)],[1392, 1390])).
% 0.72/0.92 tff(1394,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a275) | c2_1(a275) | (~c1_1(a275)))),
% 0.72/0.92 inference(quant_inst,[status(thm)],[])).
% 0.72/0.92 tff(1395,plain,
% 0.72/0.92 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280))),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1394, 1393])).
% 0.72/0.92 tff(1396,plain,
% 0.72/0.92 (hskp27),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1395, 142, 1387, 1389, 1382, 1381, 772, 1388, 1383])).
% 0.72/0.92 tff(1397,plain,
% 0.72/0.92 (c3_1(a276)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[787, 1396])).
% 0.72/0.92 tff(1398,plain,
% 0.72/0.92 (c2_1(a276)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[795, 1396])).
% 0.72/0.92 tff(1399,plain,
% 0.72/0.92 (c1_1(a276)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[803, 1396])).
% 0.72/0.92 tff(1400,plain,
% 0.72/0.92 ($false),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[810, 142, 1399, 1398, 1397, 1387, 1389, 1386, 53, 1388])).
% 0.72/0.92 tff(1401,plain,(hskp30 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.72/0.92 tff(1402,plain,
% 0.72/0.92 (hskp30),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1401, 43])).
% 0.72/0.92 tff(1403,plain,
% 0.72/0.92 (((~hskp30) | c3_1(a337)) <=> ((~hskp30) | c3_1(a337))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1404,axiom,((~hskp30) | c3_1(a337)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.72/0.92 tff(1405,plain,
% 0.72/0.92 ((~hskp30) | c3_1(a337)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 0.72/0.92 tff(1406,plain,
% 0.72/0.92 ((~hskp30) | c3_1(a337)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1405, 1403])).
% 0.72/0.92 tff(1407,plain,
% 0.72/0.92 ((~hskp30) | c3_1(a337)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1406, 1403])).
% 0.72/0.92 tff(1408,plain,
% 0.72/0.92 ((~hskp30) | c3_1(a337)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1407, 1403])).
% 0.72/0.92 tff(1409,plain,
% 0.72/0.92 ((~hskp30) | c3_1(a337)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1408, 1403])).
% 0.72/0.92 tff(1410,plain,
% 0.72/0.92 (c3_1(a337)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1409, 1402])).
% 0.72/0.92 tff(1411,plain,
% 0.72/0.92 (((~hskp30) | c2_1(a337)) <=> ((~hskp30) | c2_1(a337))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1412,axiom,((~hskp30) | c2_1(a337)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.72/0.92 tff(1413,plain,
% 0.72/0.92 ((~hskp30) | c2_1(a337)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1412, 1411])).
% 0.72/0.92 tff(1414,plain,
% 0.72/0.92 ((~hskp30) | c2_1(a337)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1413, 1411])).
% 0.72/0.92 tff(1415,plain,
% 0.72/0.92 ((~hskp30) | c2_1(a337)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1414, 1411])).
% 0.72/0.92 tff(1416,plain,
% 0.72/0.92 ((~hskp30) | c2_1(a337)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1415, 1411])).
% 0.72/0.92 tff(1417,plain,
% 0.72/0.92 ((~hskp30) | c2_1(a337)),
% 0.72/0.92 inference(modus_ponens,[status(thm)],[1416, 1411])).
% 0.72/0.92 tff(1418,plain,
% 0.72/0.92 (c2_1(a337)),
% 0.72/0.92 inference(unit_resolution,[status(thm)],[1417, 1402])).
% 0.72/0.92 tff(1419,plain,
% 0.72/0.92 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c2_1(a337)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c2_1(a337)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1420,plain,
% 0.72/0.92 ((hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a337)) | (~c2_1(a337)) | (~c3_1(a337))) <=> (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c2_1(a337)))),
% 0.72/0.92 inference(rewrite,[status(thm)],[])).
% 0.72/0.92 tff(1421,plain,
% 0.72/0.92 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a337)) | (~c2_1(a337)) | (~c3_1(a337)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c2_1(a337))))),
% 0.72/0.92 inference(monotonicity,[status(thm)],[1420])).
% 0.72/0.92 tff(1422,plain,
% 0.72/0.92 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a337)) | (~c2_1(a337)) | (~c3_1(a337)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c2_1(a337)))),
% 0.72/0.93 inference(transitivity,[status(thm)],[1421, 1419])).
% 0.72/0.93 tff(1423,plain,
% 0.72/0.93 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a337)) | (~c2_1(a337)) | (~c3_1(a337)))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(1424,plain,
% 0.72/0.93 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c2_1(a337))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 0.72/0.93 tff(1425,plain,
% 0.72/0.93 (hskp8 | hskp7 | (~c1_1(a337))),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1424, 142, 1418, 1410, 570])).
% 0.72/0.93 tff(1426,plain,
% 0.72/0.93 (~c1_1(a337)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1425, 560, 32])).
% 0.72/0.93 tff(1427,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c2_1(a298) | (~ndr1_0) | c1_1(a337) | (~c3_1(a337)) | (~c2_1(a337)) | (~c1_1(a298)) | (~c0_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a298) | (~ndr1_0) | c1_1(a337) | (~c3_1(a337)) | (~c2_1(a337)) | (~c1_1(a298)) | (~c0_1(a298)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1428,plain,
% 0.72/0.93 ((hskp8 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c0_1(a298)) | c1_1(a337) | (~c2_1(a337)) | (~c3_1(a337))) <=> (hskp8 | c2_1(a298) | (~ndr1_0) | c1_1(a337) | (~c3_1(a337)) | (~c2_1(a337)) | (~c1_1(a298)) | (~c0_1(a298)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1429,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c0_1(a298)) | c1_1(a337) | (~c2_1(a337)) | (~c3_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c2_1(a298) | (~ndr1_0) | c1_1(a337) | (~c3_1(a337)) | (~c2_1(a337)) | (~c1_1(a298)) | (~c0_1(a298))))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[1428])).
% 0.72/0.93 tff(1430,plain,
% 0.72/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c0_1(a298)) | c1_1(a337) | (~c2_1(a337)) | (~c3_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a298) | (~ndr1_0) | c1_1(a337) | (~c3_1(a337)) | (~c2_1(a337)) | (~c1_1(a298)) | (~c0_1(a298)))),
% 0.72/0.93 inference(transitivity,[status(thm)],[1429, 1427])).
% 0.72/0.93 tff(1431,plain,
% 0.72/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c0_1(a298)) | c1_1(a337) | (~c2_1(a337)) | (~c3_1(a337)))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(1432,plain,
% 0.72/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a298) | (~ndr1_0) | c1_1(a337) | (~c3_1(a337)) | (~c2_1(a337)) | (~c1_1(a298)) | (~c0_1(a298))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 0.72/0.93 tff(1433,plain,
% 0.72/0.93 (~c0_1(a298)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1432, 142, 32, 1418, 1410, 621, 619, 1196, 1426])).
% 0.72/0.93 tff(1434,plain,
% 0.72/0.93 (hskp9),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1072, 1433])).
% 0.72/0.93 tff(1435,plain,
% 0.72/0.93 (~c1_1(a280)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[236, 1434])).
% 0.72/0.93 tff(1436,plain,
% 0.72/0.93 (c3_1(a280)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[244, 1434])).
% 0.72/0.93 tff(1437,plain,
% 0.72/0.93 (c0_1(a280)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[693, 142, 32, 560, 1436, 1435, 687])).
% 0.72/0.93 tff(1438,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[676, 142, 43, 621, 620, 1436, 1435, 206, 1437, 1433])).
% 0.72/0.93 tff(1439,plain,(hskp7 | hskp16 | (~c1_1(a298)) | (~c3_1(a298)) | hskp8 | c2_1(a298)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1440,plain,
% 0.72/0.93 (hskp7),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1439, 559, 43, 551, 32, 543])).
% 0.72/0.93 tff(1441,plain,
% 0.72/0.93 (~c3_1(a274)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[69, 1440])).
% 0.72/0.93 tff(1442,plain,
% 0.72/0.93 (c1_1(a274)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[77, 1440])).
% 0.72/0.93 tff(1443,plain,
% 0.72/0.93 (c0_1(a274)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[397, 1440])).
% 0.72/0.93 tff(1444,plain,
% 0.72/0.93 (hskp23),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[482, 1443, 32, 390, 1442, 1441])).
% 0.72/0.93 tff(1445,plain,
% 0.72/0.93 (~c2_1(a313)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[22, 1444])).
% 0.72/0.93 tff(1446,plain,
% 0.72/0.93 (~c1_1(a313)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[28, 1444])).
% 0.72/0.93 tff(1447,plain,
% 0.72/0.93 (~c3_1(a313)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[16, 1444])).
% 0.72/0.93 tff(1448,plain,
% 0.72/0.93 (c0_1(a313)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[492, 142, 54, 1446, 1445, 1447, 10])).
% 0.72/0.93 tff(1449,plain,
% 0.72/0.93 (c2_1(a274)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[516, 1448, 1446, 1445, 1447, 1441, 1442])).
% 0.72/0.93 tff(1450,plain,
% 0.72/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a313) | c3_1(a313) | c3_1(a274) | c0_1(a273) | (~ndr1_0) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a313) | c3_1(a313) | c3_1(a274) | c0_1(a273) | (~ndr1_0) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c0_1(a313)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1451,plain,
% 0.72/0.93 (((~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a313) | c1_1(a313) | (~c0_1(a313)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273))) <=> (c1_1(a313) | c3_1(a313) | c3_1(a274) | c0_1(a273) | (~ndr1_0) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c0_1(a313)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1452,plain,
% 0.72/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a313) | c1_1(a313) | (~c0_1(a313)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a313) | c3_1(a313) | c3_1(a274) | c0_1(a273) | (~ndr1_0) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c0_1(a313))))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[1451])).
% 0.72/0.93 tff(1453,plain,
% 0.72/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a313) | c1_1(a313) | (~c0_1(a313)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a313) | c3_1(a313) | c3_1(a274) | c0_1(a273) | (~ndr1_0) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c0_1(a313)))),
% 0.72/0.93 inference(transitivity,[status(thm)],[1452, 1450])).
% 0.72/0.93 tff(1454,plain,
% 0.72/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a313) | c1_1(a313) | (~c0_1(a313)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273)))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(1455,plain,
% 0.72/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a313) | c3_1(a313) | c3_1(a274) | c0_1(a273) | (~ndr1_0) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)) | (~c0_1(a313))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 0.72/0.93 tff(1456,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1455, 142, 411, 1061, 1053, 508, 506, 409, 1045, 1038, 1028, 494])).
% 0.72/0.93 tff(1457,plain,((~hskp6) | (~c0_1(a274)) | c1_1(a313) | c3_1(a313) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a313))), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1458,plain,
% 0.72/0.93 (~hskp6),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1457, 494, 508, 506, 409, 1028, 411])).
% 0.72/0.93 tff(1459,plain,
% 0.72/0.93 (c0_1(a298)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1085, 1458, 411, 410, 1028, 43, 621, 620, 619])).
% 0.72/0.93 tff(1460,plain,
% 0.72/0.93 (~hskp14),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1152, 1459, 507, 506, 494, 621, 620, 508])).
% 0.72/0.93 tff(1461,assumption,(hskp12), introduced(assumption)).
% 0.72/0.93 tff(1462,plain,
% 0.72/0.93 (((~hskp12) | (~c3_1(a284))) <=> ((~hskp12) | (~c3_1(a284)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1463,plain,
% 0.72/0.93 (((~c3_1(a284)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a284)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1464,axiom,((~c3_1(a284)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.72/0.93 tff(1465,plain,
% 0.72/0.93 ((~hskp12) | (~c3_1(a284))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 0.72/0.93 tff(1466,plain,
% 0.72/0.93 ((~hskp12) | (~c3_1(a284))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1465, 1462])).
% 0.72/0.93 tff(1467,plain,
% 0.72/0.93 (~c3_1(a284)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1466, 1461])).
% 0.72/0.93 tff(1468,plain,
% 0.72/0.93 (((~hskp12) | (~c0_1(a284))) <=> ((~hskp12) | (~c0_1(a284)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1469,plain,
% 0.72/0.93 (((~c0_1(a284)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a284)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1470,axiom,((~c0_1(a284)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.72/0.93 tff(1471,plain,
% 0.72/0.93 ((~hskp12) | (~c0_1(a284))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1470, 1469])).
% 0.72/0.93 tff(1472,plain,
% 0.72/0.93 ((~hskp12) | (~c0_1(a284))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1471, 1468])).
% 0.72/0.93 tff(1473,plain,
% 0.72/0.93 (~c0_1(a284)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1472, 1461])).
% 0.72/0.93 tff(1474,plain,
% 0.72/0.93 (((~hskp12) | c2_1(a284)) <=> ((~hskp12) | c2_1(a284))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1475,axiom,((~hskp12) | c2_1(a284)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.72/0.93 tff(1476,plain,
% 0.72/0.93 ((~hskp12) | c2_1(a284)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1475, 1474])).
% 0.72/0.93 tff(1477,plain,
% 0.72/0.93 ((~hskp12) | c2_1(a284)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1476, 1474])).
% 0.72/0.93 tff(1478,plain,
% 0.72/0.93 ((~hskp12) | c2_1(a284)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1477, 1474])).
% 0.72/0.93 tff(1479,plain,
% 0.72/0.93 ((~hskp12) | c2_1(a284)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1478, 1474])).
% 0.72/0.93 tff(1480,plain,
% 0.72/0.93 ((~hskp12) | c2_1(a284)),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1479, 1474])).
% 0.72/0.93 tff(1481,plain,
% 0.72/0.93 (c2_1(a284)),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1480, 1461])).
% 0.72/0.93 tff(1482,assumption,(~hskp14), introduced(assumption)).
% 0.72/0.93 tff(1483,plain,
% 0.72/0.93 (((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | c0_1(a284) | c3_1(a284) | (~ndr1_0) | (~c2_1(a284)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | c0_1(a284) | c3_1(a284) | (~ndr1_0) | (~c2_1(a284)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1484,plain,
% 0.72/0.93 ((hskp14 | (~ndr1_0) | c0_1(a284) | c3_1(a284) | (~c2_1(a284))) <=> (hskp14 | c0_1(a284) | c3_1(a284) | (~ndr1_0) | (~c2_1(a284)))),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1485,plain,
% 0.72/0.93 (((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | (~ndr1_0) | c0_1(a284) | c3_1(a284) | (~c2_1(a284)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | c0_1(a284) | c3_1(a284) | (~ndr1_0) | (~c2_1(a284))))),
% 0.72/0.93 inference(monotonicity,[status(thm)],[1484])).
% 0.72/0.93 tff(1486,plain,
% 0.72/0.93 (((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | (~ndr1_0) | c0_1(a284) | c3_1(a284) | (~c2_1(a284)))) <=> ((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | c0_1(a284) | c3_1(a284) | (~ndr1_0) | (~c2_1(a284)))),
% 0.72/0.93 inference(transitivity,[status(thm)],[1485, 1483])).
% 0.72/0.93 tff(1487,plain,
% 0.72/0.93 ((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp14 | (~ndr1_0) | c0_1(a284) | c3_1(a284) | (~c2_1(a284)))),
% 0.72/0.93 inference(quant_inst,[status(thm)],[])).
% 0.72/0.93 tff(1488,plain,
% 0.72/0.93 ((~![U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp14 | c0_1(a284) | c3_1(a284) | (~ndr1_0) | (~c2_1(a284))),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1487, 1486])).
% 0.72/0.93 tff(1489,plain,
% 0.72/0.93 ($false),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1488, 142, 1482, 1481, 1473, 1467, 169])).
% 0.72/0.93 tff(1490,plain,((~hskp12) | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.72/0.93 tff(1491,plain,
% 0.72/0.93 (~hskp12),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1490, 1460])).
% 0.72/0.93 tff(1492,plain,
% 0.72/0.93 ((hskp25 | hskp14 | hskp12) <=> (hskp25 | hskp14 | hskp12)),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1493,plain,
% 0.72/0.93 (((hskp14 | hskp25) | hskp12) <=> (hskp25 | hskp14 | hskp12)),
% 0.72/0.93 inference(rewrite,[status(thm)],[])).
% 0.72/0.93 tff(1494,axiom,((hskp14 | hskp25) | hskp12), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.72/0.93 tff(1495,plain,
% 0.72/0.93 (hskp25 | hskp14 | hskp12),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 0.72/0.93 tff(1496,plain,
% 0.72/0.93 (hskp25 | hskp14 | hskp12),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1495, 1492])).
% 0.72/0.93 tff(1497,plain,
% 0.72/0.93 (hskp25 | hskp14 | hskp12),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1496, 1492])).
% 0.72/0.93 tff(1498,plain,
% 0.72/0.93 (hskp25 | hskp14 | hskp12),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1497, 1492])).
% 0.72/0.93 tff(1499,plain,
% 0.72/0.93 (hskp25 | hskp14 | hskp12),
% 0.72/0.93 inference(modus_ponens,[status(thm)],[1498, 1492])).
% 0.72/0.93 tff(1500,plain,
% 0.72/0.93 (hskp25),
% 0.72/0.93 inference(unit_resolution,[status(thm)],[1499, 1491, 1460])).
% 0.72/0.93 tff(1501,plain,
% 0.72/0.93 (((~hskp25) | (~c3_1(a352))) <=> ((~hskp25) | (~c3_1(a352)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1502,plain,
% 0.77/0.93 (((~c3_1(a352)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a352)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1503,axiom,((~c3_1(a352)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.77/0.93 tff(1504,plain,
% 0.77/0.93 ((~hskp25) | (~c3_1(a352))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1503, 1502])).
% 0.77/0.93 tff(1505,plain,
% 0.77/0.93 ((~hskp25) | (~c3_1(a352))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1504, 1501])).
% 0.77/0.93 tff(1506,plain,
% 0.77/0.93 (~c3_1(a352)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1505, 1500])).
% 0.77/0.93 tff(1507,plain,
% 0.77/0.93 (((~hskp25) | (~c2_1(a352))) <=> ((~hskp25) | (~c2_1(a352)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1508,plain,
% 0.77/0.93 (((~c2_1(a352)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a352)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1509,axiom,((~c2_1(a352)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 0.77/0.93 tff(1510,plain,
% 0.77/0.93 ((~hskp25) | (~c2_1(a352))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 0.77/0.93 tff(1511,plain,
% 0.77/0.93 ((~hskp25) | (~c2_1(a352))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1510, 1507])).
% 0.77/0.93 tff(1512,plain,
% 0.77/0.93 (~c2_1(a352)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1511, 1500])).
% 0.77/0.93 tff(1513,plain,
% 0.77/0.93 (((~hskp25) | c1_1(a352)) <=> ((~hskp25) | c1_1(a352))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1514,axiom,((~hskp25) | c1_1(a352)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.77/0.93 tff(1515,plain,
% 0.77/0.93 ((~hskp25) | c1_1(a352)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1514, 1513])).
% 0.77/0.93 tff(1516,plain,
% 0.77/0.93 ((~hskp25) | c1_1(a352)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1515, 1513])).
% 0.77/0.93 tff(1517,plain,
% 0.77/0.93 ((~hskp25) | c1_1(a352)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1516, 1513])).
% 0.77/0.93 tff(1518,plain,
% 0.77/0.93 ((~hskp25) | c1_1(a352)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1517, 1513])).
% 0.77/0.93 tff(1519,plain,
% 0.77/0.93 ((~hskp25) | c1_1(a352)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1518, 1513])).
% 0.77/0.93 tff(1520,plain,
% 0.77/0.93 (c1_1(a352)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1519, 1500])).
% 0.77/0.93 tff(1521,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a352) | c3_1(a352) | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~ndr1_0) | (~c0_1(a313)) | (~c1_1(a352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a352) | c3_1(a352) | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~ndr1_0) | (~c0_1(a313)) | (~c1_1(a352)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1522,plain,
% 0.77/0.93 (((~ndr1_0) | c2_1(a352) | (~c1_1(a352)) | c3_1(a352) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313))) <=> (c2_1(a352) | c3_1(a352) | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~ndr1_0) | (~c0_1(a313)) | (~c1_1(a352)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1523,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a352) | (~c1_1(a352)) | c3_1(a352) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a352) | c3_1(a352) | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~ndr1_0) | (~c0_1(a313)) | (~c1_1(a352))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[1522])).
% 0.77/0.93 tff(1524,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a352) | (~c1_1(a352)) | c3_1(a352) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a352) | c3_1(a352) | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~ndr1_0) | (~c0_1(a313)) | (~c1_1(a352)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[1523, 1521])).
% 0.77/0.93 tff(1525,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a352) | (~c1_1(a352)) | c3_1(a352) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1526,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a352) | c3_1(a352) | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~ndr1_0) | (~c0_1(a313)) | (~c1_1(a352))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1525, 1524])).
% 0.77/0.93 tff(1527,plain,
% 0.77/0.93 ($false),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1526, 142, 1520, 1512, 1506, 508, 507, 506, 505, 494])).
% 0.77/0.93 tff(1528,plain,((~c0_1(a313)) | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a274)) | (~c1_1(a274)) | (~c2_1(a274)) | hskp16 | c2_1(a298) | c3_1(a274)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.93 tff(1529,plain,
% 0.77/0.93 ($false),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1528, 1449, 1448, 559, 1447, 1446, 551, 1443, 1442, 1445, 43, 543, 1441])).
% 0.77/0.93 tff(1530,plain,(hskp2 | hskp16 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.77/0.93 tff(1531,plain,
% 0.77/0.93 (hskp2),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1530, 32, 43])).
% 0.77/0.93 tff(1532,plain,
% 0.77/0.93 (c0_1(a269)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[877, 1531])).
% 0.77/0.93 tff(1533,plain,
% 0.77/0.93 (~c1_1(a269)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[834, 1531])).
% 0.77/0.93 tff(1534,plain,
% 0.77/0.93 (~c2_1(a269)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1337, 1531])).
% 0.77/0.93 tff(1535,plain,
% 0.77/0.93 ($false),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[720, 142, 560, 606, 605, 997, 604, 714, 30, 618])).
% 0.77/0.93 tff(1536,plain,(hskp7 | (~c0_1(a269)) | c1_1(a269) | c2_1(a269) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.77/0.93 tff(1537,plain,
% 0.77/0.93 (hskp7),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1536, 1534, 1533, 1532, 43])).
% 0.77/0.93 tff(1538,plain,
% 0.77/0.93 (~c3_1(a274)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[69, 1537])).
% 0.77/0.93 tff(1539,plain,
% 0.77/0.93 (c1_1(a274)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[77, 1537])).
% 0.77/0.93 tff(1540,plain,
% 0.77/0.93 (c0_1(a274)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[397, 1537])).
% 0.77/0.93 tff(1541,plain,
% 0.77/0.93 (hskp23),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1128, 1540, 1533, 1534, 1532, 1539, 1538])).
% 0.77/0.93 tff(1542,plain,
% 0.77/0.93 (~c1_1(a313)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[28, 1541])).
% 0.77/0.93 tff(1543,plain,
% 0.77/0.93 (c1_1(a269) | (~c3_1(a269))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[893, 142, 32, 30, 107])).
% 0.77/0.93 tff(1544,plain,
% 0.77/0.93 (~c3_1(a269)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1543, 714])).
% 0.77/0.93 tff(1545,plain,
% 0.77/0.93 (c0_1(a269)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[886, 1544, 30, 714])).
% 0.77/0.93 tff(1546,plain,
% 0.77/0.93 (hskp7),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1536, 1545, 714, 30, 43])).
% 0.77/0.93 tff(1547,plain,
% 0.77/0.93 (~c3_1(a274)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[69, 1546])).
% 0.77/0.93 tff(1548,plain,
% 0.77/0.93 (c0_1(a274)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[397, 1546])).
% 0.77/0.93 tff(1549,plain,
% 0.77/0.93 (c1_1(a274)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[77, 1546])).
% 0.77/0.93 tff(1550,plain,
% 0.77/0.93 (c2_1(a274)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1005, 1549, 30, 1545, 1547, 714, 1548])).
% 0.77/0.93 tff(1551,plain,
% 0.77/0.93 (hskp18),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1022, 142, 1548, 1549, 1545, 714, 30, 527, 1550])).
% 0.77/0.93 tff(1552,plain,
% 0.77/0.93 (~c2_1(a298)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[542, 1551])).
% 0.77/0.93 tff(1553,plain,
% 0.77/0.93 (c3_1(a298)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[550, 1551])).
% 0.77/0.93 tff(1554,plain,
% 0.77/0.93 (c1_1(a298)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[558, 1551])).
% 0.77/0.93 tff(1555,plain,
% 0.77/0.93 (hskp23),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1128, 1548, 30, 714, 1545, 1549, 1547])).
% 0.77/0.93 tff(1556,plain,
% 0.77/0.93 (~c3_1(a313)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[16, 1555])).
% 0.77/0.93 tff(1557,plain,
% 0.77/0.93 (~c2_1(a313)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[22, 1555])).
% 0.77/0.93 tff(1558,plain,
% 0.77/0.93 (~c1_1(a313)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[28, 1555])).
% 0.77/0.93 tff(1559,plain,
% 0.77/0.93 (~c0_1(a313)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1528, 1558, 1557, 1556, 1554, 1553, 1548, 1549, 1550, 43, 1552, 1547])).
% 0.77/0.93 tff(1560,assumption,(~hskp9), introduced(assumption)).
% 0.77/0.93 tff(1561,assumption,(hskp25), introduced(assumption)).
% 0.77/0.93 tff(1562,plain,
% 0.77/0.93 (~c2_1(a352)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1511, 1561])).
% 0.77/0.93 tff(1563,plain,
% 0.77/0.93 (c1_1(a352)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1519, 1561])).
% 0.77/0.93 tff(1564,plain,
% 0.77/0.93 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | c2_1(a352) | (~ndr1_0) | c0_1(a352) | (~c1_1(a352)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c2_1(a352) | (~ndr1_0) | c0_1(a352) | (~c1_1(a352)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1565,plain,
% 0.77/0.93 ((hskp9 | (~ndr1_0) | c2_1(a352) | c0_1(a352) | (~c1_1(a352))) <=> (hskp9 | c2_1(a352) | (~ndr1_0) | c0_1(a352) | (~c1_1(a352)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1566,plain,
% 0.77/0.93 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a352) | c0_1(a352) | (~c1_1(a352)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | c2_1(a352) | (~ndr1_0) | c0_1(a352) | (~c1_1(a352))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[1565])).
% 0.77/0.93 tff(1567,plain,
% 0.77/0.93 (((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a352) | c0_1(a352) | (~c1_1(a352)))) <=> ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c2_1(a352) | (~ndr1_0) | c0_1(a352) | (~c1_1(a352)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[1566, 1564])).
% 0.77/0.93 tff(1568,plain,
% 0.77/0.93 ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | (~ndr1_0) | c2_1(a352) | c0_1(a352) | (~c1_1(a352)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1569,plain,
% 0.77/0.93 ((~![U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | c2_1(a352) | (~ndr1_0) | c0_1(a352) | (~c1_1(a352))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1568, 1567])).
% 0.77/0.93 tff(1570,plain,
% 0.77/0.93 (c0_1(a352)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1569, 142, 1560, 1563, 1562, 216])).
% 0.77/0.93 tff(1571,plain,
% 0.77/0.93 (~c3_1(a352)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1505, 1561])).
% 0.77/0.93 tff(1572,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a352) | c3_1(a352) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c0_1(a352)) | (~c1_1(a352)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a352) | c3_1(a352) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c0_1(a352)) | (~c1_1(a352)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1573,plain,
% 0.77/0.93 (((~ndr1_0) | c2_1(a352) | (~c1_1(a352)) | c3_1(a352) | c3_1(a352) | c2_1(a352) | (~c0_1(a352)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269))) <=> (c2_1(a352) | c3_1(a352) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c0_1(a352)) | (~c1_1(a352)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1574,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a352) | (~c1_1(a352)) | c3_1(a352) | c3_1(a352) | c2_1(a352) | (~c0_1(a352)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a352) | c3_1(a352) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c0_1(a352)) | (~c1_1(a352))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[1573])).
% 0.77/0.93 tff(1575,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a352) | (~c1_1(a352)) | c3_1(a352) | c3_1(a352) | c2_1(a352) | (~c0_1(a352)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a352) | c3_1(a352) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c0_1(a352)) | (~c1_1(a352)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[1574, 1572])).
% 0.77/0.93 tff(1576,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a352) | (~c1_1(a352)) | c3_1(a352) | c3_1(a352) | c2_1(a352) | (~c0_1(a352)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1577,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a352) | c3_1(a352) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c0_1(a352)) | (~c1_1(a352))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 0.77/0.93 tff(1578,plain,
% 0.77/0.93 ($false),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1577, 142, 1563, 997, 1562, 1571, 714, 30, 505, 1570])).
% 0.77/0.93 tff(1579,plain,((~hskp25) | (~c0_1(a269)) | c1_1(a269) | c2_1(a269) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.77/0.93 tff(1580,plain,
% 0.77/0.93 (~hskp25),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1579, 1560, 714, 30, 997])).
% 0.77/0.93 tff(1581,assumption,(~hskp25), introduced(assumption)).
% 0.77/0.93 tff(1582,plain,
% 0.77/0.93 (~hskp12),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1490, 1482])).
% 0.77/0.93 tff(1583,plain,
% 0.77/0.93 ($false),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1499, 1582, 1482, 1581])).
% 0.77/0.93 tff(1584,plain,(hskp14 | hskp25), inference(lemma,lemma(discharge,[]))).
% 0.77/0.93 tff(1585,plain,
% 0.77/0.93 (hskp14),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1584, 1580])).
% 0.77/0.93 tff(1586,plain,
% 0.77/0.93 (~c2_1(a287)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[182, 1585])).
% 0.77/0.93 tff(1587,plain,
% 0.77/0.93 (~c0_1(a287)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[188, 1585])).
% 0.77/0.93 tff(1588,plain,
% 0.77/0.93 (c1_1(a287)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[223, 1585])).
% 0.77/0.93 tff(1589,plain,
% 0.77/0.93 ($false),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[230, 142, 1560, 1588, 1587, 1586, 216])).
% 0.77/0.93 tff(1590,plain,(hskp9 | c1_1(a269) | c2_1(a269) | (~c0_1(a269))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.93 tff(1591,plain,
% 0.77/0.93 (hskp9),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1590, 714, 30, 1545])).
% 0.77/0.93 tff(1592,plain,
% 0.77/0.93 (~c1_1(a280)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[236, 1591])).
% 0.77/0.93 tff(1593,plain,
% 0.77/0.93 (c2_1(a280)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[269, 1591])).
% 0.77/0.93 tff(1594,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c0_1(a280)) | c0_1(a313))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c0_1(a280)) | c0_1(a313))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1595,plain,
% 0.77/0.93 (((~ndr1_0) | c1_1(a280) | (~c2_1(a280)) | (~c0_1(a280)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a313) | c1_1(a313) | c0_1(a313)) <=> (c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c0_1(a280)) | c0_1(a313))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1596,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a280) | (~c2_1(a280)) | (~c0_1(a280)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a313) | c1_1(a313) | c0_1(a313))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c0_1(a280)) | c0_1(a313)))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[1595])).
% 0.77/0.93 tff(1597,plain,
% 0.77/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a280) | (~c2_1(a280)) | (~c0_1(a280)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a313) | c1_1(a313) | c0_1(a313))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c0_1(a280)) | c0_1(a313))),
% 0.77/0.93 inference(transitivity,[status(thm)],[1596, 1594])).
% 0.77/0.93 tff(1598,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a280) | (~c2_1(a280)) | (~c0_1(a280)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a313) | c1_1(a313) | c0_1(a313))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(1599,plain,
% 0.77/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c0_1(a280)) | c0_1(a313)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 0.77/0.93 tff(1600,plain,
% 0.77/0.93 (~c0_1(a280)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[1599, 142, 1593, 1558, 1557, 1556, 1592, 645, 1559])).
% 0.77/0.93 tff(1601,plain,
% 0.77/0.93 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(1602,plain,
% 0.77/0.93 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[1601])).
% 0.77/0.93 tff(1603,plain,
% 0.77/0.93 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(1604,plain,
% 0.77/0.93 (^[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)) | (~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))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_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) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(1605,plain,
% 0.77/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[1604])).
% 0.77/0.94 tff(1606,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.77/0.94 tff(1607,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1606, 1605])).
% 0.77/0.94 tff(1608,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1607, 1603])).
% 0.77/0.94 tff(1609,plain,(
% 0.77/0.94 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(skolemize,[status(sab)],[1608])).
% 0.77/0.94 tff(1610,plain,
% 0.77/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1609, 1602])).
% 0.77/0.94 tff(1611,assumption,(~hskp5), introduced(assumption)).
% 0.77/0.94 tff(1612,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a280) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a280) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)) | c0_1(a280) | (~c2_1(a280)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1613,plain,
% 0.77/0.94 ((hskp5 | (~ndr1_0) | c2_1(a269) | c3_1(a269) | (~c0_1(a269)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280))) <=> (hskp5 | c1_1(a280) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)) | c0_1(a280) | (~c2_1(a280)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1614,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a269) | c3_1(a269) | (~c0_1(a269)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a280) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)) | c0_1(a280) | (~c2_1(a280))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1613])).
% 0.77/0.94 tff(1615,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a269) | c3_1(a269) | (~c0_1(a269)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a280) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)) | c0_1(a280) | (~c2_1(a280)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1614, 1612])).
% 0.77/0.94 tff(1616,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a269) | c3_1(a269) | (~c0_1(a269)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1617,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a280) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)) | c0_1(a280) | (~c2_1(a280))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1616, 1615])).
% 0.77/0.94 tff(1618,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1617, 142, 1611, 1593, 1545, 1592, 30, 1610, 1600, 1544])).
% 0.77/0.94 tff(1619,plain,(c1_1(a269) | hskp5 | c2_1(a269) | hskp16 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(1620,plain,
% 0.77/0.94 (hskp5),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1619, 1534, 1533, 43, 32])).
% 0.77/0.94 tff(1621,plain,
% 0.77/0.94 (~c1_1(a272)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[593, 1620])).
% 0.77/0.94 tff(1622,plain,
% 0.77/0.94 (~c3_1(a313)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[16, 1541])).
% 0.77/0.94 tff(1623,plain,
% 0.77/0.94 (c0_1(a272)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[601, 1620])).
% 0.77/0.94 tff(1624,plain,
% 0.77/0.94 (~c2_1(a313)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[22, 1541])).
% 0.77/0.94 tff(1625,plain,
% 0.77/0.94 (hskp18),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1371, 1624, 1623, 1622, 1621, 1542, 1540, 1539, 1538])).
% 0.77/0.94 tff(1626,plain,
% 0.77/0.94 (~c2_1(a298)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[542, 1625])).
% 0.77/0.94 tff(1627,plain,
% 0.77/0.94 (c3_1(a298)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[550, 1625])).
% 0.77/0.94 tff(1628,plain,
% 0.77/0.94 (~c3_1(a272)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[587, 1620])).
% 0.77/0.94 tff(1629,plain,
% 0.77/0.94 (c2_1(a274)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1005, 1538, 1533, 1532, 1534, 1539, 1540])).
% 0.77/0.94 tff(1630,plain,
% 0.77/0.94 (~hskp6),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1069, 1629, 1623, 1538, 1621, 1628, 1540])).
% 0.77/0.94 tff(1631,plain,
% 0.77/0.94 (c1_1(a298)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[558, 1625])).
% 0.77/0.94 tff(1632,plain,
% 0.77/0.94 (c0_1(a298)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1085, 1631, 1540, 1539, 1629, 43, 1630, 1627, 1626])).
% 0.77/0.94 tff(1633,plain,
% 0.77/0.94 (hskp9),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1590, 1534, 1533, 1532])).
% 0.77/0.94 tff(1634,plain,
% 0.77/0.94 (~c1_1(a280)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[236, 1633])).
% 0.77/0.94 tff(1635,plain,
% 0.77/0.94 (c3_1(a280)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[244, 1633])).
% 0.77/0.94 tff(1636,plain,
% 0.77/0.94 (c2_1(a280)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[269, 1633])).
% 0.77/0.94 tff(1637,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c2_1(a298) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c1_1(a298)) | (~c0_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a298) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c1_1(a298)) | (~c0_1(a298)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1638,plain,
% 0.77/0.94 ((hskp8 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c0_1(a298)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280))) <=> (hskp8 | c2_1(a298) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c1_1(a298)) | (~c0_1(a298)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1639,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c0_1(a298)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c2_1(a298) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c1_1(a298)) | (~c0_1(a298))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1638])).
% 0.77/0.94 tff(1640,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c0_1(a298)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a298) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c1_1(a298)) | (~c0_1(a298)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1639, 1637])).
% 0.77/0.94 tff(1641,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c0_1(a298)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1642,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a298) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c1_1(a298)) | (~c0_1(a298))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 0.77/0.94 tff(1643,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1642, 142, 32, 1631, 1636, 1635, 1626, 1634, 1196, 1632])).
% 0.77/0.94 tff(1644,plain,(hskp8 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(1645,plain,
% 0.77/0.94 (hskp8),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1644, 43])).
% 0.77/0.94 tff(1646,plain,
% 0.77/0.94 (~c3_1(a275)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[368, 1645])).
% 0.77/0.94 tff(1647,plain,
% 0.77/0.94 (~c2_1(a275)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[374, 1645])).
% 0.77/0.94 tff(1648,plain,
% 0.77/0.94 (~c0_1(a275)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[380, 1645])).
% 0.77/0.94 tff(1649,plain,
% 0.77/0.94 (hskp2 | c1_1(a275)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[904, 142, 1648, 1647, 1646, 10])).
% 0.77/0.94 tff(1650,plain,
% 0.77/0.94 (c1_1(a275)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1649, 54])).
% 0.77/0.94 tff(1651,plain,
% 0.77/0.94 (hskp9 | (~c1_1(a275))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1313, 142, 1648, 1647, 216])).
% 0.77/0.94 tff(1652,plain,
% 0.77/0.94 (hskp9),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1651, 1650])).
% 0.77/0.94 tff(1653,plain,
% 0.77/0.94 (~c1_1(a280)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[236, 1652])).
% 0.77/0.94 tff(1654,plain,
% 0.77/0.94 (c3_1(a280)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[244, 1652])).
% 0.77/0.94 tff(1655,plain,
% 0.77/0.94 (c2_1(a280)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[269, 1652])).
% 0.77/0.94 tff(1656,plain,
% 0.77/0.94 (((~hskp30) | c0_1(a337)) <=> ((~hskp30) | c0_1(a337))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1657,axiom,((~hskp30) | c0_1(a337)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.77/0.94 tff(1658,plain,
% 0.77/0.94 ((~hskp30) | c0_1(a337)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 0.77/0.94 tff(1659,plain,
% 0.77/0.94 ((~hskp30) | c0_1(a337)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1658, 1656])).
% 0.77/0.94 tff(1660,plain,
% 0.77/0.94 ((~hskp30) | c0_1(a337)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1659, 1656])).
% 0.77/0.94 tff(1661,plain,
% 0.77/0.94 ((~hskp30) | c0_1(a337)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1660, 1656])).
% 0.77/0.94 tff(1662,plain,
% 0.77/0.94 ((~hskp30) | c0_1(a337)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1661, 1656])).
% 0.77/0.94 tff(1663,plain,
% 0.77/0.94 (c0_1(a337)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1662, 1402])).
% 0.77/0.94 tff(1664,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c0_1(a337)) | (~c3_1(a337)) | (~c2_1(a337)) | (~c1_1(a275)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c0_1(a337)) | (~c3_1(a337)) | (~c2_1(a337)) | (~c1_1(a275)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1665,plain,
% 0.77/0.94 ((hskp27 | (~ndr1_0) | (~c2_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)) | c0_1(a275) | c2_1(a275) | (~c1_1(a275))) <=> (hskp27 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c0_1(a337)) | (~c3_1(a337)) | (~c2_1(a337)) | (~c1_1(a275)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(1666,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | (~c2_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)) | c0_1(a275) | c2_1(a275) | (~c1_1(a275)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c0_1(a337)) | (~c3_1(a337)) | (~c2_1(a337)) | (~c1_1(a275))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[1665])).
% 0.77/0.94 tff(1667,plain,
% 0.77/0.94 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | (~c2_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)) | c0_1(a275) | c2_1(a275) | (~c1_1(a275)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c0_1(a337)) | (~c3_1(a337)) | (~c2_1(a337)) | (~c1_1(a275)))),
% 0.77/0.94 inference(transitivity,[status(thm)],[1666, 1664])).
% 0.77/0.94 tff(1668,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | (~c2_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)) | c0_1(a275) | c2_1(a275) | (~c1_1(a275)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(1669,plain,
% 0.77/0.94 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a275) | c2_1(a275) | (~ndr1_0) | (~c0_1(a337)) | (~c3_1(a337)) | (~c2_1(a337)) | (~c1_1(a275))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 0.77/0.94 tff(1670,plain,
% 0.77/0.94 (hskp27 | (~c1_1(a275))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1669, 142, 1663, 1418, 1410, 1648, 1647, 772])).
% 0.77/0.94 tff(1671,plain,
% 0.77/0.94 (hskp27),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[1670, 1650])).
% 0.77/0.94 tff(1672,plain,
% 0.77/0.94 (c3_1(a276)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[787, 1671])).
% 0.77/0.94 tff(1673,plain,
% 0.77/0.94 (c2_1(a276)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[795, 1671])).
% 0.77/0.94 tff(1674,plain,
% 0.77/0.94 (c1_1(a276)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[803, 1671])).
% 0.77/0.94 tff(1675,plain,
% 0.77/0.94 (~c0_1(a280)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[810, 142, 1674, 1673, 1672, 1655, 1654, 1653, 53])).
% 0.78/0.94 tff(1676,plain,
% 0.78/0.94 (hskp3),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[276, 142, 1655, 1654, 1653, 262, 1675])).
% 0.78/0.94 tff(1677,plain,
% 0.78/0.94 (c3_1(a270)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[290, 1676])).
% 0.78/0.94 tff(1678,assumption,(~c0_1(a280)), introduced(assumption)).
% 0.78/0.94 tff(1679,assumption,(~c1_1(a280)), introduced(assumption)).
% 0.78/0.94 tff(1680,assumption,(c2_1(a280)), introduced(assumption)).
% 0.78/0.94 tff(1681,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c0_1(a313)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c0_1(a313)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1682,plain,
% 0.78/0.94 ((hskp4 | (~ndr1_0) | c1_1(a313) | c3_1(a313) | (~c0_1(a313)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280))) <=> (hskp4 | c1_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c0_1(a313)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1683,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a313) | c3_1(a313) | (~c0_1(a313)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c1_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c0_1(a313))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1682])).
% 0.78/0.94 tff(1684,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a313) | c3_1(a313) | (~c0_1(a313)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c0_1(a313)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1683, 1681])).
% 0.78/0.94 tff(1685,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a313) | c3_1(a313) | (~c0_1(a313)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1686,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c1_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c0_1(a313))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 0.78/0.94 tff(1687,plain,
% 0.78/0.94 (~c0_1(a313)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1686, 142, 467, 1680, 29, 17, 1679, 580, 1678])).
% 0.78/0.94 tff(1688,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[492, 142, 54, 29, 23, 17, 10, 1687])).
% 0.78/0.94 tff(1689,plain,((~hskp23) | hskp2 | hskp4 | (~c2_1(a280)) | c1_1(a280) | c0_1(a280)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1690,plain,
% 0.78/0.94 (~hskp23),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1689, 54, 390, 1655, 1653, 1675])).
% 0.78/0.94 tff(1691,plain,
% 0.78/0.94 (~c2_1(a270)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[282, 1676])).
% 0.78/0.94 tff(1692,plain,
% 0.78/0.94 (c0_1(a270)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[345, 1676])).
% 0.78/0.94 tff(1693,assumption,(c1_1(a270)), introduced(assumption)).
% 0.78/0.94 tff(1694,assumption,(~c2_1(a270)), introduced(assumption)).
% 0.78/0.94 tff(1695,assumption,(c3_1(a270)), introduced(assumption)).
% 0.78/0.94 tff(1696,assumption,(c3_1(a276)), introduced(assumption)).
% 0.78/0.94 tff(1697,assumption,(c1_1(a276)), introduced(assumption)).
% 0.78/0.94 tff(1698,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c3_1(a276)) | (~c1_1(a276)) | (~c0_1(a276)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c3_1(a276)) | (~c1_1(a276)) | (~c0_1(a276)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1699,plain,
% 0.78/0.94 ((hskp23 | (~ndr1_0) | (~c1_1(a276)) | (~c3_1(a276)) | (~c0_1(a276)) | c2_1(a270) | (~c3_1(a270)) | (~c1_1(a270))) <=> (hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c3_1(a276)) | (~c1_1(a276)) | (~c0_1(a276)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1700,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a276)) | (~c3_1(a276)) | (~c0_1(a276)) | c2_1(a270) | (~c3_1(a270)) | (~c1_1(a270)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c3_1(a276)) | (~c1_1(a276)) | (~c0_1(a276))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1699])).
% 0.78/0.94 tff(1701,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a276)) | (~c3_1(a276)) | (~c0_1(a276)) | c2_1(a270) | (~c3_1(a270)) | (~c1_1(a270)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c3_1(a276)) | (~c1_1(a276)) | (~c0_1(a276)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1700, 1698])).
% 0.78/0.94 tff(1702,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a276)) | (~c3_1(a276)) | (~c0_1(a276)) | c2_1(a270) | (~c3_1(a270)) | (~c1_1(a270)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1703,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c3_1(a276)) | (~c1_1(a276)) | (~c0_1(a276))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 0.78/0.94 tff(1704,plain,
% 0.78/0.94 (hskp23 | (~c1_1(a270)) | (~c0_1(a276))),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1703, 142, 1697, 1696, 1695, 1694, 42])).
% 0.78/0.94 tff(1705,plain,
% 0.78/0.94 (~c0_1(a276)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1704, 1693, 31])).
% 0.78/0.94 tff(1706,assumption,(c0_1(a270)), introduced(assumption)).
% 0.78/0.94 tff(1707,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a280) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c3_1(a276)) | (~c1_1(a276)) | c0_1(a276) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a280) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c3_1(a276)) | (~c1_1(a276)) | c0_1(a276) | c0_1(a280) | (~c2_1(a280)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1708,plain,
% 0.78/0.94 (((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a276) | (~c3_1(a276)) | (~c1_1(a276)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280))) <=> (c1_1(a280) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c3_1(a276)) | (~c1_1(a276)) | c0_1(a276) | c0_1(a280) | (~c2_1(a280)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1709,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a276) | (~c3_1(a276)) | (~c1_1(a276)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a280) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c3_1(a276)) | (~c1_1(a276)) | c0_1(a276) | c0_1(a280) | (~c2_1(a280))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1708])).
% 0.78/0.94 tff(1710,plain,
% 0.78/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a276) | (~c3_1(a276)) | (~c1_1(a276)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a280) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c3_1(a276)) | (~c1_1(a276)) | c0_1(a276) | c0_1(a280) | (~c2_1(a280)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1709, 1707])).
% 0.78/0.94 tff(1711,plain,
% 0.78/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a276) | (~c3_1(a276)) | (~c1_1(a276)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1712,plain,
% 0.78/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a280) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c3_1(a276)) | (~c1_1(a276)) | c0_1(a276) | c0_1(a280) | (~c2_1(a280))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 0.78/0.94 tff(1713,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1712, 142, 1697, 1696, 1680, 1706, 1679, 1694, 308, 1678, 1693, 1705])).
% 0.78/0.94 tff(1714,plain,((~c1_1(a270)) | (~c1_1(a276)) | (~c3_1(a276)) | (~c2_1(a280)) | (~c0_1(a270)) | c1_1(a280) | c2_1(a270) | c0_1(a280) | hskp23 | (~c3_1(a270))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1715,plain,
% 0.78/0.94 (~c1_1(a270)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1714, 1674, 1672, 1655, 1692, 1653, 1691, 1675, 1690, 1677])).
% 0.78/0.94 tff(1716,assumption,(hskp7), introduced(assumption)).
% 0.78/0.94 tff(1717,plain,
% 0.78/0.94 (c0_1(a274)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[397, 1716])).
% 0.78/0.94 tff(1718,assumption,(~c1_1(a270)), introduced(assumption)).
% 0.78/0.94 tff(1719,assumption,(~c3_1(a275)), introduced(assumption)).
% 0.78/0.94 tff(1720,assumption,(~c0_1(a275)), introduced(assumption)).
% 0.78/0.94 tff(1721,assumption,(c1_1(a275)), introduced(assumption)).
% 0.78/0.94 tff(1722,plain,
% 0.78/0.94 (c1_1(a274)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[77, 1716])).
% 0.78/0.94 tff(1723,plain,
% 0.78/0.94 (~c3_1(a274)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[69, 1716])).
% 0.78/0.94 tff(1724,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[993, 142, 411, 410, 1706, 1695, 1720, 1719, 409, 987, 1721, 1718])).
% 0.78/0.94 tff(1725,plain,(c1_1(a270) | (~c0_1(a274)) | (~c1_1(a274)) | (~c0_1(a270)) | (~c3_1(a270)) | c0_1(a275) | c3_1(a275) | c3_1(a274) | (~c1_1(a275))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1726,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1725, 1723, 1722, 1721, 1706, 1695, 1720, 1719, 1718, 1717])).
% 0.78/0.94 tff(1727,plain,((~hskp7) | (~c1_1(a275)) | (~c0_1(a270)) | (~c3_1(a270)) | c0_1(a275) | c3_1(a275) | c1_1(a270)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1728,plain,
% 0.78/0.94 (~hskp7),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1727, 1650, 1692, 1677, 1648, 1646, 1715])).
% 0.78/0.94 tff(1729,plain,
% 0.78/0.94 (hskp18),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[63, 1728, 43])).
% 0.78/0.94 tff(1730,plain,
% 0.78/0.94 (~c2_1(a298)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[542, 1729])).
% 0.78/0.94 tff(1731,plain,
% 0.78/0.94 (c3_1(a298)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[550, 1729])).
% 0.78/0.94 tff(1732,plain,
% 0.78/0.94 (c1_1(a298)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[558, 1729])).
% 0.78/0.94 tff(1733,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | c2_1(a298) | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c1_1(a298)) | (~c3_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c2_1(a298) | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1734,plain,
% 0.78/0.94 ((hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a270) | c2_1(a270) | (~c0_1(a270))) <=> (hskp7 | c2_1(a298) | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.78/0.94 inference(rewrite,[status(thm)],[])).
% 0.78/0.94 tff(1735,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a270) | c2_1(a270) | (~c0_1(a270)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | c2_1(a298) | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c1_1(a298)) | (~c3_1(a298))))),
% 0.78/0.94 inference(monotonicity,[status(thm)],[1734])).
% 0.78/0.94 tff(1736,plain,
% 0.78/0.94 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a270) | c2_1(a270) | (~c0_1(a270)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c2_1(a298) | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.78/0.94 inference(transitivity,[status(thm)],[1735, 1733])).
% 0.78/0.94 tff(1737,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c1_1(a270) | c2_1(a270) | (~c0_1(a270)))),
% 0.78/0.94 inference(quant_inst,[status(thm)],[])).
% 0.78/0.94 tff(1738,plain,
% 0.78/0.94 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c2_1(a298) | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c1_1(a298)) | (~c3_1(a298))),
% 0.78/0.94 inference(modus_ponens,[status(thm)],[1737, 1736])).
% 0.78/0.94 tff(1739,plain,
% 0.78/0.94 ($false),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1738, 142, 1728, 1732, 1731, 1692, 1730, 1691, 618, 1715])).
% 0.78/0.94 tff(1740,plain,(hskp2 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.78/0.94 tff(1741,plain,
% 0.78/0.94 (hskp2),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1740, 43])).
% 0.78/0.94 tff(1742,plain,
% 0.78/0.94 (~c1_1(a269)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[834, 1741])).
% 0.78/0.94 tff(1743,plain,
% 0.78/0.94 (~c2_1(a269)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1337, 1741])).
% 0.78/0.94 tff(1744,plain,
% 0.78/0.94 (c1_1(a275)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1649, 878])).
% 0.78/0.94 tff(1745,plain,
% 0.78/0.94 (hskp9),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1651, 1744])).
% 0.78/0.94 tff(1746,plain,
% 0.78/0.94 (~c1_1(a280)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[236, 1745])).
% 0.78/0.94 tff(1747,plain,
% 0.78/0.94 (c3_1(a280)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[244, 1745])).
% 0.78/0.94 tff(1748,plain,
% 0.78/0.94 (c2_1(a280)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[269, 1745])).
% 0.78/0.94 tff(1749,plain,
% 0.78/0.94 (hskp27),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[1670, 1744])).
% 0.78/0.94 tff(1750,plain,
% 0.78/0.94 (c3_1(a276)),
% 0.78/0.94 inference(unit_resolution,[status(thm)],[787, 1749])).
% 0.78/0.95 tff(1751,plain,
% 0.78/0.95 (c2_1(a276)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[795, 1749])).
% 0.78/0.95 tff(1752,plain,
% 0.78/0.95 (c1_1(a276)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[803, 1749])).
% 0.78/0.95 tff(1753,plain,
% 0.78/0.95 (~c0_1(a280)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[810, 142, 1752, 1751, 1750, 1748, 1747, 1746, 53])).
% 0.78/0.95 tff(1754,plain,
% 0.78/0.95 (~hskp4),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[389, 878, 43])).
% 0.78/0.95 tff(1755,plain,
% 0.78/0.95 (hskp3),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[276, 142, 1748, 1747, 1746, 262, 1753])).
% 0.78/0.95 tff(1756,plain,
% 0.78/0.95 (~c2_1(a270)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[282, 1755])).
% 0.78/0.95 tff(1757,plain,
% 0.78/0.95 (c3_1(a269)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[886, 750, 714, 30])).
% 0.78/0.95 tff(1758,plain,
% 0.78/0.95 (c3_1(a270)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[290, 1755])).
% 0.78/0.95 tff(1759,plain,
% 0.78/0.95 (c0_1(a270)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[345, 1755])).
% 0.78/0.95 tff(1760,plain,
% 0.78/0.95 (c1_1(a270)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1725, 1759, 410, 411, 1758, 1648, 1646, 409, 1744])).
% 0.78/0.95 tff(1761,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c3_1(a270)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c3_1(a270)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1762,plain,
% 0.78/0.95 ((hskp23 | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c0_1(a270)) | c2_1(a270) | (~c3_1(a270)) | (~c1_1(a270))) <=> (hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c3_1(a270)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1763,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c0_1(a270)) | c2_1(a270) | (~c3_1(a270)) | (~c1_1(a270)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c3_1(a270))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1762])).
% 0.78/0.95 tff(1764,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c0_1(a270)) | c2_1(a270) | (~c3_1(a270)) | (~c1_1(a270)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c3_1(a270)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1763, 1761])).
% 0.78/0.95 tff(1765,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | (~c0_1(a270)) | c2_1(a270) | (~c3_1(a270)) | (~c1_1(a270)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1766,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c3_1(a270))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 0.78/0.95 tff(1767,plain,
% 0.78/0.95 (hskp23),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1766, 142, 1759, 1758, 1756, 42, 1760])).
% 0.78/0.95 tff(1768,plain,
% 0.78/0.95 (~c1_1(a313)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[28, 1767])).
% 0.78/0.95 tff(1769,plain,
% 0.78/0.95 (~c3_1(a313)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[16, 1767])).
% 0.78/0.95 tff(1770,plain,
% 0.78/0.95 (c3_1(a313) | (~c0_1(a313))),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1686, 142, 467, 1680, 508, 1679, 580, 1678])).
% 0.78/0.95 tff(1771,plain,
% 0.78/0.95 (~c0_1(a313)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1770, 506])).
% 0.78/0.95 tff(1772,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a269) | c1_1(a313) | (~c2_1(a313)) | c3_1(a313) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a269) | c1_1(a313) | (~c2_1(a313)) | c3_1(a313) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1773,plain,
% 0.78/0.95 (((~ndr1_0) | c1_1(a313) | c3_1(a313) | (~c2_1(a313)) | c1_1(a269) | c2_1(a269) | (~c3_1(a269)) | c2_1(a269) | c1_1(a269) | c0_1(a269)) <=> (c0_1(a269) | c1_1(a313) | (~c2_1(a313)) | c3_1(a313) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1774,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a313) | c3_1(a313) | (~c2_1(a313)) | c1_1(a269) | c2_1(a269) | (~c3_1(a269)) | c2_1(a269) | c1_1(a269) | c0_1(a269))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a269) | c1_1(a313) | (~c2_1(a313)) | c3_1(a313) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1773])).
% 0.78/0.95 tff(1775,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a313) | c3_1(a313) | (~c2_1(a313)) | c1_1(a269) | c2_1(a269) | (~c3_1(a269)) | c2_1(a269) | c1_1(a269) | c0_1(a269))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a269) | c1_1(a313) | (~c2_1(a313)) | c3_1(a313) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1774, 1772])).
% 0.78/0.95 tff(1776,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a313) | c3_1(a313) | (~c2_1(a313)) | c1_1(a269) | c2_1(a269) | (~c3_1(a269)) | c2_1(a269) | c1_1(a269) | c0_1(a269))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1777,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a269) | c1_1(a313) | (~c2_1(a313)) | c3_1(a313) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1776, 1775])).
% 0.78/0.95 tff(1778,plain,
% 0.78/0.95 ((~c2_1(a313)) | c3_1(a313)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1777, 142, 750, 508, 714, 30, 731, 1757])).
% 0.78/0.95 tff(1779,plain,
% 0.78/0.95 (~c2_1(a313)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1778, 506])).
% 0.78/0.95 tff(1780,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[492, 142, 878, 508, 1779, 506, 10, 1771])).
% 0.78/0.95 tff(1781,plain,(c3_1(a313) | c1_1(a313) | hskp4 | (~c2_1(a280)) | c1_1(a280) | c0_1(a280) | c0_1(a269) | c1_1(a269) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1782,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1781, 1769, 1768, 1754, 1748, 1746, 1753, 750, 714, 30])).
% 0.78/0.95 tff(1783,plain,(c0_1(a269) | c1_1(a269) | c2_1(a269) | (~c1_1(a274)) | (~c0_1(a274)) | c3_1(a274) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1784,plain,
% 0.78/0.95 (c0_1(a269)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1783, 78, 30, 714, 398, 70, 43])).
% 0.78/0.95 tff(1785,plain,
% 0.78/0.95 (c2_1(a274)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1005, 1784, 714, 70, 30, 78, 398])).
% 0.78/0.95 tff(1786,plain,
% 0.78/0.95 ((~c0_1(a269)) | (~c2_1(a274))),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1022, 142, 55, 398, 78, 714, 30, 527])).
% 0.78/0.95 tff(1787,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1786, 1785, 1784])).
% 0.78/0.95 tff(1788,plain,(hskp18 | c1_1(a269) | c2_1(a269) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1789,plain,
% 0.78/0.95 (hskp18),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1788, 714, 30, 43])).
% 0.78/0.95 tff(1790,plain,
% 0.78/0.95 (~c2_1(a298)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[542, 1789])).
% 0.78/0.95 tff(1791,plain,
% 0.78/0.95 (c3_1(a298)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[550, 1789])).
% 0.78/0.95 tff(1792,plain,
% 0.78/0.95 (c1_1(a298)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[558, 1789])).
% 0.78/0.95 tff(1793,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a269) | c2_1(a298) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c1_1(a298)) | (~c3_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a269) | c2_1(a298) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1794,plain,
% 0.78/0.95 ((hskp11 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c0_1(a269) | c2_1(a269) | (~c3_1(a269))) <=> (hskp11 | c0_1(a269) | c2_1(a298) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1795,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c0_1(a269) | c2_1(a269) | (~c3_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a269) | c2_1(a298) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c1_1(a298)) | (~c3_1(a298))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1794])).
% 0.78/0.95 tff(1796,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c0_1(a269) | c2_1(a269) | (~c3_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a269) | c2_1(a298) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c1_1(a298)) | (~c3_1(a298)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1795, 1793])).
% 0.78/0.95 tff(1797,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a298) | (~c1_1(a298)) | (~c3_1(a298)) | c0_1(a269) | c2_1(a269) | (~c3_1(a269)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1798,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a269) | c2_1(a298) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c1_1(a298)) | (~c3_1(a298))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 0.78/0.95 tff(1799,plain,
% 0.78/0.95 (hskp11),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1798, 142, 1792, 1791, 750, 1790, 30, 318, 1757])).
% 0.78/0.95 tff(1800,plain,
% 0.78/0.95 (~c1_1(a282)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[331, 1799])).
% 0.78/0.95 tff(1801,plain,
% 0.78/0.95 (~c0_1(a282)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[337, 1799])).
% 0.78/0.95 tff(1802,plain,
% 0.78/0.95 (c2_1(a282)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[353, 1799])).
% 0.78/0.95 tff(1803,assumption,(~c1_1(a282)), introduced(assumption)).
% 0.78/0.95 tff(1804,assumption,(~c0_1(a282)), introduced(assumption)).
% 0.78/0.95 tff(1805,assumption,(c2_1(a282)), introduced(assumption)).
% 0.78/0.95 tff(1806,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a282) | c1_1(a282) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a282)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a282) | c1_1(a282) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a282)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1807,plain,
% 0.78/0.95 (((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)) | c1_1(a282) | c0_1(a282) | (~c2_1(a282))) <=> (c0_1(a282) | c1_1(a282) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a282)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1808,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)) | c1_1(a282) | c0_1(a282) | (~c2_1(a282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a282) | c1_1(a282) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a282)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1807])).
% 0.78/0.95 tff(1809,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)) | c1_1(a282) | c0_1(a282) | (~c2_1(a282)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a282) | c1_1(a282) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a282)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1808, 1806])).
% 0.78/0.95 tff(1810,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)) | c1_1(a282) | c0_1(a282) | (~c2_1(a282)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1811,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a282) | c1_1(a282) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a282)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1810, 1809])).
% 0.78/0.95 tff(1812,plain,
% 0.78/0.95 (~c1_1(a270)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1811, 142, 621, 620, 1805, 1706, 1804, 1803, 1694, 308, 1071])).
% 0.78/0.95 tff(1813,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c3_1(a270)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c3_1(a270)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1814,plain,
% 0.78/0.95 ((hskp16 | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)) | (~c0_1(a270)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298))) <=> (hskp16 | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c3_1(a270)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1815,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)) | (~c0_1(a270)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c3_1(a270)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1814])).
% 0.78/0.95 tff(1816,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)) | (~c0_1(a270)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c3_1(a270)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1815, 1813])).
% 0.78/0.95 tff(1817,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)) | (~c0_1(a270)) | c0_1(a298) | (~c3_1(a298)) | (~c1_1(a298)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1818,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | (~ndr1_0) | c1_1(a270) | (~c0_1(a270)) | (~c3_1(a270)) | (~c1_1(a298)) | c0_1(a298) | (~c3_1(a298))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 0.78/0.95 tff(1819,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1818, 142, 43, 621, 620, 1706, 1695, 206, 1071, 1812])).
% 0.78/0.95 tff(1820,plain,(c0_1(a298) | hskp16 | (~c1_1(a298)) | (~c3_1(a298)) | (~c0_1(a270)) | (~c3_1(a270)) | (~c2_1(a282)) | c0_1(a282) | c1_1(a282) | c2_1(a270)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1821,plain,
% 0.78/0.95 (c0_1(a298)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1820, 1759, 1792, 1791, 43, 1758, 1802, 1801, 1800, 1756])).
% 0.78/0.95 tff(1822,plain,
% 0.78/0.95 (hskp23 | (~c0_1(a298))),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[660, 142, 1792, 1791, 1790, 42])).
% 0.78/0.95 tff(1823,plain,
% 0.78/0.95 (hskp23),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1822, 1821])).
% 0.78/0.95 tff(1824,plain,
% 0.78/0.95 (~c1_1(a313)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[28, 1823])).
% 0.78/0.95 tff(1825,plain,
% 0.78/0.95 (~c3_1(a313)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[16, 1823])).
% 0.78/0.95 tff(1826,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1781, 1825, 1824, 1754, 1748, 1746, 1753, 750, 714, 30])).
% 0.78/0.95 tff(1827,plain,(c0_1(a269) | c1_1(a269) | c2_1(a269) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1828,plain,
% 0.78/0.95 (c0_1(a269)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1827, 714, 30, 43])).
% 0.78/0.95 tff(1829,plain,
% 0.78/0.95 (hskp7),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1536, 1828, 30, 714, 43])).
% 0.78/0.95 tff(1830,plain,
% 0.78/0.95 (c0_1(a274)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[397, 1829])).
% 0.78/0.95 tff(1831,plain,
% 0.78/0.95 (c1_1(a274)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[77, 1829])).
% 0.78/0.95 tff(1832,plain,
% 0.78/0.95 (~c3_1(a274)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[69, 1829])).
% 0.78/0.95 tff(1833,plain,
% 0.78/0.95 (c2_1(a274)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1005, 1832, 714, 1828, 30, 1831, 1830])).
% 0.78/0.95 tff(1834,plain,
% 0.78/0.95 (hskp0),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1102, 142, 1830, 1831, 1832, 1096, 1833])).
% 0.78/0.95 tff(1835,plain,
% 0.78/0.95 (~c3_1(a267)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1109, 1834])).
% 0.78/0.95 tff(1836,plain,
% 0.78/0.95 (hskp23),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1128, 1830, 714, 30, 1828, 1831, 1832])).
% 0.78/0.95 tff(1837,plain,
% 0.78/0.95 (~c2_1(a313)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[22, 1836])).
% 0.78/0.95 tff(1838,plain,
% 0.78/0.95 (~c1_1(a313)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[28, 1836])).
% 0.78/0.95 tff(1839,plain,
% 0.78/0.95 (~c3_1(a313)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[16, 1836])).
% 0.78/0.95 tff(1840,plain,
% 0.78/0.95 (~c0_1(a313)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1528, 1833, 1792, 1839, 1838, 1791, 1830, 1831, 1837, 43, 1790, 1832])).
% 0.78/0.95 tff(1841,plain,
% 0.78/0.95 (hskp9),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1590, 1828, 30, 714])).
% 0.78/0.95 tff(1842,plain,
% 0.78/0.95 (~c1_1(a280)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[236, 1841])).
% 0.78/0.95 tff(1843,plain,
% 0.78/0.95 (c2_1(a280)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[269, 1841])).
% 0.78/0.95 tff(1844,plain,
% 0.78/0.95 (~c0_1(a280)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1599, 142, 1843, 1838, 1837, 1839, 1842, 645, 1840])).
% 0.78/0.95 tff(1845,plain,
% 0.78/0.95 (c3_1(a280)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[244, 1841])).
% 0.78/0.95 tff(1846,plain,
% 0.78/0.95 (hskp6),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1083, 142, 1845, 1830, 1831, 1842, 1016, 1844, 1833])).
% 0.78/0.95 tff(1847,plain,
% 0.78/0.95 (~c0_1(a273)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1044, 1846])).
% 0.78/0.95 tff(1848,plain,
% 0.78/0.95 (c0_1(a267)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1239, 1834])).
% 0.78/0.95 tff(1849,plain,
% 0.78/0.95 (c2_1(a273)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1052, 1846])).
% 0.78/0.95 tff(1850,plain,
% 0.78/0.95 (c1_1(a273)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1060, 1846])).
% 0.78/0.95 tff(1851,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a274) | c0_1(a273) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | c1_1(a267) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a274) | c0_1(a273) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | c1_1(a267) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1852,plain,
% 0.78/0.95 (((~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a267) | c1_1(a267) | (~c0_1(a267)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273))) <=> (c3_1(a274) | c0_1(a273) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | c1_1(a267) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1853,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a267) | c1_1(a267) | (~c0_1(a267)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a274) | c0_1(a273) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | c1_1(a267) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1852])).
% 0.78/0.95 tff(1854,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a267) | c1_1(a267) | (~c0_1(a267)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a274) | c0_1(a273) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | c1_1(a267) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1853, 1851])).
% 0.78/0.95 tff(1855,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a274) | (~c2_1(a274)) | (~c0_1(a274)) | c3_1(a267) | c1_1(a267) | (~c0_1(a267)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1856,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a274) | c0_1(a273) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | c1_1(a267) | (~c2_1(a273)) | (~c1_1(a273)) | (~c2_1(a274)) | (~c0_1(a274))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1855, 1854])).
% 0.78/0.95 tff(1857,plain,
% 0.78/0.95 (c1_1(a267)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1856, 142, 1830, 1850, 1849, 1848, 1832, 1847, 1835, 1038, 1833])).
% 0.78/0.95 tff(1858,plain,
% 0.78/0.95 (~c2_1(a267)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1115, 1834])).
% 0.78/0.95 tff(1859,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a269) | c2_1(a269) | c2_1(a267) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c1_1(a267)) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a269) | c2_1(a269) | c2_1(a267) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c1_1(a267)) | (~c0_1(a269)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1860,plain,
% 0.78/0.95 (((~ndr1_0) | c2_1(a267) | (~c1_1(a267)) | c3_1(a267) | c3_1(a267) | c2_1(a267) | (~c0_1(a267)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269))) <=> (c1_1(a269) | c2_1(a269) | c2_1(a267) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c1_1(a267)) | (~c0_1(a269)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1861,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a267) | (~c1_1(a267)) | c3_1(a267) | c3_1(a267) | c2_1(a267) | (~c0_1(a267)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a269) | c2_1(a269) | c2_1(a267) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c1_1(a267)) | (~c0_1(a269))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1860])).
% 0.78/0.95 tff(1862,plain,
% 0.78/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a267) | (~c1_1(a267)) | c3_1(a267) | c3_1(a267) | c2_1(a267) | (~c0_1(a267)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a269) | c2_1(a269) | c2_1(a267) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c1_1(a267)) | (~c0_1(a269)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1861, 1859])).
% 0.78/0.95 tff(1863,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a267) | (~c1_1(a267)) | c3_1(a267) | c3_1(a267) | c2_1(a267) | (~c0_1(a267)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1864,plain,
% 0.78/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a269) | c2_1(a269) | c2_1(a267) | c3_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c1_1(a267)) | (~c0_1(a269))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1863, 1862])).
% 0.78/0.95 tff(1865,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1864, 142, 1828, 1848, 714, 30, 1858, 1835, 505, 1857])).
% 0.78/0.95 tff(1866,plain,(c1_1(a269) | c2_1(a269) | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1867,plain,
% 0.78/0.95 ($false),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1866, 1743, 1742, 43])).
% 0.78/0.95 tff(1868,plain,(hskp16), inference(lemma,lemma(discharge,[]))).
% 0.78/0.95 tff(1869,plain,
% 0.78/0.95 (((~hskp16) | (~c2_1(a293))) <=> ((~hskp16) | (~c2_1(a293)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1870,plain,
% 0.78/0.95 (((~c2_1(a293)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a293)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1871,axiom,((~c2_1(a293)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.78/0.95 tff(1872,plain,
% 0.78/0.95 ((~hskp16) | (~c2_1(a293))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 0.78/0.95 tff(1873,plain,
% 0.78/0.95 ((~hskp16) | (~c2_1(a293))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1872, 1869])).
% 0.78/0.95 tff(1874,plain,
% 0.78/0.95 (~c2_1(a293)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1873, 1868])).
% 0.78/0.95 tff(1875,plain,
% 0.78/0.95 (((~hskp16) | c1_1(a293)) <=> ((~hskp16) | c1_1(a293))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1876,axiom,((~hskp16) | c1_1(a293)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.78/0.95 tff(1877,plain,
% 0.78/0.95 ((~hskp16) | c1_1(a293)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1876, 1875])).
% 0.78/0.95 tff(1878,plain,
% 0.78/0.95 ((~hskp16) | c1_1(a293)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1877, 1875])).
% 0.78/0.95 tff(1879,plain,
% 0.78/0.95 ((~hskp16) | c1_1(a293)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1878, 1875])).
% 0.78/0.95 tff(1880,plain,
% 0.78/0.95 ((~hskp16) | c1_1(a293)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1879, 1875])).
% 0.78/0.95 tff(1881,plain,
% 0.78/0.95 ((~hskp16) | c1_1(a293)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1880, 1875])).
% 0.78/0.95 tff(1882,plain,
% 0.78/0.95 (c1_1(a293)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1881, 1868])).
% 0.78/0.95 tff(1883,plain,
% 0.78/0.95 (((~hskp16) | c0_1(a293)) <=> ((~hskp16) | c0_1(a293))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1884,axiom,((~hskp16) | c0_1(a293)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 0.78/0.95 tff(1885,plain,
% 0.78/0.95 ((~hskp16) | c0_1(a293)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 0.78/0.95 tff(1886,plain,
% 0.78/0.95 ((~hskp16) | c0_1(a293)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1885, 1883])).
% 0.78/0.95 tff(1887,plain,
% 0.78/0.95 ((~hskp16) | c0_1(a293)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1886, 1883])).
% 0.78/0.95 tff(1888,plain,
% 0.78/0.95 ((~hskp16) | c0_1(a293)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1887, 1883])).
% 0.78/0.95 tff(1889,plain,
% 0.78/0.95 ((~hskp16) | c0_1(a293)),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1888, 1883])).
% 0.78/0.95 tff(1890,plain,
% 0.78/0.95 (c0_1(a293)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1889, 1868])).
% 0.78/0.95 tff(1891,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a293) | (~ndr1_0) | (~c1_1(a293)) | (~c0_1(a293)) | (~c3_1(a293)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a293) | (~ndr1_0) | (~c1_1(a293)) | (~c0_1(a293)) | (~c3_1(a293)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1892,plain,
% 0.78/0.95 ((hskp23 | (~ndr1_0) | (~c1_1(a293)) | (~c3_1(a293)) | (~c0_1(a293)) | c2_1(a293) | (~c3_1(a293)) | (~c1_1(a293))) <=> (hskp23 | c2_1(a293) | (~ndr1_0) | (~c1_1(a293)) | (~c0_1(a293)) | (~c3_1(a293)))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1893,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a293)) | (~c3_1(a293)) | (~c0_1(a293)) | c2_1(a293) | (~c3_1(a293)) | (~c1_1(a293)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | c2_1(a293) | (~ndr1_0) | (~c1_1(a293)) | (~c0_1(a293)) | (~c3_1(a293))))),
% 0.78/0.95 inference(monotonicity,[status(thm)],[1892])).
% 0.78/0.95 tff(1894,plain,
% 0.78/0.95 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a293)) | (~c3_1(a293)) | (~c0_1(a293)) | c2_1(a293) | (~c3_1(a293)) | (~c1_1(a293)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a293) | (~ndr1_0) | (~c1_1(a293)) | (~c0_1(a293)) | (~c3_1(a293)))),
% 0.78/0.95 inference(transitivity,[status(thm)],[1893, 1891])).
% 0.78/0.95 tff(1895,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp23 | (~ndr1_0) | (~c1_1(a293)) | (~c3_1(a293)) | (~c0_1(a293)) | c2_1(a293) | (~c3_1(a293)) | (~c1_1(a293)))),
% 0.78/0.95 inference(quant_inst,[status(thm)],[])).
% 0.78/0.95 tff(1896,plain,
% 0.78/0.95 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp23 | c2_1(a293) | (~ndr1_0) | (~c1_1(a293)) | (~c0_1(a293)) | (~c3_1(a293))),
% 0.78/0.95 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 0.78/0.95 tff(1897,plain,
% 0.78/0.95 (hskp23 | (~c3_1(a293))),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1896, 142, 1890, 1882, 1874, 42])).
% 0.78/0.95 tff(1898,plain,
% 0.78/0.95 (~c3_1(a293)),
% 0.78/0.95 inference(unit_resolution,[status(thm)],[1897, 31])).
% 0.78/0.95 tff(1899,plain,
% 0.78/0.95 (((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293))) <=> ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1900,plain,
% 0.78/0.95 ((hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a293))) <=> (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.95 inference(rewrite,[status(thm)],[])).
% 0.78/0.95 tff(1901,plain,
% 0.78/0.95 (((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a293)))) <=> ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293)))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1900])).
% 0.78/0.96 tff(1902,plain,
% 0.78/0.96 (((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a293)))) <=> ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1901, 1899])).
% 0.78/0.96 tff(1903,plain,
% 0.78/0.96 ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a293)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1904,plain,
% 0.78/0.96 ((~![U: $i] : (hskp28 | hskp23 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)))) | hskp28 | hskp23 | (~ndr1_0) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 0.78/0.96 tff(1905,plain,
% 0.78/0.96 (hskp28 | hskp23 | c3_1(a293)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1904, 142, 1890, 1882, 408])).
% 0.78/0.96 tff(1906,plain,
% 0.78/0.96 (hskp28),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1905, 31, 1898])).
% 0.78/0.96 tff(1907,plain,
% 0.78/0.96 (c1_1(a278)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[426, 1906])).
% 0.78/0.96 tff(1908,plain,
% 0.78/0.96 (c0_1(a278)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[434, 1906])).
% 0.78/0.96 tff(1909,plain,
% 0.78/0.96 (c3_1(a278)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[442, 1906])).
% 0.78/0.96 tff(1910,plain,
% 0.78/0.96 (c2_1(a278)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[455, 1909, 1908, 1907, 31])).
% 0.78/0.96 tff(1911,plain,
% 0.78/0.96 (((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)))) <=> ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1912,plain,
% 0.78/0.96 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1913,plain,
% 0.78/0.96 ((~![U: $i] : (hskp8 | hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp7 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1912, 1911])).
% 0.78/0.96 tff(1914,plain,
% 0.78/0.96 (hskp8 | hskp7),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1913, 142, 1907, 1909, 570, 1910])).
% 0.78/0.96 tff(1915,plain,
% 0.78/0.96 (hskp7),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1914, 32])).
% 0.78/0.96 tff(1916,plain,
% 0.78/0.96 (~c3_1(a274)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[69, 1915])).
% 0.78/0.96 tff(1917,plain,
% 0.78/0.96 (c0_1(a274)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[397, 1915])).
% 0.78/0.96 tff(1918,plain,
% 0.78/0.96 (c1_1(a274)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[77, 1915])).
% 0.78/0.96 tff(1919,plain,
% 0.78/0.96 (c3_1(a269)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[886, 750, 30, 714])).
% 0.78/0.96 tff(1920,plain,
% 0.78/0.96 (hskp8),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[894, 1919, 714])).
% 0.78/0.96 tff(1921,plain,
% 0.78/0.96 (~c3_1(a275)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[368, 1920])).
% 0.78/0.96 tff(1922,plain,
% 0.78/0.96 (~c2_1(a275)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[374, 1920])).
% 0.78/0.96 tff(1923,plain,
% 0.78/0.96 (~c0_1(a275)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[380, 1920])).
% 0.78/0.96 tff(1924,plain,
% 0.78/0.96 (c1_1(a275)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[904, 142, 54, 1923, 1922, 1921, 10])).
% 0.78/0.96 tff(1925,plain,
% 0.78/0.96 (hskp28),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1905, 1898, 31])).
% 0.78/0.96 tff(1926,plain,
% 0.78/0.96 (c1_1(a278)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[426, 1925])).
% 0.78/0.96 tff(1927,plain,
% 0.78/0.96 (c0_1(a278)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[434, 1925])).
% 0.78/0.96 tff(1928,plain,
% 0.78/0.96 (c3_1(a278)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[442, 1925])).
% 0.78/0.96 tff(1929,plain,
% 0.78/0.96 (c2_1(a278)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[455, 1928, 1927, 1926, 31])).
% 0.78/0.96 tff(1930,plain,
% 0.78/0.96 (hskp9),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1313, 142, 1923, 1922, 216, 1721])).
% 0.78/0.96 tff(1931,plain,
% 0.78/0.96 (~c1_1(a280)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[236, 1930])).
% 0.78/0.96 tff(1932,plain,
% 0.78/0.96 (c3_1(a280)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[244, 1930])).
% 0.78/0.96 tff(1933,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a280) | c0_1(a275) | c3_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a280) | c0_1(a275) | c3_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1934,plain,
% 0.78/0.96 (((~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a293)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a275) | c3_1(a275) | (~c1_1(a275))) <=> (c1_1(a280) | c0_1(a275) | c3_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1935,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a293)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a275) | c3_1(a275) | (~c1_1(a275)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c1_1(a280) | c0_1(a275) | c3_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293)))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1934])).
% 0.78/0.96 tff(1936,plain,
% 0.78/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a293)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a275) | c3_1(a275) | (~c1_1(a275)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a280) | c0_1(a275) | c3_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1935, 1933])).
% 0.78/0.96 tff(1937,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a293)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c0_1(a275) | c3_1(a275) | (~c1_1(a275)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1938,plain,
% 0.78/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c1_1(a280) | c0_1(a275) | c3_1(a275) | (~ndr1_0) | (~c1_1(a275)) | (~c3_1(a280)) | (~c0_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 0.78/0.96 tff(1939,plain,
% 0.78/0.96 ((~c0_1(a280)) | c3_1(a293)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1938, 142, 1890, 1882, 1932, 1931, 1923, 1921, 987, 1721])).
% 0.78/0.96 tff(1940,plain,
% 0.78/0.96 (~c0_1(a280)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1939, 1898])).
% 0.78/0.96 tff(1941,plain,
% 0.78/0.96 (c2_1(a280)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[269, 1930])).
% 0.78/0.96 tff(1942,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c2_1(a293) | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c0_1(a293)) | c3_1(a293))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c2_1(a293) | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1943,plain,
% 0.78/0.96 ((hskp5 | (~ndr1_0) | c2_1(a293) | c3_1(a293) | (~c0_1(a293)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280))) <=> (hskp5 | c2_1(a293) | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1944,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a293) | c3_1(a293) | (~c0_1(a293)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c2_1(a293) | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c0_1(a293)) | c3_1(a293)))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1943])).
% 0.78/0.96 tff(1945,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a293) | c3_1(a293) | (~c0_1(a293)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c2_1(a293) | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1944, 1942])).
% 0.78/0.96 tff(1946,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a293) | c3_1(a293) | (~c0_1(a293)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1947,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c2_1(a293) | c1_1(a280) | (~ndr1_0) | c0_1(a280) | (~c2_1(a280)) | (~c0_1(a293)) | c3_1(a293)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 0.78/0.96 tff(1948,plain,
% 0.78/0.96 (hskp5 | c0_1(a280) | c3_1(a293)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1947, 142, 1890, 1941, 1874, 1931, 1610])).
% 0.78/0.96 tff(1949,plain,
% 0.78/0.96 (hskp5),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1948, 1940, 1898])).
% 0.78/0.96 tff(1950,plain,
% 0.78/0.96 (c0_1(a272)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[601, 1949])).
% 0.78/0.96 tff(1951,plain,
% 0.78/0.96 (~c1_1(a272)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[593, 1949])).
% 0.78/0.96 tff(1952,plain,
% 0.78/0.96 (~c3_1(a272)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[587, 1949])).
% 0.78/0.96 tff(1953,plain,
% 0.78/0.96 (~c2_1(a272)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[910, 1952, 750, 1951, 714, 30, 1950])).
% 0.78/0.96 tff(1954,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[918, 142, 55, 1927, 1926, 1950, 1951, 527, 1953, 1929])).
% 0.78/0.96 tff(1955,plain,(hskp23 | hskp18 | c0_1(a269) | c1_1(a269) | c2_1(a269) | (~c1_1(a275))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(1956,plain,
% 0.78/0.96 (hskp23),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1955, 750, 55, 714, 30, 1924])).
% 0.78/0.96 tff(1957,plain,
% 0.78/0.96 (~c3_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[16, 1956])).
% 0.78/0.96 tff(1958,plain,
% 0.78/0.96 (~c2_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[22, 1956])).
% 0.78/0.96 tff(1959,plain,
% 0.78/0.96 (~c1_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[28, 1956])).
% 0.78/0.96 tff(1960,plain,
% 0.78/0.96 (~c0_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[941, 142, 1959, 1958, 1957, 1922, 1921, 505, 1924])).
% 0.78/0.96 tff(1961,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[492, 142, 54, 1959, 1958, 1957, 10, 1960])).
% 0.78/0.96 tff(1962,plain,(c0_1(a269) | hskp2 | hskp18 | c1_1(a269) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(1963,plain,
% 0.78/0.96 (c0_1(a269)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1962, 55, 54, 714, 30])).
% 0.78/0.96 tff(1964,plain,
% 0.78/0.96 (hskp9),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1590, 1963, 30, 714])).
% 0.78/0.96 tff(1965,plain,
% 0.78/0.96 (~c1_1(a280)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[236, 1964])).
% 0.78/0.96 tff(1966,plain,
% 0.78/0.96 (c3_1(a280)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[244, 1964])).
% 0.78/0.96 tff(1967,plain,
% 0.78/0.96 (c2_1(a280)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[269, 1964])).
% 0.78/0.96 tff(1968,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c2_1(a293) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a293) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1969,plain,
% 0.78/0.96 ((hskp8 | (~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | (~c0_1(a293)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280))) <=> (hskp8 | c2_1(a293) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(1970,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | (~c0_1(a293)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c2_1(a293) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c1_1(a293)) | (~c0_1(a293))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[1969])).
% 0.78/0.96 tff(1971,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | (~c0_1(a293)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a293) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)))),
% 0.78/0.96 inference(transitivity,[status(thm)],[1970, 1968])).
% 0.78/0.96 tff(1972,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | (~c0_1(a293)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(1973,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c2_1(a293) | c1_1(a280) | (~ndr1_0) | (~c2_1(a280)) | (~c3_1(a280)) | (~c1_1(a293)) | (~c0_1(a293))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 0.78/0.96 tff(1974,plain,
% 0.78/0.96 (hskp8),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1973, 142, 1890, 1882, 1967, 1966, 1874, 1965, 1196])).
% 0.78/0.96 tff(1975,plain,
% 0.78/0.96 (~c3_1(a275)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[368, 1974])).
% 0.78/0.96 tff(1976,plain,
% 0.78/0.96 (~c2_1(a275)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[374, 1974])).
% 0.78/0.96 tff(1977,plain,
% 0.78/0.96 (~c0_1(a275)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[380, 1974])).
% 0.78/0.96 tff(1978,plain,
% 0.78/0.96 (c1_1(a275)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[904, 142, 54, 1977, 1976, 1975, 10])).
% 0.78/0.96 tff(1979,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1122, 142, 55, 1927, 1926, 997, 714, 30, 527, 1929])).
% 0.78/0.96 tff(1980,plain,(hskp23 | hskp18 | (~c0_1(a269)) | c1_1(a269) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(1981,plain,
% 0.78/0.96 (hskp23),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1980, 55, 1963, 714, 30])).
% 0.78/0.96 tff(1982,plain,
% 0.78/0.96 (~c3_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[16, 1981])).
% 0.78/0.96 tff(1983,plain,
% 0.78/0.96 (~c2_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[22, 1981])).
% 0.78/0.96 tff(1984,plain,
% 0.78/0.96 (~c1_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[28, 1981])).
% 0.78/0.96 tff(1985,plain,
% 0.78/0.96 (~c0_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[941, 142, 1984, 1983, 1982, 1976, 1975, 505, 1978])).
% 0.78/0.96 tff(1986,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[492, 142, 54, 1984, 1983, 1982, 10, 1985])).
% 0.78/0.96 tff(1987,plain,(hskp18 | hskp2 | c1_1(a269) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(1988,plain,
% 0.78/0.96 (hskp18),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1987, 54, 714, 30])).
% 0.78/0.96 tff(1989,plain,
% 0.78/0.96 (~c2_1(a298)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[542, 1988])).
% 0.78/0.96 tff(1990,plain,
% 0.78/0.96 (c3_1(a298)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[550, 1988])).
% 0.78/0.96 tff(1991,plain,
% 0.78/0.96 (c1_1(a298)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[558, 1988])).
% 0.78/0.96 tff(1992,assumption,(hskp5), introduced(assumption)).
% 0.78/0.96 tff(1993,plain,
% 0.78/0.96 (~c3_1(a272)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[587, 1992])).
% 0.78/0.96 tff(1994,plain,
% 0.78/0.96 (c0_1(a272)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[601, 1992])).
% 0.78/0.96 tff(1995,plain,
% 0.78/0.96 (~c1_1(a272)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[593, 1992])).
% 0.78/0.96 tff(1996,plain,
% 0.78/0.96 (hskp7),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[747, 1995, 621, 30, 714, 1993, 1994, 620, 619])).
% 0.78/0.96 tff(1997,plain,
% 0.78/0.96 (~c3_1(a274)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[69, 1996])).
% 0.78/0.96 tff(1998,plain,
% 0.78/0.96 (c0_1(a274)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[397, 1996])).
% 0.78/0.96 tff(1999,plain,
% 0.78/0.96 (c1_1(a274)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[77, 1996])).
% 0.78/0.96 tff(2000,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[943, 1999, 1998, 30, 750, 714, 1995, 1994, 1997, 1993])).
% 0.78/0.96 tff(2001,plain,((~hskp5) | c2_1(a269) | c0_1(a269) | c1_1(a269) | (~c1_1(a298)) | (~c3_1(a298)) | c2_1(a298)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(2002,plain,
% 0.78/0.96 (~hskp5),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2001, 750, 30, 714, 1991, 1990, 1989])).
% 0.78/0.96 tff(2003,plain,
% 0.78/0.96 (hskp11),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1798, 142, 1991, 1990, 750, 1989, 30, 318, 1919])).
% 0.78/0.96 tff(2004,plain,
% 0.78/0.96 (~c1_1(a282)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[331, 2003])).
% 0.78/0.96 tff(2005,plain,
% 0.78/0.96 (~c0_1(a282)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[337, 2003])).
% 0.78/0.96 tff(2006,plain,
% 0.78/0.96 (c2_1(a282)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[353, 2003])).
% 0.78/0.96 tff(2007,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c2_1(a293) | c0_1(a282) | c1_1(a282) | (~ndr1_0) | (~c2_1(a282)) | (~c0_1(a293)) | c3_1(a293))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c2_1(a293) | c0_1(a282) | c1_1(a282) | (~ndr1_0) | (~c2_1(a282)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2008,plain,
% 0.78/0.96 ((hskp5 | (~ndr1_0) | c2_1(a293) | c3_1(a293) | (~c0_1(a293)) | c1_1(a282) | c0_1(a282) | (~c2_1(a282))) <=> (hskp5 | c2_1(a293) | c0_1(a282) | c1_1(a282) | (~ndr1_0) | (~c2_1(a282)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2009,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a293) | c3_1(a293) | (~c0_1(a293)) | c1_1(a282) | c0_1(a282) | (~c2_1(a282)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c2_1(a293) | c0_1(a282) | c1_1(a282) | (~ndr1_0) | (~c2_1(a282)) | (~c0_1(a293)) | c3_1(a293)))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[2008])).
% 0.78/0.96 tff(2010,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a293) | c3_1(a293) | (~c0_1(a293)) | c1_1(a282) | c0_1(a282) | (~c2_1(a282)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c2_1(a293) | c0_1(a282) | c1_1(a282) | (~ndr1_0) | (~c2_1(a282)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.96 inference(transitivity,[status(thm)],[2009, 2007])).
% 0.78/0.96 tff(2011,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a293) | c3_1(a293) | (~c0_1(a293)) | c1_1(a282) | c0_1(a282) | (~c2_1(a282)))),
% 0.78/0.96 inference(quant_inst,[status(thm)],[])).
% 0.78/0.96 tff(2012,plain,
% 0.78/0.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c2_1(a293) | c0_1(a282) | c1_1(a282) | (~ndr1_0) | (~c2_1(a282)) | (~c0_1(a293)) | c3_1(a293)),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2011, 2010])).
% 0.78/0.96 tff(2013,plain,
% 0.78/0.96 (hskp5 | c3_1(a293)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2012, 142, 1890, 2006, 1874, 2005, 2004, 1610])).
% 0.78/0.96 tff(2014,plain,
% 0.78/0.96 (c3_1(a293)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2013, 2002])).
% 0.78/0.96 tff(2015,plain,
% 0.78/0.96 (hskp23),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1897, 2014])).
% 0.78/0.96 tff(2016,plain,
% 0.78/0.96 (~c3_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[16, 2015])).
% 0.78/0.96 tff(2017,plain,
% 0.78/0.96 (~c2_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[22, 2015])).
% 0.78/0.96 tff(2018,plain,
% 0.78/0.96 (~c1_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[28, 2015])).
% 0.78/0.96 tff(2019,plain,
% 0.78/0.96 (~c0_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[941, 142, 2018, 2017, 2016, 1922, 1921, 505, 1924])).
% 0.78/0.96 tff(2020,plain,
% 0.78/0.96 ($false),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[492, 142, 54, 2018, 2017, 2016, 10, 2019])).
% 0.78/0.96 tff(2021,plain,(c0_1(a269) | hskp2 | c2_1(a269) | c1_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.96 tff(2022,plain,
% 0.78/0.96 (c0_1(a269)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2021, 54, 30, 714])).
% 0.78/0.96 tff(2023,plain,
% 0.78/0.96 (hskp7 | (~c0_1(a269))),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[720, 142, 1991, 1990, 1989, 714, 30, 618])).
% 0.78/0.96 tff(2024,plain,
% 0.78/0.96 (hskp7),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2023, 2022])).
% 0.78/0.96 tff(2025,plain,
% 0.78/0.96 (c0_1(a274)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[397, 2024])).
% 0.78/0.96 tff(2026,plain,
% 0.78/0.96 (~c3_1(a274)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[69, 2024])).
% 0.78/0.96 tff(2027,plain,
% 0.78/0.96 (c1_1(a274)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[77, 2024])).
% 0.78/0.96 tff(2028,plain,
% 0.78/0.96 (c2_1(a274)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1005, 2027, 30, 2022, 2026, 714, 2025])).
% 0.78/0.96 tff(2029,plain,
% 0.78/0.96 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(2030,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[2029])).
% 0.78/0.96 tff(2031,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2032,plain,
% 0.78/0.96 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(2033,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[2032])).
% 0.78/0.96 tff(2034,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 0.78/0.96 tff(2035,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2034, 2033])).
% 0.78/0.96 tff(2036,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2035, 2031])).
% 0.78/0.96 tff(2037,plain,(
% 0.78/0.96 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.78/0.96 inference(skolemize,[status(sab)],[2036])).
% 0.78/0.96 tff(2038,plain,
% 0.78/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2037, 2030])).
% 0.78/0.96 tff(2039,plain,
% 0.78/0.96 (hskp0),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1102, 142, 2025, 2027, 2026, 1096, 2028])).
% 0.78/0.96 tff(2040,plain,
% 0.78/0.96 (~c2_1(a267)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1115, 2039])).
% 0.78/0.96 tff(2041,plain,
% 0.78/0.96 (hskp23),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1128, 2027, 714, 30, 2022, 2025, 2026])).
% 0.78/0.96 tff(2042,plain,
% 0.78/0.96 (~c3_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[16, 2041])).
% 0.78/0.96 tff(2043,plain,
% 0.78/0.96 (~c2_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[22, 2041])).
% 0.78/0.96 tff(2044,plain,
% 0.78/0.96 (~c1_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[28, 2041])).
% 0.78/0.96 tff(2045,plain,
% 0.78/0.96 (c0_1(a313)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[492, 142, 54, 2044, 2043, 2042, 10])).
% 0.78/0.96 tff(2046,plain,
% 0.78/0.96 (~hskp6),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1457, 2045, 2044, 2042, 2026, 2028, 2025])).
% 0.78/0.96 tff(2047,plain,
% 0.78/0.96 (hskp9),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1590, 2022, 30, 714])).
% 0.78/0.96 tff(2048,plain,
% 0.78/0.96 (~c1_1(a280)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[236, 2047])).
% 0.78/0.96 tff(2049,plain,
% 0.78/0.96 (c3_1(a280)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[244, 2047])).
% 0.78/0.96 tff(2050,plain,
% 0.78/0.96 (hskp6 | c0_1(a280)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[1083, 142, 2049, 2025, 2027, 2048, 1016, 2028])).
% 0.78/0.96 tff(2051,plain,
% 0.78/0.96 (c0_1(a280)),
% 0.78/0.96 inference(unit_resolution,[status(thm)],[2050, 2046])).
% 0.78/0.96 tff(2052,plain,
% 0.78/0.96 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(2053,plain,
% 0.78/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[2052])).
% 0.78/0.96 tff(2054,plain,
% 0.78/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2055,plain,
% 0.78/0.96 (^[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)) | (~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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_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)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_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)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.78/0.96 inference(bind,[status(th)],[])).
% 0.78/0.96 tff(2056,plain,
% 0.78/0.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.96 inference(quant_intro,[status(thm)],[2055])).
% 0.78/0.96 tff(2057,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 0.78/0.96 tff(2058,plain,
% 0.78/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 0.78/0.96 tff(2059,plain,
% 0.78/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2058, 2054])).
% 0.78/0.96 tff(2060,plain,(
% 0.78/0.96 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.96 inference(skolemize,[status(sab)],[2059])).
% 0.78/0.96 tff(2061,plain,
% 0.78/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.96 inference(modus_ponens,[status(thm)],[2060, 2053])).
% 0.78/0.96 tff(2062,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp1 | c2_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c0_1(a313)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp1 | c2_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c0_1(a313)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2063,plain,
% 0.78/0.96 ((hskp1 | (~ndr1_0) | c2_1(a313) | c3_1(a313) | (~c0_1(a313)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280))) <=> (hskp1 | c2_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c0_1(a313)))),
% 0.78/0.96 inference(rewrite,[status(thm)],[])).
% 0.78/0.96 tff(2064,plain,
% 0.78/0.96 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a313) | c3_1(a313) | (~c0_1(a313)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp1 | c2_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c0_1(a313))))),
% 0.78/0.96 inference(monotonicity,[status(thm)],[2063])).
% 0.78/0.97 tff(2065,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a313) | c3_1(a313) | (~c0_1(a313)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp1 | c2_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c0_1(a313)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2064, 2062])).
% 0.78/0.97 tff(2066,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp1 | (~ndr1_0) | c2_1(a313) | c3_1(a313) | (~c0_1(a313)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2067,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp1 | c2_1(a313) | c3_1(a313) | c1_1(a280) | (~ndr1_0) | (~c3_1(a280)) | (~c0_1(a280)) | (~c0_1(a313))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 0.78/0.97 tff(2068,plain,
% 0.78/0.97 (hskp1 | (~c0_1(a280)) | (~c0_1(a313))),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2067, 142, 2049, 2043, 2042, 2048, 2061])).
% 0.78/0.97 tff(2069,plain,
% 0.78/0.97 (hskp1),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2068, 2051, 2045])).
% 0.78/0.97 tff(2070,plain,
% 0.78/0.97 (((~hskp1) | (~c2_1(a268))) <=> ((~hskp1) | (~c2_1(a268)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2071,plain,
% 0.78/0.97 (((~c2_1(a268)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a268)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2072,axiom,((~c2_1(a268)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.78/0.97 tff(2073,plain,
% 0.78/0.97 ((~hskp1) | (~c2_1(a268))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2072, 2071])).
% 0.78/0.97 tff(2074,plain,
% 0.78/0.97 ((~hskp1) | (~c2_1(a268))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2073, 2070])).
% 0.78/0.97 tff(2075,plain,
% 0.78/0.97 (~c2_1(a268)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2074, 2069])).
% 0.78/0.97 tff(2076,plain,
% 0.78/0.97 (((~hskp1) | (~c1_1(a268))) <=> ((~hskp1) | (~c1_1(a268)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2077,plain,
% 0.78/0.97 (((~c1_1(a268)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a268)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2078,axiom,((~c1_1(a268)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.78/0.97 tff(2079,plain,
% 0.78/0.97 ((~hskp1) | (~c1_1(a268))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2078, 2077])).
% 0.78/0.97 tff(2080,plain,
% 0.78/0.97 ((~hskp1) | (~c1_1(a268))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2079, 2076])).
% 0.78/0.97 tff(2081,plain,
% 0.78/0.97 (~c1_1(a268)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2080, 2069])).
% 0.78/0.97 tff(2082,plain,
% 0.78/0.97 (c0_1(a267)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1239, 2039])).
% 0.78/0.97 tff(2083,plain,
% 0.78/0.97 (((~hskp1) | c3_1(a268)) <=> ((~hskp1) | c3_1(a268))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2084,axiom,((~hskp1) | c3_1(a268)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.78/0.97 tff(2085,plain,
% 0.78/0.97 ((~hskp1) | c3_1(a268)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2084, 2083])).
% 0.78/0.97 tff(2086,plain,
% 0.78/0.97 ((~hskp1) | c3_1(a268)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2085, 2083])).
% 0.78/0.97 tff(2087,plain,
% 0.78/0.97 ((~hskp1) | c3_1(a268)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2086, 2083])).
% 0.78/0.97 tff(2088,plain,
% 0.78/0.97 ((~hskp1) | c3_1(a268)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2087, 2083])).
% 0.78/0.97 tff(2089,plain,
% 0.78/0.97 ((~hskp1) | c3_1(a268)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2088, 2083])).
% 0.78/0.97 tff(2090,plain,
% 0.78/0.97 (c3_1(a268)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2089, 2069])).
% 0.78/0.97 tff(2091,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a274) | c1_1(a268) | c2_1(a268) | c2_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c1_1(a267)) | (~c3_1(a268)) | (~c2_1(a274)) | (~c1_1(a274)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a274) | c1_1(a268) | c2_1(a268) | c2_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c1_1(a267)) | (~c3_1(a268)) | (~c2_1(a274)) | (~c1_1(a274)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2092,plain,
% 0.78/0.97 (((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c2_1(a274)) | c2_1(a267) | (~c0_1(a267)) | (~c1_1(a267)) | c2_1(a268) | c1_1(a268) | (~c3_1(a268))) <=> (c3_1(a274) | c1_1(a268) | c2_1(a268) | c2_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c1_1(a267)) | (~c3_1(a268)) | (~c2_1(a274)) | (~c1_1(a274)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2093,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c2_1(a274)) | c2_1(a267) | (~c0_1(a267)) | (~c1_1(a267)) | c2_1(a268) | c1_1(a268) | (~c3_1(a268)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c3_1(a274) | c1_1(a268) | c2_1(a268) | c2_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c1_1(a267)) | (~c3_1(a268)) | (~c2_1(a274)) | (~c1_1(a274))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2092])).
% 0.78/0.97 tff(2094,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c2_1(a274)) | c2_1(a267) | (~c0_1(a267)) | (~c1_1(a267)) | c2_1(a268) | c1_1(a268) | (~c3_1(a268)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a274) | c1_1(a268) | c2_1(a268) | c2_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c1_1(a267)) | (~c3_1(a268)) | (~c2_1(a274)) | (~c1_1(a274)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2093, 2091])).
% 0.78/0.97 tff(2095,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c2_1(a274)) | c2_1(a267) | (~c0_1(a267)) | (~c1_1(a267)) | c2_1(a268) | c1_1(a268) | (~c3_1(a268)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2096,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c3_1(a274) | c1_1(a268) | c2_1(a268) | c2_1(a267) | (~ndr1_0) | (~c0_1(a267)) | (~c1_1(a267)) | (~c3_1(a268)) | (~c2_1(a274)) | (~c1_1(a274))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 0.78/0.97 tff(2097,plain,
% 0.78/0.97 (~c1_1(a267)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2096, 142, 2027, 2090, 2082, 2026, 2081, 2075, 2040, 2038, 2028])).
% 0.78/0.97 tff(2098,plain,
% 0.78/0.97 (c2_1(a280)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[269, 2047])).
% 0.78/0.97 tff(2099,plain,
% 0.78/0.97 (hskp8),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[1973, 142, 1890, 1882, 2098, 2049, 1874, 2048, 1196])).
% 0.78/0.97 tff(2100,plain,
% 0.78/0.97 (~c3_1(a275)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[368, 2099])).
% 0.78/0.97 tff(2101,plain,
% 0.78/0.97 (~c2_1(a275)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[374, 2099])).
% 0.78/0.97 tff(2102,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a313) | c3_1(a313) | c2_1(a275) | c3_1(a275) | c2_1(a267) | (~ndr1_0) | (~c0_1(a267)) | c1_1(a267) | (~c1_1(a275)) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a313) | c3_1(a313) | c2_1(a275) | c3_1(a275) | c2_1(a267) | (~ndr1_0) | (~c0_1(a267)) | c1_1(a267) | (~c1_1(a275)) | (~c0_1(a313)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2103,plain,
% 0.78/0.97 (((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a267) | c1_1(a267) | (~c0_1(a267))) <=> (c2_1(a313) | c3_1(a313) | c2_1(a275) | c3_1(a275) | c2_1(a267) | (~ndr1_0) | (~c0_1(a267)) | c1_1(a267) | (~c1_1(a275)) | (~c0_1(a313)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2104,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a267) | c1_1(a267) | (~c0_1(a267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a313) | c3_1(a313) | c2_1(a275) | c3_1(a275) | c2_1(a267) | (~ndr1_0) | (~c0_1(a267)) | c1_1(a267) | (~c1_1(a275)) | (~c0_1(a313))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2103])).
% 0.78/0.97 tff(2105,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a267) | c1_1(a267) | (~c0_1(a267)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a313) | c3_1(a313) | c2_1(a275) | c3_1(a275) | c2_1(a267) | (~ndr1_0) | (~c0_1(a267)) | c1_1(a267) | (~c1_1(a275)) | (~c0_1(a313)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2104, 2102])).
% 0.78/0.97 tff(2106,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a267) | c1_1(a267) | (~c0_1(a267)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2107,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a313) | c3_1(a313) | c2_1(a275) | c3_1(a275) | c2_1(a267) | (~ndr1_0) | (~c0_1(a267)) | c1_1(a267) | (~c1_1(a275)) | (~c0_1(a313))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 0.78/0.97 tff(2108,plain,
% 0.78/0.97 (~c1_1(a275)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2107, 142, 2082, 2043, 2042, 2101, 2100, 2040, 505, 2045, 2097])).
% 0.78/0.97 tff(2109,plain,
% 0.78/0.97 (~c0_1(a275)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[380, 2099])).
% 0.78/0.97 tff(2110,plain,
% 0.78/0.97 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(2111,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[2110])).
% 0.78/0.97 tff(2112,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2113,plain,
% 0.78/0.97 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(2114,plain,
% 0.78/0.97 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[2113])).
% 0.78/0.97 tff(2115,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 0.78/0.97 tff(2116,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2115, 2114])).
% 0.78/0.97 tff(2117,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2116, 2112])).
% 0.78/0.97 tff(2118,plain,(
% 0.78/0.97 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.97 inference(skolemize,[status(sab)],[2117])).
% 0.78/0.97 tff(2119,plain,
% 0.78/0.97 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2118, 2111])).
% 0.78/0.97 tff(2120,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a280) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)) | (~c3_1(a280)) | (~c0_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a280) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2121,plain,
% 0.78/0.97 ((hskp21 | (~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c2_1(a274)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280))) <=> (hskp21 | c1_1(a280) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2122,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c2_1(a274)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c1_1(a280) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)) | (~c3_1(a280)) | (~c0_1(a280))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2121])).
% 0.78/0.97 tff(2123,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c2_1(a274)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a280) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2122, 2120])).
% 0.78/0.97 tff(2124,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c2_1(a274)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2125,plain,
% 0.78/0.97 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c1_1(a280) | c3_1(a274) | (~ndr1_0) | (~c2_1(a274)) | (~c1_1(a274)) | (~c3_1(a280)) | (~c0_1(a280))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2124, 2123])).
% 0.78/0.97 tff(2126,plain,
% 0.78/0.97 (hskp21 | (~c0_1(a280))),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2125, 142, 2049, 2027, 2048, 2026, 2119, 2028])).
% 0.78/0.97 tff(2127,plain,
% 0.78/0.97 (hskp21),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2126, 2051])).
% 0.78/0.97 tff(2128,plain,
% 0.78/0.97 (((~hskp21) | (~c1_1(a307))) <=> ((~hskp21) | (~c1_1(a307)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2129,plain,
% 0.78/0.97 (((~c1_1(a307)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a307)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2130,axiom,((~c1_1(a307)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.78/0.97 tff(2131,plain,
% 0.78/0.97 ((~hskp21) | (~c1_1(a307))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2130, 2129])).
% 0.78/0.97 tff(2132,plain,
% 0.78/0.97 ((~hskp21) | (~c1_1(a307))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2131, 2128])).
% 0.78/0.97 tff(2133,plain,
% 0.78/0.97 (~c1_1(a307)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2132, 2127])).
% 0.78/0.97 tff(2134,plain,
% 0.78/0.97 (((~hskp21) | c2_1(a307)) <=> ((~hskp21) | c2_1(a307))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2135,axiom,((~hskp21) | c2_1(a307)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.78/0.97 tff(2136,plain,
% 0.78/0.97 ((~hskp21) | c2_1(a307)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2135, 2134])).
% 0.78/0.97 tff(2137,plain,
% 0.78/0.97 ((~hskp21) | c2_1(a307)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2136, 2134])).
% 0.78/0.97 tff(2138,plain,
% 0.78/0.97 ((~hskp21) | c2_1(a307)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2137, 2134])).
% 0.78/0.97 tff(2139,plain,
% 0.78/0.97 ((~hskp21) | c2_1(a307)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2138, 2134])).
% 0.78/0.97 tff(2140,plain,
% 0.78/0.97 ((~hskp21) | c2_1(a307)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2139, 2134])).
% 0.78/0.97 tff(2141,plain,
% 0.78/0.97 (c2_1(a307)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2140, 2127])).
% 0.78/0.97 tff(2142,plain,
% 0.78/0.97 (((~hskp21) | c0_1(a307)) <=> ((~hskp21) | c0_1(a307))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2143,axiom,((~hskp21) | c0_1(a307)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.78/0.97 tff(2144,plain,
% 0.78/0.97 ((~hskp21) | c0_1(a307)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2143, 2142])).
% 0.78/0.97 tff(2145,plain,
% 0.78/0.97 ((~hskp21) | c0_1(a307)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2144, 2142])).
% 0.78/0.97 tff(2146,plain,
% 0.78/0.97 ((~hskp21) | c0_1(a307)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2145, 2142])).
% 0.78/0.97 tff(2147,plain,
% 0.78/0.97 ((~hskp21) | c0_1(a307)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2146, 2142])).
% 0.78/0.97 tff(2148,plain,
% 0.78/0.97 ((~hskp21) | c0_1(a307)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2147, 2142])).
% 0.78/0.97 tff(2149,plain,
% 0.78/0.97 (c0_1(a307)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2148, 2127])).
% 0.78/0.97 tff(2150,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a307) | c0_1(a275) | c2_1(a275) | (~ndr1_0) | c1_1(a275) | (~c2_1(a307)) | (~c0_1(a307)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a307) | c0_1(a275) | c2_1(a275) | (~ndr1_0) | c1_1(a275) | (~c2_1(a307)) | (~c0_1(a307)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2151,plain,
% 0.78/0.97 (((~ndr1_0) | c1_1(a307) | (~c2_1(a307)) | (~c0_1(a307)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a275) | c1_1(a275) | c0_1(a275)) <=> (c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a307) | c0_1(a275) | c2_1(a275) | (~ndr1_0) | c1_1(a275) | (~c2_1(a307)) | (~c0_1(a307)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2152,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a307) | (~c2_1(a307)) | (~c0_1(a307)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a275) | c1_1(a275) | c0_1(a275))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a307) | c0_1(a275) | c2_1(a275) | (~ndr1_0) | c1_1(a275) | (~c2_1(a307)) | (~c0_1(a307))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2151])).
% 0.78/0.97 tff(2153,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a307) | (~c2_1(a307)) | (~c0_1(a307)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a275) | c1_1(a275) | c0_1(a275))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a307) | c0_1(a275) | c2_1(a275) | (~ndr1_0) | c1_1(a275) | (~c2_1(a307)) | (~c0_1(a307)))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2152, 2150])).
% 0.78/0.97 tff(2154,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a307) | (~c2_1(a307)) | (~c0_1(a307)) | c3_1(a313) | c1_1(a313) | c2_1(a313) | c2_1(a275) | c1_1(a275) | c0_1(a275))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2155,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c1_1(a307) | c0_1(a275) | c2_1(a275) | (~ndr1_0) | c1_1(a275) | (~c2_1(a307)) | (~c0_1(a307))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 0.78/0.97 tff(2156,plain,
% 0.78/0.97 ($false),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2155, 142, 2149, 2141, 2044, 2043, 2042, 2133, 2109, 2101, 645, 2108])).
% 0.78/0.97 tff(2157,plain,(hskp2 | c1_1(a269) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.97 tff(2158,plain,
% 0.78/0.97 (hskp2),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2157, 714, 30])).
% 0.78/0.97 tff(2159,plain,
% 0.78/0.97 (c0_1(a269)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[877, 2158])).
% 0.78/0.97 tff(2160,assumption,(~c3_1(a293)), introduced(assumption)).
% 0.78/0.97 tff(2161,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a293) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a293) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2162,plain,
% 0.78/0.97 (((~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | c3_1(a293) | c3_1(a293) | c2_1(a293) | (~c0_1(a293)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269))) <=> (c2_1(a293) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2163,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | c3_1(a293) | c3_1(a293) | c2_1(a293) | (~c0_1(a293)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a293) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293)))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2162])).
% 0.78/0.97 tff(2164,plain,
% 0.78/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | c3_1(a293) | c3_1(a293) | c2_1(a293) | (~c0_1(a293)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a293) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293))),
% 0.78/0.97 inference(transitivity,[status(thm)],[2163, 2161])).
% 0.78/0.97 tff(2165,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | c3_1(a293) | c3_1(a293) | c2_1(a293) | (~c0_1(a293)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))),
% 0.78/0.97 inference(quant_inst,[status(thm)],[])).
% 0.78/0.97 tff(2166,plain,
% 0.78/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a293) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a293)) | (~c0_1(a293)) | c3_1(a293)),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 0.78/0.97 tff(2167,plain,
% 0.78/0.97 ($false),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2166, 142, 1890, 1882, 2159, 1874, 714, 30, 505, 2160])).
% 0.78/0.97 tff(2168,plain,(c3_1(a293) | c1_1(a269) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.97 tff(2169,plain,
% 0.78/0.97 (c3_1(a293)),
% 0.78/0.97 inference(unit_resolution,[status(thm)],[2168, 714, 30])).
% 0.78/0.97 tff(2170,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | c2_1(a293) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a293)) | (~c3_1(a293)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c2_1(a293) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a293)) | (~c3_1(a293)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2171,plain,
% 0.78/0.97 ((hskp7 | (~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | (~c3_1(a293)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269))) <=> (hskp7 | c2_1(a293) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a293)) | (~c3_1(a293)))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(2172,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | (~c3_1(a293)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | c2_1(a293) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a293)) | (~c3_1(a293))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[2171])).
% 0.78/0.97 tff(2173,plain,
% 0.78/0.97 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | (~c3_1(a293)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c2_1(a293) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a293)) | (~c3_1(a293)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[2172, 2170])).
% 0.78/0.98 tff(2174,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | (~c3_1(a293)) | c1_1(a269) | c2_1(a269) | (~c0_1(a269)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2175,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c2_1(a293) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c0_1(a269)) | (~c1_1(a293)) | (~c3_1(a293))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2174, 2173])).
% 0.78/0.98 tff(2176,plain,
% 0.78/0.98 (hskp7 | (~c0_1(a269)) | (~c3_1(a293))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2175, 142, 1882, 1874, 714, 30, 618])).
% 0.78/0.98 tff(2177,plain,
% 0.78/0.98 (hskp7),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2176, 2169, 2159])).
% 0.78/0.98 tff(2178,plain,
% 0.78/0.98 (c0_1(a274)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[397, 2177])).
% 0.78/0.98 tff(2179,plain,
% 0.78/0.98 (~c3_1(a274)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[69, 2177])).
% 0.78/0.98 tff(2180,plain,
% 0.78/0.98 (c1_1(a274)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[77, 2177])).
% 0.78/0.98 tff(2181,plain,
% 0.78/0.98 (c2_1(a274)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1005, 2180, 30, 2159, 2179, 714, 2178])).
% 0.78/0.98 tff(2182,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a293) | c3_1(a274) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c2_1(a274)) | (~c1_1(a274)) | (~c1_1(a293)) | (~c0_1(a293)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a293) | c3_1(a274) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c2_1(a274)) | (~c1_1(a274)) | (~c1_1(a293)) | (~c0_1(a293)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2183,plain,
% 0.78/0.98 (((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c2_1(a274)) | c2_1(a293) | (~c0_1(a293)) | (~c1_1(a293)) | c2_1(a269) | c1_1(a269) | (~c3_1(a269))) <=> (c2_1(a293) | c3_1(a274) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c2_1(a274)) | (~c1_1(a274)) | (~c1_1(a293)) | (~c0_1(a293)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2184,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c2_1(a274)) | c2_1(a293) | (~c0_1(a293)) | (~c1_1(a293)) | c2_1(a269) | c1_1(a269) | (~c3_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a293) | c3_1(a274) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c2_1(a274)) | (~c1_1(a274)) | (~c1_1(a293)) | (~c0_1(a293))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[2183])).
% 0.78/0.98 tff(2185,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c2_1(a274)) | c2_1(a293) | (~c0_1(a293)) | (~c1_1(a293)) | c2_1(a269) | c1_1(a269) | (~c3_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a293) | c3_1(a274) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c2_1(a274)) | (~c1_1(a274)) | (~c1_1(a293)) | (~c0_1(a293)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[2184, 2182])).
% 0.78/0.98 tff(2186,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a274)) | c3_1(a274) | (~c2_1(a274)) | c2_1(a293) | (~c0_1(a293)) | (~c1_1(a293)) | c2_1(a269) | c1_1(a269) | (~c3_1(a269)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2187,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a293) | c3_1(a274) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | (~c3_1(a269)) | (~c2_1(a274)) | (~c1_1(a274)) | (~c1_1(a293)) | (~c0_1(a293))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2186, 2185])).
% 0.78/0.98 tff(2188,plain,
% 0.78/0.98 (~c3_1(a269)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2187, 142, 1890, 1882, 2180, 1874, 2179, 714, 30, 2038, 2181])).
% 0.78/0.98 tff(2189,plain,
% 0.78/0.98 (hskp9),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1590, 2159, 30, 714])).
% 0.78/0.98 tff(2190,plain,
% 0.78/0.98 (~c1_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[236, 2189])).
% 0.78/0.98 tff(2191,plain,
% 0.78/0.98 (c3_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[244, 2189])).
% 0.78/0.98 tff(2192,plain,
% 0.78/0.98 (c2_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[269, 2189])).
% 0.78/0.98 tff(2193,plain,
% 0.78/0.98 (hskp8),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1973, 142, 1890, 1882, 2192, 2191, 1874, 2190, 1196])).
% 0.78/0.98 tff(2194,plain,
% 0.78/0.98 (~c3_1(a275)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[368, 2193])).
% 0.78/0.98 tff(2195,plain,
% 0.78/0.98 (~c2_1(a275)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[374, 2193])).
% 0.78/0.98 tff(2196,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a275) | c3_1(a275) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)) | (~c1_1(a275)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a275) | c3_1(a275) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)) | (~c1_1(a275)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2197,plain,
% 0.78/0.98 (((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a269) | c2_1(a269) | (~c0_1(a269)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269))) <=> (c2_1(a275) | c3_1(a275) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)) | (~c1_1(a275)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2198,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a269) | c2_1(a269) | (~c0_1(a269)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a275) | c3_1(a275) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)) | (~c1_1(a275))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[2197])).
% 0.78/0.98 tff(2199,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a269) | c2_1(a269) | (~c0_1(a269)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a275) | c3_1(a275) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)) | (~c1_1(a275)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[2198, 2196])).
% 0.78/0.98 tff(2200,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a275) | (~c1_1(a275)) | c3_1(a275) | c3_1(a269) | c2_1(a269) | (~c0_1(a269)) | c2_1(a269) | c1_1(a269) | (~c0_1(a269)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2201,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a275) | c3_1(a275) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | (~c0_1(a269)) | (~c1_1(a275))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2200, 2199])).
% 0.78/0.98 tff(2202,plain,
% 0.78/0.98 (~c1_1(a275)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2201, 142, 2159, 2195, 2194, 714, 30, 505, 2188])).
% 0.78/0.98 tff(2203,plain,
% 0.78/0.98 (~c0_1(a275)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[380, 2193])).
% 0.78/0.98 tff(2204,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a280) | c0_1(a275) | c2_1(a275) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | c1_1(a275) | (~c2_1(a280)) | (~c0_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a280) | c0_1(a275) | c2_1(a275) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | c1_1(a275) | (~c2_1(a280)) | (~c0_1(a280)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2205,plain,
% 0.78/0.98 (((~ndr1_0) | c1_1(a280) | (~c2_1(a280)) | (~c0_1(a280)) | c3_1(a269) | c1_1(a269) | c2_1(a269) | c2_1(a275) | c1_1(a275) | c0_1(a275)) <=> (c1_1(a280) | c0_1(a275) | c2_1(a275) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | c1_1(a275) | (~c2_1(a280)) | (~c0_1(a280)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2206,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a280) | (~c2_1(a280)) | (~c0_1(a280)) | c3_1(a269) | c1_1(a269) | c2_1(a269) | c2_1(a275) | c1_1(a275) | c0_1(a275))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a280) | c0_1(a275) | c2_1(a275) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | c1_1(a275) | (~c2_1(a280)) | (~c0_1(a280))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[2205])).
% 0.78/0.98 tff(2207,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a280) | (~c2_1(a280)) | (~c0_1(a280)) | c3_1(a269) | c1_1(a269) | c2_1(a269) | c2_1(a275) | c1_1(a275) | c0_1(a275))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a280) | c0_1(a275) | c2_1(a275) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | c1_1(a275) | (~c2_1(a280)) | (~c0_1(a280)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[2206, 2204])).
% 0.78/0.98 tff(2208,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a280) | (~c2_1(a280)) | (~c0_1(a280)) | c3_1(a269) | c1_1(a269) | c2_1(a269) | c2_1(a275) | c1_1(a275) | c0_1(a275))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2209,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a280) | c0_1(a275) | c2_1(a275) | c1_1(a269) | c2_1(a269) | (~ndr1_0) | c3_1(a269) | c1_1(a275) | (~c2_1(a280)) | (~c0_1(a280))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2208, 2207])).
% 0.78/0.98 tff(2210,plain,
% 0.78/0.98 (~c0_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2209, 142, 2192, 2190, 2203, 2195, 714, 30, 645, 2188, 2202])).
% 0.78/0.98 tff(2211,plain,
% 0.78/0.98 (hskp5 | c3_1(a269) | c0_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1617, 142, 2192, 2159, 2190, 30, 1610])).
% 0.78/0.98 tff(2212,plain,
% 0.78/0.98 (hskp5),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2211, 2210, 2188])).
% 0.78/0.98 tff(2213,plain,
% 0.78/0.98 (~c3_1(a272)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[587, 2212])).
% 0.78/0.98 tff(2214,plain,
% 0.78/0.98 (~c1_1(a272)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[593, 2212])).
% 0.78/0.98 tff(2215,plain,
% 0.78/0.98 (hskp6 | c0_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1083, 142, 2191, 2178, 2180, 2190, 1016, 2181])).
% 0.78/0.98 tff(2216,plain,
% 0.78/0.98 (hskp6),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2215, 2210])).
% 0.78/0.98 tff(2217,plain,
% 0.78/0.98 (c0_1(a272)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[601, 2212])).
% 0.78/0.98 tff(2218,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1069, 2217, 2216, 2181, 2179, 2214, 2213, 2178])).
% 0.78/0.98 tff(2219,plain,(c1_1(a269) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2220,plain,
% 0.78/0.98 (c1_1(a269)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2219, 30])).
% 0.78/0.98 tff(2221,plain,
% 0.78/0.98 (~c0_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[812, 750, 30, 749])).
% 0.78/0.98 tff(2222,plain,
% 0.78/0.98 (hskp3),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[276, 142, 762, 761, 760, 262, 2221])).
% 0.78/0.98 tff(2223,plain,
% 0.78/0.98 (~c2_1(a270)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[282, 2222])).
% 0.78/0.98 tff(2224,plain,
% 0.78/0.98 (c0_1(a270)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[345, 2222])).
% 0.78/0.98 tff(2225,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c1_1(a280) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a280)) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a280) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2226,plain,
% 0.78/0.98 ((hskp8 | (~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280))) <=> (hskp8 | c1_1(a280) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2227,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | c1_1(a280) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a280)) | (~c3_1(a280))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[2226])).
% 0.78/0.98 tff(2228,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a280) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[2227, 2225])).
% 0.78/0.98 tff(2229,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c0_1(a270)) | c1_1(a280) | (~c2_1(a280)) | (~c3_1(a280)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2230,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | c1_1(a280) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c0_1(a270)) | (~c2_1(a280)) | (~c3_1(a280))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2229, 2228])).
% 0.78/0.98 tff(2231,plain,
% 0.78/0.98 (~c1_1(a270)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2230, 142, 32, 762, 761, 2224, 760, 2223, 1196])).
% 0.78/0.98 tff(2232,plain,
% 0.78/0.98 (c3_1(a270)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[290, 2222])).
% 0.78/0.98 tff(2233,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[297, 142, 32, 2232, 2223, 107, 2231])).
% 0.78/0.98 tff(2234,plain,(c0_1(a269) | hskp8 | c2_1(a269) | (~c1_1(a269))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2235,plain,
% 0.78/0.98 (hskp8),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2234, 750, 30, 2220])).
% 0.78/0.98 tff(2236,plain,
% 0.78/0.98 (~c3_1(a275)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[368, 2235])).
% 0.78/0.98 tff(2237,plain,
% 0.78/0.98 (~c2_1(a275)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[374, 2235])).
% 0.78/0.98 tff(2238,plain,
% 0.78/0.98 (~c0_1(a275)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[380, 2235])).
% 0.78/0.98 tff(2239,plain,
% 0.78/0.98 (~hskp2),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[834, 2220])).
% 0.78/0.98 tff(2240,plain,
% 0.78/0.98 (c1_1(a275)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[904, 142, 2239, 2238, 2237, 2236, 10])).
% 0.78/0.98 tff(2241,plain,
% 0.78/0.98 (hskp7),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[837, 1995, 2220, 30, 1993, 750, 1994])).
% 0.78/0.98 tff(2242,plain,
% 0.78/0.98 (~c3_1(a274)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[69, 2241])).
% 0.78/0.98 tff(2243,plain,
% 0.78/0.98 (c0_1(a274)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[397, 2241])).
% 0.78/0.98 tff(2244,plain,
% 0.78/0.98 (c1_1(a274)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[77, 2241])).
% 0.78/0.98 tff(2245,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[995, 2244, 2243, 30, 1994, 1995, 2242, 750, 1993])).
% 0.78/0.98 tff(2246,plain,((~hskp5) | c2_1(a269) | c0_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2247,plain,
% 0.78/0.98 (~hskp5),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2246, 750, 30])).
% 0.78/0.98 tff(2248,plain,
% 0.78/0.98 (~c0_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[812, 750, 30, 2220])).
% 0.78/0.98 tff(2249,plain,
% 0.78/0.98 (hskp9),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[758, 750, 2220])).
% 0.78/0.98 tff(2250,plain,
% 0.78/0.98 (~c1_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[236, 2249])).
% 0.78/0.98 tff(2251,plain,
% 0.78/0.98 (c2_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[269, 2249])).
% 0.78/0.98 tff(2252,plain,
% 0.78/0.98 (hskp5 | c3_1(a293)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1947, 142, 1890, 2251, 1874, 2250, 1610, 2248])).
% 0.78/0.98 tff(2253,plain,
% 0.78/0.98 (c3_1(a293)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2252, 2247])).
% 0.78/0.98 tff(2254,plain,
% 0.78/0.98 (hskp23),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1897, 2253])).
% 0.78/0.98 tff(2255,plain,
% 0.78/0.98 (~c3_1(a313)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[16, 2254])).
% 0.78/0.98 tff(2256,plain,
% 0.78/0.98 (~c2_1(a313)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[22, 2254])).
% 0.78/0.98 tff(2257,plain,
% 0.78/0.98 (~c1_1(a313)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[28, 2254])).
% 0.78/0.98 tff(2258,plain,
% 0.78/0.98 (~c0_1(a313)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[941, 142, 2257, 2256, 2255, 2237, 2236, 505, 2240])).
% 0.78/0.98 tff(2259,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[492, 142, 2239, 2257, 2256, 2255, 10, 2258])).
% 0.78/0.98 tff(2260,plain,(c0_1(a269) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2261,plain,
% 0.78/0.98 (c0_1(a269)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2260, 30])).
% 0.78/0.98 tff(2262,plain,
% 0.78/0.98 (hskp30),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1301, 32, 2261, 30, 2220])).
% 0.78/0.98 tff(2263,plain,
% 0.78/0.98 (c3_1(a337)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1409, 2262])).
% 0.78/0.98 tff(2264,plain,
% 0.78/0.98 (c2_1(a337)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1417, 2262])).
% 0.78/0.98 tff(2265,assumption,(~c1_1(a337)), introduced(assumption)).
% 0.78/0.98 tff(2266,plain,
% 0.78/0.98 (c0_1(a269)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2234, 30, 32, 749])).
% 0.78/0.98 tff(2267,assumption,(c3_1(a337)), introduced(assumption)).
% 0.78/0.98 tff(2268,assumption,(c2_1(a337)), introduced(assumption)).
% 0.78/0.98 tff(2269,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | c1_1(a337) | (~c3_1(a337)) | (~c2_1(a337)) | (~c0_1(a269)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | c1_1(a337) | (~c3_1(a337)) | (~c2_1(a337)) | (~c0_1(a269)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2270,plain,
% 0.78/0.98 ((hskp8 | (~ndr1_0) | c2_1(a269) | (~c1_1(a269)) | (~c0_1(a269)) | c1_1(a337) | (~c2_1(a337)) | (~c3_1(a337))) <=> (hskp8 | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | c1_1(a337) | (~c3_1(a337)) | (~c2_1(a337)) | (~c0_1(a269)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2271,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a269) | (~c1_1(a269)) | (~c0_1(a269)) | c1_1(a337) | (~c2_1(a337)) | (~c3_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | c1_1(a337) | (~c3_1(a337)) | (~c2_1(a337)) | (~c0_1(a269))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[2270])).
% 0.78/0.98 tff(2272,plain,
% 0.78/0.98 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a269) | (~c1_1(a269)) | (~c0_1(a269)) | c1_1(a337) | (~c2_1(a337)) | (~c3_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | c1_1(a337) | (~c3_1(a337)) | (~c2_1(a337)) | (~c0_1(a269)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[2271, 2269])).
% 0.78/0.98 tff(2273,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a269) | (~c1_1(a269)) | (~c0_1(a269)) | c1_1(a337) | (~c2_1(a337)) | (~c3_1(a337)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2274,plain,
% 0.78/0.98 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp8 | (~c1_1(a269)) | c2_1(a269) | (~ndr1_0) | c1_1(a337) | (~c3_1(a337)) | (~c2_1(a337)) | (~c0_1(a269))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2273, 2272])).
% 0.78/0.98 tff(2275,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2274, 142, 32, 2268, 2267, 2266, 749, 30, 1196, 2265])).
% 0.78/0.98 tff(2276,plain,(c1_1(a337) | hskp8 | (~c2_1(a337)) | (~c3_1(a337)) | (~c1_1(a269)) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2277,plain,
% 0.78/0.98 (c1_1(a337)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2276, 2264, 30, 2263, 2220, 32])).
% 0.78/0.98 tff(2278,plain,
% 0.78/0.98 (hskp4),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[482, 32, 31, 411, 410, 409])).
% 0.78/0.98 tff(2279,plain,
% 0.78/0.98 (~c1_1(a271)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[90, 2278])).
% 0.78/0.98 tff(2280,plain,
% 0.78/0.98 (~c0_1(a271)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[96, 2278])).
% 0.78/0.98 tff(2281,plain,
% 0.78/0.98 (c2_1(a271)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[158, 2280, 32, 2279, 2239])).
% 0.78/0.98 tff(2282,plain,
% 0.78/0.98 (~c3_1(a271)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[84, 2278])).
% 0.78/0.98 tff(2283,plain,
% 0.78/0.98 (hskp14),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[175, 142, 2280, 2282, 169, 2281])).
% 0.78/0.98 tff(2284,plain,
% 0.78/0.98 (~c2_1(a287)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[182, 2283])).
% 0.78/0.98 tff(2285,plain,
% 0.78/0.98 (~c0_1(a287)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[188, 2283])).
% 0.78/0.98 tff(2286,plain,
% 0.78/0.98 (c1_1(a287)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[223, 2283])).
% 0.78/0.98 tff(2287,plain,
% 0.78/0.98 (c0_1(a337)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1662, 2262])).
% 0.78/0.98 tff(2288,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c3_1(a337)) | (~c1_1(a287)) | (~c3_1(a287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c3_1(a337)) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2289,plain,
% 0.78/0.98 (((~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287))) <=> (c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c3_1(a337)) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2290,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c3_1(a337)) | (~c1_1(a287)) | (~c3_1(a287))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[2289])).
% 0.78/0.98 tff(2291,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c3_1(a337)) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[2290, 2288])).
% 0.78/0.98 tff(2292,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(2293,plain,
% 0.78/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c3_1(a337)) | (~c1_1(a287)) | (~c3_1(a287))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 0.78/0.98 tff(2294,plain,
% 0.78/0.98 (~c3_1(a287)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2293, 142, 2287, 2263, 2286, 2285, 2284, 712, 2277])).
% 0.78/0.98 tff(2295,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[195, 142, 2239, 2285, 2284, 2280, 2279, 2282, 10, 2294])).
% 0.78/0.98 tff(2296,plain,(hskp8 | c2_1(a269) | hskp23 | (~c0_1(a274)) | (~c1_1(a274)) | c3_1(a274)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2297,plain,
% 0.78/0.98 ($false),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2296, 1918, 1917, 31, 30, 32, 1916])).
% 0.78/0.98 tff(2298,plain,(hskp8 | hskp23 | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.98 tff(2299,plain,
% 0.78/0.98 (hskp8),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2298, 31, 30])).
% 0.78/0.98 tff(2300,plain,
% 0.78/0.98 (~c0_1(a275)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[380, 2299])).
% 0.78/0.98 tff(2301,plain,
% 0.78/0.98 (~c3_1(a275)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[368, 2299])).
% 0.78/0.98 tff(2302,assumption,(c2_1(a278)), introduced(assumption)).
% 0.78/0.98 tff(2303,plain,
% 0.78/0.98 (hskp8 | hskp7),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1913, 142, 446, 445, 570, 2302])).
% 0.78/0.98 tff(2304,plain,
% 0.78/0.98 (hskp8),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2303, 560])).
% 0.78/0.98 tff(2305,plain,
% 0.78/0.98 (~c2_1(a275)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[374, 2304])).
% 0.78/0.98 tff(2306,plain,
% 0.78/0.98 (c1_1(a275)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[904, 142, 54, 1720, 2305, 1719, 10])).
% 0.78/0.98 tff(2307,plain,
% 0.78/0.98 (hskp9 | c2_1(a275) | (~c1_1(a275))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[1313, 142, 1720, 216])).
% 0.78/0.98 tff(2308,plain,
% 0.78/0.98 (hskp9),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[2307, 2306, 2305])).
% 0.78/0.98 tff(2309,plain,
% 0.78/0.98 (~c1_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[236, 2308])).
% 0.78/0.98 tff(2310,plain,
% 0.78/0.98 (c3_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[244, 2308])).
% 0.78/0.98 tff(2311,plain,
% 0.78/0.98 (c2_1(a280)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[269, 2308])).
% 0.78/0.98 tff(2312,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a280) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a280) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2313,plain,
% 0.78/0.98 (((~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c1_1(a280) | (~c0_1(a280)) | (~c2_1(a280))) <=> (c1_1(a280) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(2314,plain,
% 0.78/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c1_1(a280) | (~c0_1(a280)) | (~c2_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a280) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[2313])).
% 0.78/0.99 tff(2315,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c1_1(a280) | (~c0_1(a280)) | (~c2_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a280) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[2314, 2312])).
% 0.78/0.99 tff(2316,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)) | c1_1(a280) | (~c3_1(a280)) | (~c0_1(a280)) | c1_1(a280) | (~c0_1(a280)) | (~c2_1(a280)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(2317,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a280) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)) | (~c2_1(a280)) | (~c3_1(a280)) | (~c0_1(a280))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[2316, 2315])).
% 0.78/0.99 tff(2318,plain,
% 0.78/0.99 (~c0_1(a280)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2317, 142, 446, 445, 2311, 2310, 2309, 53, 2302])).
% 0.78/0.99 tff(2319,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a280) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c0_1(a280) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a280) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c0_1(a280) | (~c3_1(a280)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2320,plain,
% 0.78/0.99 ((hskp6 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c1_1(a280) | c0_1(a280) | (~c3_1(a280))) <=> (hskp6 | c1_1(a280) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c0_1(a280) | (~c3_1(a280)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2321,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c1_1(a280) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c0_1(a280) | (~c3_1(a280))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[2320])).
% 0.78/0.99 tff(2322,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a280) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c0_1(a280) | (~c3_1(a280)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[2321, 2319])).
% 0.78/0.99 tff(2323,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c1_1(a280) | c0_1(a280) | (~c3_1(a280)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(2324,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c1_1(a280) | (~ndr1_0) | (~c1_1(a278)) | (~c2_1(a278)) | (~c0_1(a278)) | c0_1(a280) | (~c3_1(a280))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[2323, 2322])).
% 0.78/0.99 tff(2325,plain,
% 0.78/0.99 (hskp6),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2324, 142, 447, 446, 2310, 2309, 1016, 2318, 2302])).
% 0.78/0.99 tff(2326,plain,
% 0.78/0.99 (~c0_1(a273)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1044, 2325])).
% 0.78/0.99 tff(2327,plain,
% 0.78/0.99 (c1_1(a273)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1060, 2325])).
% 0.78/0.99 tff(2328,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a293) | c1_1(a280) | c0_1(a273) | (~ndr1_0) | (~c1_1(a273)) | (~c3_1(a273)) | c0_1(a280) | (~c2_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a293) | c1_1(a280) | c0_1(a273) | (~ndr1_0) | (~c1_1(a273)) | (~c3_1(a273)) | c0_1(a280) | (~c2_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2329,plain,
% 0.78/0.99 (((~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | (~c0_1(a293)) | c0_1(a273) | (~c3_1(a273)) | (~c1_1(a273)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280))) <=> (c2_1(a293) | c1_1(a280) | c0_1(a273) | (~ndr1_0) | (~c1_1(a273)) | (~c3_1(a273)) | c0_1(a280) | (~c2_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2330,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | (~c0_1(a293)) | c0_1(a273) | (~c3_1(a273)) | (~c1_1(a273)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a293) | c1_1(a280) | c0_1(a273) | (~ndr1_0) | (~c1_1(a273)) | (~c3_1(a273)) | c0_1(a280) | (~c2_1(a280)) | (~c1_1(a293)) | (~c0_1(a293))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[2329])).
% 0.78/0.99 tff(2331,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | (~c0_1(a293)) | c0_1(a273) | (~c3_1(a273)) | (~c1_1(a273)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a293) | c1_1(a280) | c0_1(a273) | (~ndr1_0) | (~c1_1(a273)) | (~c3_1(a273)) | c0_1(a280) | (~c2_1(a280)) | (~c1_1(a293)) | (~c0_1(a293)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[2330, 2328])).
% 0.78/0.99 tff(2332,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | (~c0_1(a293)) | c0_1(a273) | (~c3_1(a273)) | (~c1_1(a273)) | c1_1(a280) | c0_1(a280) | (~c2_1(a280)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(2333,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a293) | c1_1(a280) | c0_1(a273) | (~ndr1_0) | (~c1_1(a273)) | (~c3_1(a273)) | c0_1(a280) | (~c2_1(a280)) | (~c1_1(a293)) | (~c0_1(a293))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[2332, 2331])).
% 0.78/0.99 tff(2334,plain,
% 0.78/0.99 (~c3_1(a273)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2333, 142, 1890, 1882, 2311, 2327, 1874, 2309, 2326, 308, 2318])).
% 0.78/0.99 tff(2335,plain,
% 0.78/0.99 (hskp3),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[276, 142, 2311, 2310, 2309, 262, 2318])).
% 0.78/0.99 tff(2336,plain,
% 0.78/0.99 (~c2_1(a270)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[282, 2335])).
% 0.78/0.99 tff(2337,plain,
% 0.78/0.99 (c3_1(a270)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[290, 2335])).
% 0.78/0.99 tff(2338,plain,
% 0.78/0.99 (c2_1(a273)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1052, 2325])).
% 0.78/0.99 tff(2339,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a293) | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)) | (~c2_1(a273)) | (~c1_1(a273)) | c3_1(a273) | (~c1_1(a293)) | (~c0_1(a293)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a293) | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)) | (~c2_1(a273)) | (~c1_1(a273)) | c3_1(a273) | (~c1_1(a293)) | (~c0_1(a293)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2340,plain,
% 0.78/0.99 (((~ndr1_0) | (~c1_1(a273)) | c3_1(a273) | (~c2_1(a273)) | c2_1(a293) | (~c0_1(a293)) | (~c1_1(a293)) | c2_1(a270) | c1_1(a270) | (~c3_1(a270))) <=> (c2_1(a293) | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)) | (~c2_1(a273)) | (~c1_1(a273)) | c3_1(a273) | (~c1_1(a293)) | (~c0_1(a293)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2341,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a273)) | c3_1(a273) | (~c2_1(a273)) | c2_1(a293) | (~c0_1(a293)) | (~c1_1(a293)) | c2_1(a270) | c1_1(a270) | (~c3_1(a270)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c2_1(a293) | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)) | (~c2_1(a273)) | (~c1_1(a273)) | c3_1(a273) | (~c1_1(a293)) | (~c0_1(a293))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[2340])).
% 0.78/0.99 tff(2342,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a273)) | c3_1(a273) | (~c2_1(a273)) | c2_1(a293) | (~c0_1(a293)) | (~c1_1(a293)) | c2_1(a270) | c1_1(a270) | (~c3_1(a270)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a293) | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)) | (~c2_1(a273)) | (~c1_1(a273)) | c3_1(a273) | (~c1_1(a293)) | (~c0_1(a293)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[2341, 2339])).
% 0.78/0.99 tff(2343,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a273)) | c3_1(a273) | (~c2_1(a273)) | c2_1(a293) | (~c0_1(a293)) | (~c1_1(a293)) | c2_1(a270) | c1_1(a270) | (~c3_1(a270)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(2344,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | c3_1(U) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c2_1(a293) | c2_1(a270) | (~ndr1_0) | c1_1(a270) | (~c3_1(a270)) | (~c2_1(a273)) | (~c1_1(a273)) | c3_1(a273) | (~c1_1(a293)) | (~c0_1(a293))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 0.78/0.99 tff(2345,plain,
% 0.78/0.99 (c1_1(a270)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2344, 142, 1890, 1882, 2327, 2338, 2337, 1874, 2336, 2038, 2334])).
% 0.78/0.99 tff(2346,plain,
% 0.78/0.99 (hskp5),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1947, 142, 1890, 2311, 1874, 2309, 1610, 2318, 2160])).
% 0.78/0.99 tff(2347,plain,
% 0.78/0.99 (~c3_1(a272)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[587, 2346])).
% 0.78/0.99 tff(2348,plain,
% 0.78/0.99 (~c1_1(a272)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[593, 2346])).
% 0.78/0.99 tff(2349,plain,
% 0.78/0.99 (c0_1(a272)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[601, 2346])).
% 0.78/0.99 tff(2350,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a273) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | (~c2_1(a273)) | (~c1_1(a273)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a273) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | (~c2_1(a273)) | (~c1_1(a273)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2351,plain,
% 0.78/0.99 (((~ndr1_0) | c3_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a272) | c1_1(a272) | (~c0_1(a272)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273))) <=> (c0_1(a273) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | (~c2_1(a273)) | (~c1_1(a273)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2352,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a272) | c1_1(a272) | (~c0_1(a272)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a273) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | (~c2_1(a273)) | (~c1_1(a273))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[2351])).
% 0.78/0.99 tff(2353,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a272) | c1_1(a272) | (~c0_1(a272)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a273) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | (~c2_1(a273)) | (~c1_1(a273)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[2352, 2350])).
% 0.78/0.99 tff(2354,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a272) | (~c2_1(a272)) | (~c0_1(a272)) | c3_1(a272) | c1_1(a272) | (~c0_1(a272)) | c0_1(a273) | (~c2_1(a273)) | (~c1_1(a273)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(2355,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a273) | c1_1(a272) | c3_1(a272) | (~ndr1_0) | (~c0_1(a272)) | (~c2_1(a272)) | (~c2_1(a273)) | (~c1_1(a273))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[2354, 2353])).
% 0.78/0.99 tff(2356,plain,
% 0.78/0.99 (~c2_1(a272)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2355, 142, 2327, 2338, 2349, 2326, 2348, 2347, 1038])).
% 0.78/0.99 tff(2357,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | c1_1(a272) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | c2_1(a272) | (~c0_1(a272)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a272) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | c2_1(a272) | (~c0_1(a272)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2358,plain,
% 0.78/0.99 ((hskp7 | (~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c3_1(a270)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272))) <=> (hskp7 | c1_1(a272) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | c2_1(a272) | (~c0_1(a272)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2359,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c3_1(a270)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | c1_1(a272) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | c2_1(a272) | (~c0_1(a272))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[2358])).
% 0.78/0.99 tff(2360,plain,
% 0.78/0.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c3_1(a270)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a272) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | c2_1(a272) | (~c0_1(a272)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[2359, 2357])).
% 0.78/0.99 tff(2361,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a270) | (~c1_1(a270)) | (~c3_1(a270)) | c1_1(a272) | c2_1(a272) | (~c0_1(a272)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(2362,plain,
% 0.78/0.99 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a272) | c2_1(a270) | (~ndr1_0) | (~c1_1(a270)) | (~c3_1(a270)) | c2_1(a272) | (~c0_1(a272))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[2361, 2360])).
% 0.78/0.99 tff(2363,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2362, 142, 560, 2349, 2337, 2348, 2336, 618, 2356, 2345])).
% 0.78/0.99 tff(2364,plain,(hskp7 | c3_1(a293) | (~c0_1(a278)) | (~c1_1(a278)) | (~c2_1(a278)) | (~c3_1(a278)) | c0_1(a275) | hskp2 | c3_1(a275)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.99 tff(2365,plain,
% 0.78/0.99 (hskp7),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2364, 1720, 1908, 1907, 1910, 1909, 1898, 2239, 1719])).
% 0.78/0.99 tff(2366,plain,
% 0.78/0.99 (~c3_1(a274)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[69, 2365])).
% 0.78/0.99 tff(2367,plain,
% 0.78/0.99 (c1_1(a274)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[77, 2365])).
% 0.78/0.99 tff(2368,plain,
% 0.78/0.99 (c0_1(a274)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[397, 2365])).
% 0.78/0.99 tff(2369,plain,
% 0.78/0.99 (hskp8),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2296, 2368, 31, 30, 2367, 2366])).
% 0.78/0.99 tff(2370,plain,
% 0.78/0.99 (~c2_1(a275)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[374, 2369])).
% 0.78/0.99 tff(2371,plain,
% 0.78/0.99 (c1_1(a275)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[904, 142, 2239, 1720, 2370, 1719, 10])).
% 0.78/0.99 tff(2372,plain,
% 0.78/0.99 (hskp9),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2307, 2371, 2370])).
% 0.78/0.99 tff(2373,plain,
% 0.78/0.99 (~c1_1(a280)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[236, 2372])).
% 0.78/0.99 tff(2374,plain,
% 0.78/0.99 (c3_1(a280)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[244, 2372])).
% 0.78/0.99 tff(2375,plain,
% 0.78/0.99 (c2_1(a280)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[269, 2372])).
% 0.78/0.99 tff(2376,plain,
% 0.78/0.99 (~c0_1(a280)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2317, 142, 1907, 1909, 2375, 2374, 2373, 53, 1910])).
% 0.78/0.99 tff(2377,plain,
% 0.78/0.99 (hskp5),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1947, 142, 1890, 2375, 1874, 2373, 1610, 2376, 1898])).
% 0.78/0.99 tff(2378,plain,
% 0.78/0.99 (c0_1(a272)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[601, 2377])).
% 0.78/0.99 tff(2379,plain,
% 0.78/0.99 (~c1_1(a272)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[593, 2377])).
% 0.78/0.99 tff(2380,plain,
% 0.78/0.99 (c2_1(a272)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[930, 2379, 31, 2367, 2366, 2368, 2378])).
% 0.78/0.99 tff(2381,plain,
% 0.78/0.99 (~c3_1(a272)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[587, 2377])).
% 0.78/0.99 tff(2382,plain,
% 0.78/0.99 (hskp6),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2324, 142, 1908, 1907, 2374, 2373, 1016, 2376, 1910])).
% 0.78/0.99 tff(2383,plain,
% 0.78/0.99 (~c0_1(a273)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1044, 2382])).
% 0.78/0.99 tff(2384,plain,
% 0.78/0.99 (c2_1(a273)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1052, 2382])).
% 0.78/0.99 tff(2385,plain,
% 0.78/0.99 (c1_1(a273)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1060, 2382])).
% 0.78/0.99 tff(2386,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2355, 142, 2385, 2384, 2378, 2383, 2379, 2381, 1038, 2380])).
% 0.78/0.99 tff(2387,plain,(c0_1(a275) | hskp23 | c3_1(a275) | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.99 tff(2388,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2387, 2301, 2300, 31, 30])).
% 0.78/0.99 tff(2389,plain,(hskp23 | c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.99 tff(2390,plain,
% 0.78/0.99 (hskp23),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2389, 30])).
% 0.78/0.99 tff(2391,plain,
% 0.78/0.99 (~c3_1(a313)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[16, 2390])).
% 0.78/0.99 tff(2392,plain,
% 0.78/0.99 (~c2_1(a313)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[22, 2390])).
% 0.78/0.99 tff(2393,plain,
% 0.78/0.99 (~c1_1(a313)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[28, 2390])).
% 0.78/0.99 tff(2394,plain,
% 0.78/0.99 (c0_1(a313)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[492, 142, 2239, 2393, 2392, 2391, 10])).
% 0.78/0.99 tff(2395,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a293) | (~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a293) | (~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a313)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2396,plain,
% 0.78/0.99 (((~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | c3_1(a293) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313))) <=> (c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a293) | (~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a313)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2397,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | c3_1(a293) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a293) | (~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a313))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[2396])).
% 0.78/0.99 tff(2398,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | c3_1(a293) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a293) | (~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a313)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[2397, 2395])).
% 0.78/0.99 tff(2399,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a293) | (~c1_1(a293)) | c3_1(a293) | c3_1(a313) | c2_1(a313) | (~c0_1(a313)) | c2_1(a313) | c1_1(a313) | (~c0_1(a313)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(2400,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | c3_1(U) | c3_1(V) | c2_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a313) | c2_1(a313) | c3_1(a313) | c2_1(a293) | (~ndr1_0) | (~c1_1(a293)) | c3_1(a293) | (~c0_1(a313))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[2399, 2398])).
% 0.78/0.99 tff(2401,plain,
% 0.78/0.99 (c3_1(a293) | (~c0_1(a313))),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2400, 142, 1882, 2393, 2392, 2391, 1874, 505])).
% 0.78/0.99 tff(2402,plain,
% 0.78/0.99 (c3_1(a293)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2401, 2394])).
% 0.78/0.99 tff(2403,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1526, 142, 1563, 1562, 1571, 508, 507, 506, 505, 494])).
% 0.78/0.99 tff(2404,plain,((~hskp25) | c1_1(a313) | c2_1(a313) | c3_1(a313) | (~c0_1(a313))), inference(lemma,lemma(discharge,[]))).
% 0.78/0.99 tff(2405,plain,
% 0.78/0.99 (~hskp25),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2404, 2393, 2392, 2391, 2394])).
% 0.78/0.99 tff(2406,plain,
% 0.78/0.99 (hskp14),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1584, 2405])).
% 0.78/0.99 tff(2407,plain,
% 0.78/0.99 (~c2_1(a287)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[182, 2406])).
% 0.78/0.99 tff(2408,plain,
% 0.78/0.99 (~c0_1(a287)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[188, 2406])).
% 0.78/0.99 tff(2409,plain,
% 0.78/0.99 (c1_1(a287)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[223, 2406])).
% 0.78/0.99 tff(2410,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)) | (~c1_1(a293)) | (~c0_1(a293)) | (~c3_1(a293)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)) | (~c1_1(a293)) | (~c0_1(a293)) | (~c3_1(a293)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2411,plain,
% 0.78/0.99 (((~ndr1_0) | (~c1_1(a293)) | (~c3_1(a293)) | (~c0_1(a293)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287))) <=> (c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)) | (~c1_1(a293)) | (~c0_1(a293)) | (~c3_1(a293)))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(2412,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a293)) | (~c3_1(a293)) | (~c0_1(a293)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)) | (~c1_1(a293)) | (~c0_1(a293)) | (~c3_1(a293))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[2411])).
% 0.78/0.99 tff(2413,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a293)) | (~c3_1(a293)) | (~c0_1(a293)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)) | (~c1_1(a293)) | (~c0_1(a293)) | (~c3_1(a293)))),
% 0.78/0.99 inference(transitivity,[status(thm)],[2412, 2410])).
% 0.78/0.99 tff(2414,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a293)) | (~c3_1(a293)) | (~c0_1(a293)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287)))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(2415,plain,
% 0.78/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a287)) | (~c3_1(a287)) | (~c1_1(a293)) | (~c0_1(a293)) | (~c3_1(a293))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 0.78/0.99 tff(2416,plain,
% 0.78/0.99 (~c3_1(a287)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2415, 142, 1890, 1882, 2409, 2408, 2407, 712, 2402])).
% 0.78/0.99 tff(2417,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1150, 142, 2409, 2393, 2392, 2391, 2407, 505, 2394, 2416])).
% 0.78/0.99 tff(2418,plain,(c2_1(a269)), inference(lemma,lemma(discharge,[]))).
% 0.78/0.99 tff(2419,plain,
% 0.78/0.99 (~hskp2),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1337, 2418])).
% 0.78/0.99 tff(2420,plain,
% 0.78/0.99 (c0_1(a313)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[492, 142, 2419, 29, 23, 17, 10])).
% 0.78/0.99 tff(2421,plain,
% 0.78/0.99 (c3_1(a293) | (~c0_1(a313))),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2400, 142, 1882, 29, 23, 17, 1874, 505])).
% 0.78/0.99 tff(2422,plain,
% 0.78/0.99 (c3_1(a293)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2421, 2420])).
% 0.78/0.99 tff(2423,plain,
% 0.78/0.99 (~hskp25),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2404, 2420, 29, 17, 23])).
% 0.78/0.99 tff(2424,plain,
% 0.78/0.99 (hskp14),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1584, 2423])).
% 0.78/0.99 tff(2425,plain,
% 0.78/0.99 (~c2_1(a287)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[182, 2424])).
% 0.78/0.99 tff(2426,plain,
% 0.78/0.99 (~c0_1(a287)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[188, 2424])).
% 0.78/0.99 tff(2427,plain,
% 0.78/0.99 (c1_1(a287)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[223, 2424])).
% 0.78/0.99 tff(2428,plain,
% 0.78/0.99 (~c3_1(a287)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[2415, 142, 1890, 1882, 2427, 2426, 2425, 712, 2422])).
% 0.78/0.99 tff(2429,plain,
% 0.78/0.99 ($false),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1150, 142, 2427, 29, 23, 17, 2425, 505, 2420, 2428])).
% 0.78/0.99 tff(2430,plain,(~hskp23), inference(lemma,lemma(discharge,[]))).
% 0.78/0.99 tff(2431,plain,
% 0.78/0.99 (~c3_1(a293)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1897, 2430])).
% 0.78/0.99 tff(2432,plain,
% 0.78/0.99 (hskp28),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[1905, 2430, 2431])).
% 0.78/0.99 tff(2433,plain,
% 0.78/0.99 (c1_1(a278)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[426, 2432])).
% 0.78/0.99 tff(2434,plain,
% 0.78/0.99 (c0_1(a278)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[434, 2432])).
% 0.78/0.99 tff(2435,plain,
% 0.78/0.99 (c3_1(a278)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[442, 2432])).
% 0.78/0.99 tff(2436,plain,
% 0.78/0.99 (c2_1(a278)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[455, 2435, 2434, 2433, 2430])).
% 0.78/0.99 tff(2437,plain,
% 0.78/0.99 (hskp4),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[482, 1917, 31, 32, 1918, 1916])).
% 0.78/0.99 tff(2438,plain,
% 0.78/0.99 (~c1_1(a271)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[90, 2437])).
% 0.78/0.99 tff(2439,plain,
% 0.78/0.99 (~c0_1(a271)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[96, 2437])).
% 0.78/0.99 tff(2440,plain,
% 0.78/0.99 (c2_1(a271)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[158, 2439, 32, 2438, 2419])).
% 0.78/0.99 tff(2441,plain,
% 0.78/0.99 (~c3_1(a271)),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[84, 2437])).
% 0.78/0.99 tff(2442,plain,
% 0.78/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a287)) | (~c3_1(a287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(2443,plain,
% 0.78/1.00 (((~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287))) <=> (c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(2444,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a287)) | (~c3_1(a287))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[2443])).
% 0.78/1.00 tff(2445,plain,
% 0.78/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a287)) | (~c3_1(a287)))),
% 0.78/1.00 inference(transitivity,[status(thm)],[2444, 2442])).
% 0.78/1.00 tff(2446,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | c0_1(a287) | (~c3_1(a287)) | (~c1_1(a287)) | c2_1(a287) | c0_1(a287) | (~c3_1(a287)))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(2447,plain,
% 0.78/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a287) | c2_1(a287) | (~ndr1_0) | (~c1_1(a278)) | (~c3_1(a278)) | (~c0_1(a278)) | (~c1_1(a287)) | (~c3_1(a287))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[2446, 2445])).
% 0.78/1.00 tff(2448,plain,
% 0.78/1.00 (~c3_1(a287)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[2447, 142, 447, 446, 445, 1137, 1136, 1135, 712])).
% 0.78/1.00 tff(2449,plain,
% 0.78/1.00 ($false),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[195, 142, 2419, 1136, 1135, 110, 109, 108, 10, 2448])).
% 0.78/1.00 tff(2450,plain,((~hskp14) | c0_1(a271) | c1_1(a271) | c3_1(a271) | (~c0_1(a278)) | (~c1_1(a278)) | (~c3_1(a278))), inference(lemma,lemma(discharge,[]))).
% 0.78/1.00 tff(2451,plain,
% 0.78/1.00 (~hskp14),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[2450, 2439, 2438, 2441, 1908, 1907, 1909])).
% 0.78/1.00 tff(2452,plain,
% 0.78/1.00 ($false),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[175, 142, 2451, 2439, 2441, 169, 2440])).
% 0.78/1.00 tff(2453,plain,(hskp8 | hskp23), inference(lemma,lemma(discharge,[]))).
% 0.78/1.00 tff(2454,plain,
% 0.78/1.00 (hskp8),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[2453, 2430])).
% 0.78/1.00 tff(2455,plain,
% 0.78/1.00 (~c3_1(a275)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[368, 2454])).
% 0.78/1.00 tff(2456,plain,
% 0.78/1.00 (~c2_1(a275)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[374, 2454])).
% 0.78/1.00 tff(2457,plain,
% 0.78/1.00 (~c0_1(a275)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[380, 2454])).
% 0.78/1.00 tff(2458,plain,
% 0.78/1.00 (c1_1(a275)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[904, 142, 2419, 2457, 2456, 2455, 10])).
% 0.78/1.00 tff(2459,plain,
% 0.78/1.00 (hskp9 | (~c1_1(a275))),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1313, 142, 2457, 2456, 216])).
% 0.78/1.00 tff(2460,plain,
% 0.78/1.00 (hskp9),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[2459, 2458])).
% 0.78/1.00 tff(2461,plain,
% 0.78/1.00 (~c1_1(a280)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[236, 2460])).
% 0.78/1.00 tff(2462,plain,
% 0.78/1.00 (c3_1(a280)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[244, 2460])).
% 0.78/1.00 tff(2463,plain,
% 0.78/1.00 (c2_1(a280)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[269, 2460])).
% 0.78/1.00 tff(2464,plain,
% 0.78/1.00 (~c0_1(a280)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[2317, 142, 2433, 2435, 2463, 2462, 2461, 53, 2436])).
% 0.78/1.00 tff(2465,plain,
% 0.78/1.00 (hskp5),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1947, 142, 1890, 2463, 1874, 2461, 1610, 2464, 2431])).
% 0.78/1.00 tff(2466,plain,
% 0.78/1.00 (c0_1(a272)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[601, 2465])).
% 0.78/1.00 tff(2467,plain,
% 0.78/1.00 (hskp7),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[2364, 2457, 2434, 2433, 2436, 2435, 2431, 2419, 2455])).
% 0.78/1.00 tff(2468,plain,
% 0.78/1.00 (c0_1(a274)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[397, 2467])).
% 0.78/1.00 tff(2469,plain,
% 0.78/1.00 (~c3_1(a274)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[69, 2467])).
% 0.78/1.00 tff(2470,plain,
% 0.78/1.00 (c1_1(a274)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[77, 2467])).
% 0.78/1.00 tff(2471,plain,
% 0.78/1.00 (~c1_1(a272)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[593, 2465])).
% 0.78/1.00 tff(2472,plain,
% 0.78/1.00 (c2_1(a272)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[930, 2471, 2430, 2470, 2469, 2468, 2466])).
% 0.78/1.00 tff(2473,plain,
% 0.78/1.00 (~c3_1(a272)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[587, 2465])).
% 0.78/1.00 tff(2474,plain,
% 0.78/1.00 (hskp6),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[2324, 142, 2434, 2433, 2462, 2461, 1016, 2464, 2436])).
% 0.78/1.00 tff(2475,plain,
% 0.78/1.00 (~c0_1(a273)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1044, 2474])).
% 0.78/1.00 tff(2476,plain,
% 0.78/1.00 (c2_1(a273)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1052, 2474])).
% 0.78/1.00 tff(2477,plain,
% 0.78/1.00 (c1_1(a273)),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[1060, 2474])).
% 0.78/1.00 tff(2478,plain,
% 0.78/1.00 ($false),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[2355, 142, 2477, 2476, 2466, 2475, 2471, 2473, 1038, 2472])).
% 0.78/1.00 % SZS output end Proof
% 0.78/1.00 % E exiting
%------------------------------------------------------------------------------