%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN658-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:39:46 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN658-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:41:42 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(p4_type, type, (
% 0.18/0.39 p4: ( $i * $i ) > $o)).
% 0.18/0.39 tff(f5_type, type, (
% 0.18/0.39 f5: ( $i * $i * $i ) > $i)).
% 0.18/0.39 tff(c34_type, type, (
% 0.18/0.39 c34: $i)).
% 0.18/0.39 tff(c36_type, type, (
% 0.18/0.39 c36: $i)).
% 0.18/0.39 tff(f8_type, type, (
% 0.18/0.39 f8: ( $i * $i ) > $i)).
% 0.18/0.39 tff(f9_type, type, (
% 0.18/0.39 f9: ( $i * $i ) > $i)).
% 0.18/0.39 tff(c29_type, type, (
% 0.18/0.39 c29: $i)).
% 0.18/0.39 tff(c28_type, type, (
% 0.18/0.39 c28: $i)).
% 0.18/0.39 tff(c27_type, type, (
% 0.18/0.39 c27: $i)).
% 0.18/0.39 tff(p3_type, type, (
% 0.18/0.39 p3: ( $i * $i ) > $o)).
% 0.18/0.39 tff(p2_type, type, (
% 0.18/0.39 p2: ( $i * $i ) > $o)).
% 0.18/0.39 tff(c31_type, type, (
% 0.18/0.39 c31: $i)).
% 0.18/0.39 tff(p24_type, type, (
% 0.18/0.39 p24: ( $i * $i ) > $o)).
% 0.18/0.39 tff(f19_type, type, (
% 0.18/0.39 f19: $i > $i)).
% 0.18/0.39 tff(f20_type, type, (
% 0.18/0.39 f20: ( $i * $i ) > $i)).
% 0.18/0.39 tff(f22_type, type, (
% 0.18/0.39 f22: ( $i * $i * $i ) > $i)).
% 0.18/0.39 tff(p25_type, type, (
% 0.18/0.39 p25: ( $i * $i ) > $o)).
% 0.18/0.39 tff(f18_type, type, (
% 0.18/0.39 f18: $i > $i)).
% 0.18/0.39 tff(p6_type, type, (
% 0.18/0.39 p6: ( $i * $i ) > $o)).
% 0.18/0.39 tff(f10_type, type, (
% 0.18/0.39 f10: $i > $i)).
% 0.18/0.39 tff(c33_type, type, (
% 0.18/0.39 c33: $i)).
% 0.18/0.39 tff(f21_type, type, (
% 0.18/0.39 f21: $i > $i)).
% 0.18/0.39 tff(1,assumption,(~p4(c34, c34)), introduced(assumption)).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 (^[X36: $i] : refl(p4(X36, X36) <=> p4(X36, X36))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(3,plain,
% 0.18/0.39 (![X36: $i] : p4(X36, X36) <=> ![X36: $i] : p4(X36, X36)),
% 0.18/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (![X36: $i] : p4(X36, X36) <=> ![X36: $i] : p4(X36, X36)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(5,axiom,(![X36: $i] : p4(X36, X36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_4')).
% 0.18/0.39 tff(6,plain,
% 0.18/0.39 (![X36: $i] : p4(X36, X36)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.39 tff(7,plain,(
% 0.18/0.39 ![X36: $i] : p4(X36, X36)),
% 0.18/0.39 inference(skolemize,[status(sab)],[6])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 (![X36: $i] : p4(X36, X36)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 ((~![X36: $i] : p4(X36, X36)) | p4(c34, c34)),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.39 tff(11,plain,(p4(c34, c34)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(12,assumption,(~p3(c36, c36)), introduced(assumption)).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (^[X33: $i] : refl(p3(X33, X33) <=> p3(X33, X33))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (![X33: $i] : p3(X33, X33) <=> ![X33: $i] : p3(X33, X33)),
% 0.18/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (![X33: $i] : p3(X33, X33) <=> ![X33: $i] : p3(X33, X33)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(16,axiom,(![X33: $i] : p3(X33, X33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_5')).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (![X33: $i] : p3(X33, X33)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.39 tff(18,plain,(
% 0.18/0.39 ![X33: $i] : p3(X33, X33)),
% 0.18/0.39 inference(skolemize,[status(sab)],[17])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (![X33: $i] : p3(X33, X33)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 ((~![X33: $i] : p3(X33, X33)) | p3(c36, c36)),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.18/0.39 tff(22,plain,(p3(c36, c36)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(23,assumption,(~p2(f8(c27, f9(c28, c29)), f8(c27, f9(c28, c29)))), introduced(assumption)).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (^[X5: $i] : refl(p2(X5, X5) <=> p2(X5, X5))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (![X5: $i] : p2(X5, X5) <=> ![X5: $i] : p2(X5, X5)),
% 0.18/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (![X5: $i] : p2(X5, X5) <=> ![X5: $i] : p2(X5, X5)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(27,axiom,(![X5: $i] : p2(X5, X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_6')).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (![X5: $i] : p2(X5, X5)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.39 tff(29,plain,(
% 0.18/0.39 ![X5: $i] : p2(X5, X5)),
% 0.18/0.39 inference(skolemize,[status(sab)],[28])).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (![X5: $i] : p2(X5, X5)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 ((~![X5: $i] : p2(X5, X5)) | p2(f8(c27, f9(c28, c29)), f8(c27, f9(c28, c29)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 0.18/0.39 tff(33,plain,(p2(f8(c27, f9(c28, c29)), f8(c27, f9(c28, c29)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 (^[X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : refl(((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70))) <=> ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 (![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70))) <=> ![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 (![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70))) <=> ![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 (^[X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : trans(monotonicity(trans(monotonicity(rewrite((p4(f5(X65, X66, X67), f5(X68, X69, X70)) | (~p3(X66, X69))) <=> ((~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))), (((p4(f5(X65, X66, X67), f5(X68, X69, X70)) | (~p3(X66, X69))) | (~p4(X67, X70))) <=> (((~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70))) | (~p4(X67, X70))))), rewrite((((~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70))) | (~p4(X67, X70))) <=> ((~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))), (((p4(f5(X65, X66, X67), f5(X68, X69, X70)) | (~p3(X66, X69))) | (~p4(X67, X70))) <=> ((~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70))))), ((((p4(f5(X65, X66, X67), f5(X68, X69, X70)) | (~p3(X66, X69))) | (~p4(X67, X70))) | (~p2(X65, X68))) <=> (((~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70))) | (~p2(X65, X68))))), rewrite((((~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70))) | (~p2(X65, X68))) <=> ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))), ((((p4(f5(X65, X66, X67), f5(X68, X69, X70)) | (~p3(X66, X69))) | (~p4(X67, X70))) | (~p2(X65, X68))) <=> ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : (((p4(f5(X65, X66, X67), f5(X68, X69, X70)) | (~p3(X66, X69))) | (~p4(X67, X70))) | (~p2(X65, X68))) <=> ![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.18/0.40 tff(39,axiom,(![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : (((p4(f5(X65, X66, X67), f5(X68, X69, X70)) | (~p3(X66, X69))) | (~p4(X67, X70))) | (~p2(X65, X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_46')).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 (![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.18/0.40 tff(42,plain,(
% 0.18/0.40 ![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[41])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (((~![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))) | ((~p2(f8(c27, f9(c28, c29)), f8(c27, f9(c28, c29)))) | (~p4(c34, c34)) | (~p3(c36, c36)) | p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34)))) <=> ((~![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))) | (~p2(f8(c27, f9(c28, c29)), f8(c27, f9(c28, c29)))) | (~p4(c34, c34)) | (~p3(c36, c36)) | p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 ((~![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))) | ((~p2(f8(c27, f9(c28, c29)), f8(c27, f9(c28, c29)))) | (~p4(c34, c34)) | (~p3(c36, c36)) | p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 ((~![X67: $i, X68: $i, X66: $i, X65: $i, X70: $i, X69: $i] : ((~p2(X65, X68)) | (~p4(X67, X70)) | (~p3(X66, X69)) | p4(f5(X65, X66, X67), f5(X68, X69, X70)))) | (~p2(f8(c27, f9(c28, c29)), f8(c27, f9(c28, c29)))) | (~p4(c34, c34)) | (~p3(c36, c36)) | p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 ((~p2(f8(c27, f9(c28, c29)), f8(c27, f9(c28, c29)))) | (~p4(c34, c34)) | (~p3(c36, c36)) | p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 ((~p4(c34, c34)) | (~p3(c36, c36)) | p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[47, 33])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[48, 22, 11])).
% 0.18/0.40 tff(50,assumption,(~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31))), introduced(assumption)).
% 0.18/0.40 tff(51,assumption,(p6(f21(f8(c27, f9(c28, c29))), f10(c33))), introduced(assumption)).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 (^[X82: $i, X83: $i, X84: $i] : refl(p6(f21(f8(X82, f9(X83, X84))), X83) <=> p6(f21(f8(X82, f9(X83, X84))), X83))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 (![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83) <=> ![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.18/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 (![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83) <=> ![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(55,axiom,(![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_15')).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 (![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.40 tff(57,plain,(
% 0.18/0.40 ![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.18/0.40 inference(skolemize,[status(sab)],[56])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 (![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 ((~![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)) | p6(f21(f8(c27, f9(c28, c29))), c28)),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 (p6(f21(f8(c27, f9(c28, c29))), c28)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (^[X73: $i, X72: $i, X71: $i] : refl(((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73)) <=> ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73)) <=> ![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73)) <=> ![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (^[X73: $i, X72: $i, X71: $i] : trans(monotonicity(rewrite((p6(X72, X73) | (~p6(X71, X72))) <=> ((~p6(X71, X72)) | p6(X72, X73))), (((p6(X72, X73) | (~p6(X71, X72))) | (~p6(X71, X73))) <=> (((~p6(X71, X72)) | p6(X72, X73)) | (~p6(X71, X73))))), rewrite((((~p6(X71, X72)) | p6(X72, X73)) | (~p6(X71, X73))) <=> ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))), (((p6(X72, X73) | (~p6(X71, X72))) | (~p6(X71, X73))) <=> ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (![X73: $i, X72: $i, X71: $i] : ((p6(X72, X73) | (~p6(X71, X72))) | (~p6(X71, X73))) <=> ![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.18/0.40 tff(66,axiom,(![X73: $i, X72: $i, X71: $i] : ((p6(X72, X73) | (~p6(X71, X72))) | (~p6(X71, X73)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_25')).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.18/0.40 tff(69,plain,(
% 0.18/0.40 ![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.18/0.40 inference(skolemize,[status(sab)],[68])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 ((~p6(c28, f10(c33))) <=> (~p6(c28, f10(c33)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(72,axiom,(~p6(c28, f10(c33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p6_11')).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (~p6(c28, f10(c33))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (((~![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))) | ((~p6(f21(f8(c27, f9(c28, c29))), c28)) | (~p6(f21(f8(c27, f9(c28, c29))), f10(c33))) | p6(c28, f10(c33)))) <=> ((~![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))) | (~p6(f21(f8(c27, f9(c28, c29))), c28)) | (~p6(f21(f8(c27, f9(c28, c29))), f10(c33))) | p6(c28, f10(c33)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 ((~![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))) | ((~p6(f21(f8(c27, f9(c28, c29))), c28)) | (~p6(f21(f8(c27, f9(c28, c29))), f10(c33))) | p6(c28, f10(c33)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 ((~![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))) | (~p6(f21(f8(c27, f9(c28, c29))), c28)) | (~p6(f21(f8(c27, f9(c28, c29))), f10(c33))) | p6(c28, f10(c33))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[76, 73, 70, 60, 51])).
% 0.18/0.40 tff(78,plain,(~p6(f21(f8(c27, f9(c28, c29))), f10(c33))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 (^[X25: $i, X27: $i, X26: $i] : refl((p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[79])).
% 0.18/0.41 tff(81,plain,
% 0.18/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(82,plain,
% 0.18/0.41 (^[X25: $i, X27: $i, X26: $i] : trans(monotonicity(rewrite((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) <=> (p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))), (((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> ((p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))))), rewrite(((p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))), (((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(83,plain,
% 0.18/0.41 (![X25: $i, X27: $i, X26: $i] : ((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[82])).
% 0.18/0.41 tff(84,axiom,(![X25: $i, X27: $i, X26: $i] : ((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) | p4(f5(X25, c36, X26), f5(X25, c36, X27)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_48')).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.18/0.41 tff(87,plain,(
% 0.18/0.41 ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[86])).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.18/0.41 tff(89,plain,
% 0.18/0.41 (((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29)))))) <=> ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(90,plain,
% 0.18/0.41 ((p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33))) <=> (p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 (((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)))) <=> ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29))))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[90])).
% 0.18/0.41 tff(92,plain,
% 0.18/0.41 (((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)))) <=> ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29)))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[91, 89])).
% 0.18/0.41 tff(93,plain,
% 0.18/0.41 ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(94,plain,
% 0.18/0.41 ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.41 tff(95,plain,
% 0.18/0.41 (p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[94, 88, 50, 78])).
% 0.18/0.41 tff(96,assumption,(~p24(f19(f20(c34, c31)), f19(f20(c34, f22(f8(c27, f9(c28, c29)), c34, c31))))), introduced(assumption)).
% 0.18/0.41 tff(97,plain,
% 0.18/0.41 (^[X20: $i] : refl(((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20)))) <=> ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(98,plain,
% 0.18/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20)))) <=> ![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[97])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20)))) <=> ![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(100,plain,
% 0.18/0.41 (^[X20: $i] : rewrite((p24(f19(f20(c34, c31)), f19(f20(c34, X20))) | (~p25(X20, f18(f8(c27, f9(c28, c29)))))) <=> ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 (![X20: $i] : (p24(f19(f20(c34, c31)), f19(f20(c34, X20))) | (~p25(X20, f18(f8(c27, f9(c28, c29)))))) <=> ![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[100])).
% 0.18/0.41 tff(102,axiom,(![X20: $i] : (p24(f19(f20(c34, c31)), f19(f20(c34, X20))) | (~p25(X20, f18(f8(c27, f9(c28, c29))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p24_45')).
% 0.18/0.41 tff(103,plain,
% 0.18/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.42 tff(104,plain,
% 0.18/0.42 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.18/0.42 tff(105,plain,(
% 0.18/0.42 ![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[104])).
% 0.18/0.42 tff(106,plain,
% 0.18/0.42 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.18/0.42 tff(107,plain,
% 0.18/0.42 (((~![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20))))) | ((~p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, f22(f8(c27, f9(c28, c29)), c34, c31)))))) <=> ((~![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20))))) | (~p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, f22(f8(c27, f9(c28, c29)), c34, c31)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(108,plain,
% 0.18/0.42 ((~![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20))))) | ((~p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, f22(f8(c27, f9(c28, c29)), c34, c31)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(109,plain,
% 0.18/0.42 ((~![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, X20))))) | (~p25(f22(f8(c27, f9(c28, c29)), c34, c31), f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c34, c31)), f19(f20(c34, f22(f8(c27, f9(c28, c29)), c34, c31))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.18/0.42 tff(110,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[109, 106, 96, 95])).
% 0.18/0.42 tff(111,plain,(p24(f19(f20(c34, c31)), f19(f20(c34, f22(f8(c27, f9(c28, c29)), c34, c31)))) | p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(112,plain,
% 0.18/0.42 (p24(f19(f20(c34, c31)), f19(f20(c34, f22(f8(c27, f9(c28, c29)), c34, c31))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[111, 50])).
% 0.18/0.42 tff(113,plain,
% 0.18/0.42 (^[X25: $i, X27: $i, X26: $i] : refl((p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(114,plain,
% 0.18/0.42 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[113])).
% 0.18/0.42 tff(115,plain,
% 0.18/0.42 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(116,plain,
% 0.18/0.42 (^[X25: $i, X27: $i, X26: $i] : trans(monotonicity(rewrite((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)))), (((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> ((p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))))), rewrite(((p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))), (((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(117,plain,
% 0.18/0.42 (![X25: $i, X27: $i, X26: $i] : ((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[116])).
% 0.18/0.42 tff(118,axiom,(![X25: $i, X27: $i, X26: $i] : ((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_49')).
% 0.18/0.42 tff(119,plain,
% 0.18/0.42 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.18/0.42 tff(120,plain,
% 0.18/0.42 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.18/0.42 tff(121,plain,(
% 0.18/0.42 ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[120])).
% 0.18/0.42 tff(122,plain,
% 0.18/0.42 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.18/0.42 tff(123,plain,
% 0.18/0.42 (((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c34, c31)), f19(f20(c34, f22(f8(c27, f9(c28, c29)), c34, c31))))))) <=> ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))) | p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c34, c31)), f19(f20(c34, f22(f8(c27, f9(c28, c29)), c34, c31))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(124,plain,
% 0.18/0.42 ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c34, c31)), f19(f20(c34, f22(f8(c27, f9(c28, c29)), c34, c31))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(125,plain,
% 0.18/0.42 ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))) | p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c34, c31)), f19(f20(c34, f22(f8(c27, f9(c28, c29)), c34, c31)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.42 tff(126,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[125, 122, 50, 78, 112])).
% 0.18/0.42 tff(127,plain,(p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(128,plain,
% 0.18/0.42 ((~p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34))) <=> (~p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(129,axiom,(~p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p4_44')).
% 0.18/0.42 tff(130,plain,
% 0.18/0.42 (~p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.18/0.42 tff(131,plain,
% 0.18/0.42 (^[X38: $i, X37: $i, X36: $i] : refl(((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38)) <=> ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38)))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(132,plain,
% 0.18/0.42 (![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38)) <=> ![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[131])).
% 0.18/0.42 tff(133,plain,
% 0.18/0.42 (![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38)) <=> ![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(134,plain,
% 0.18/0.42 (^[X38: $i, X37: $i, X36: $i] : trans(monotonicity(rewrite((p4(X37, X38) | (~p4(X36, X37))) <=> ((~p4(X36, X37)) | p4(X37, X38))), (((p4(X37, X38) | (~p4(X36, X37))) | (~p4(X36, X38))) <=> (((~p4(X36, X37)) | p4(X37, X38)) | (~p4(X36, X38))))), rewrite((((~p4(X36, X37)) | p4(X37, X38)) | (~p4(X36, X38))) <=> ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))), (((p4(X37, X38) | (~p4(X36, X37))) | (~p4(X36, X38))) <=> ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(135,plain,
% 0.18/0.42 (![X38: $i, X37: $i, X36: $i] : ((p4(X37, X38) | (~p4(X36, X37))) | (~p4(X36, X38))) <=> ![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[134])).
% 0.18/0.42 tff(136,axiom,(![X38: $i, X37: $i, X36: $i] : ((p4(X37, X38) | (~p4(X36, X37))) | (~p4(X36, X38)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_26')).
% 0.18/0.42 tff(137,plain,
% 0.18/0.42 (![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.18/0.42 tff(138,plain,
% 0.18/0.42 (![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.18/0.42 tff(139,plain,(
% 0.18/0.42 ![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.18/0.42 inference(skolemize,[status(sab)],[138])).
% 0.18/0.42 tff(140,plain,
% 0.18/0.42 (![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.18/0.42 tff(141,plain,
% 0.18/0.42 (((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31))))) <=> ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(142,plain,
% 0.18/0.42 (((~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34))) <=> (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(143,plain,
% 0.18/0.42 (((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | ((~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)))) <=> ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[142])).
% 0.18/0.43 tff(144,plain,
% 0.18/0.43 (((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | ((~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)))) <=> ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[143, 141])).
% 0.18/0.43 tff(145,plain,
% 0.18/0.43 ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | ((~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(146,plain,
% 0.18/0.43 ((~![X38: $i, X37: $i, X36: $i] : ((~p4(X36, X38)) | (~p4(X36, X37)) | p4(X37, X38))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c34))) | (~p4(f5(f8(c27, f9(c28, c29)), c36, c34), f5(f8(c27, f9(c28, c29)), c36, c31)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.18/0.43 tff(147,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[146, 140, 130, 127, 49])).
% 0.18/0.43 % SZS output end Proof
% 0.18/0.43 % E exiting
%------------------------------------------------------------------------------