%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN569-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:39:36 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN569-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 12:37:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(p2_type, type, (
% 0.12/0.38 p2: ( $i * $i ) > $o)).
% 0.12/0.38 tff(f5_type, type, (
% 0.12/0.38 f5: ( $i * $i ) > $i)).
% 0.12/0.38 tff(f7_type, type, (
% 0.12/0.38 f7: ( $i * $i ) > $i)).
% 0.12/0.38 tff(c11_type, type, (
% 0.12/0.38 c11: $i)).
% 0.12/0.38 tff(c13_type, type, (
% 0.12/0.38 c13: $i)).
% 0.12/0.38 tff(c12_type, type, (
% 0.12/0.38 c12: $i)).
% 0.12/0.38 tff(f4_type, type, (
% 0.12/0.38 f4: ( $i * $i ) > $i)).
% 0.12/0.38 tff(c15_type, type, (
% 0.12/0.38 c15: $i)).
% 0.12/0.38 tff(p6_type, type, (
% 0.12/0.38 p6: ( $i * $i ) > $o)).
% 0.12/0.38 tff(f3_type, type, (
% 0.12/0.38 f3: $i > $i)).
% 0.12/0.38 tff(c14_type, type, (
% 0.12/0.38 c14: $i)).
% 0.12/0.38 tff(p9_type, type, (
% 0.12/0.38 p9: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(p10_type, type, (
% 0.12/0.38 p10: ( $i * $i ) > $o)).
% 0.12/0.38 tff(p8_type, type, (
% 0.12/0.38 p8: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,assumption,(~p2(f7(c13, c12), f7(c13, c12))), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[X6: $i] : refl(p2(X6, X6) <=> p2(X6, X6))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X6: $i] : p2(X6, X6) <=> ![X6: $i] : p2(X6, X6)),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![X6: $i] : p2(X6, X6) <=> ![X6: $i] : p2(X6, X6)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,axiom,(![X6: $i] : p2(X6, X6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_1')).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![X6: $i] : p2(X6, X6)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.38 tff(7,plain,(
% 0.12/0.38 ![X6: $i] : p2(X6, X6)),
% 0.12/0.38 inference(skolemize,[status(sab)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![X6: $i] : p2(X6, X6)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 ((~![X6: $i] : p2(X6, X6)) | p2(f7(c13, c12), f7(c13, c12))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.38 tff(11,plain,(p2(f7(c13, c12), f7(c13, c12))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(12,assumption,(~p6(c13, c13)), introduced(assumption)).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (^[X27: $i] : refl(p6(X27, X27) <=> p6(X27, X27))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![X27: $i] : p6(X27, X27) <=> ![X27: $i] : p6(X27, X27)),
% 0.12/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![X27: $i] : p6(X27, X27) <=> ![X27: $i] : p6(X27, X27)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(16,axiom,(![X27: $i] : p6(X27, X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_2')).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![X27: $i] : p6(X27, X27)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.38 tff(18,plain,(
% 0.12/0.38 ![X27: $i] : p6(X27, X27)),
% 0.12/0.38 inference(skolemize,[status(sab)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![X27: $i] : p6(X27, X27)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~![X27: $i] : p6(X27, X27)) | p6(c13, c13)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.12/0.38 tff(22,plain,(p6(c13, c13)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(23,assumption,(~p2(c11, c11)), introduced(assumption)).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~![X6: $i] : p2(X6, X6)) | p2(c11, c11)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[24, 8, 23])).
% 0.12/0.38 tff(26,plain,(p2(c11, c11)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (^[X25: $i, X23: $i, X26: $i, X24: $i] : refl(((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26))) <=> ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26))) <=> ![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26))) <=> ![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (^[X25: $i, X23: $i, X26: $i, X24: $i] : trans(monotonicity(rewrite((p2(f7(X23, X24), f7(X25, X26)) | (~p2(X24, X26))) <=> ((~p2(X24, X26)) | p2(f7(X23, X24), f7(X25, X26)))), (((p2(f7(X23, X24), f7(X25, X26)) | (~p2(X24, X26))) | (~p6(X23, X25))) <=> (((~p2(X24, X26)) | p2(f7(X23, X24), f7(X25, X26))) | (~p6(X23, X25))))), rewrite((((~p2(X24, X26)) | p2(f7(X23, X24), f7(X25, X26))) | (~p6(X23, X25))) <=> ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))), (((p2(f7(X23, X24), f7(X25, X26)) | (~p2(X24, X26))) | (~p6(X23, X25))) <=> ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((p2(f7(X23, X24), f7(X25, X26)) | (~p2(X24, X26))) | (~p6(X23, X25))) <=> ![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.38 tff(32,axiom,(![X25: $i, X23: $i, X26: $i, X24: $i] : ((p2(f7(X23, X24), f7(X25, X26)) | (~p2(X24, X26))) | (~p6(X23, X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_17')).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.38 tff(35,plain,(
% 0.20/0.38 ![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[34])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))) | ((~p2(c11, c11)) | (~p6(c13, c13)) | p2(f7(c13, c11), f7(c13, c11)))) <=> ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))) | (~p2(c11, c11)) | (~p6(c13, c13)) | p2(f7(c13, c11), f7(c13, c11)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))) | ((~p2(c11, c11)) | (~p6(c13, c13)) | p2(f7(c13, c11), f7(c13, c11)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p6(X23, X25)) | p2(f7(X23, X24), f7(X25, X26)))) | (~p2(c11, c11)) | (~p6(c13, c13)) | p2(f7(c13, c11), f7(c13, c11))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 ((~p2(c11, c11)) | (~p6(c13, c13)) | p2(f7(c13, c11), f7(c13, c11))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (p2(f7(c13, c11), f7(c13, c11))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[40, 26, 22])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (^[X22: $i, X21: $i, X20: $i, X19: $i] : refl(((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22))) <=> ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22))) <=> ![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22))) <=> ![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (^[X22: $i, X21: $i, X20: $i, X19: $i] : trans(monotonicity(rewrite((p2(f5(X19, X20), f5(X21, X22)) | (~p2(X19, X21))) <=> ((~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))), (((p2(f5(X19, X20), f5(X21, X22)) | (~p2(X19, X21))) | (~p2(X20, X22))) <=> (((~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22))) | (~p2(X20, X22))))), rewrite((((~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22))) | (~p2(X20, X22))) <=> ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))), (((p2(f5(X19, X20), f5(X21, X22)) | (~p2(X19, X21))) | (~p2(X20, X22))) <=> ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (![X22: $i, X21: $i, X20: $i, X19: $i] : ((p2(f5(X19, X20), f5(X21, X22)) | (~p2(X19, X21))) | (~p2(X20, X22))) <=> ![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.39 tff(47,axiom,(![X22: $i, X21: $i, X20: $i, X19: $i] : ((p2(f5(X19, X20), f5(X21, X22)) | (~p2(X19, X21))) | (~p2(X20, X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_18')).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.39 tff(50,plain,(
% 0.20/0.39 ![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[49])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (((~![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))) | ((~p2(f7(c13, c11), f7(c13, c11))) | (~p2(f7(c13, c12), f7(c13, c12))) | p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11))))) <=> ((~![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))) | (~p2(f7(c13, c11), f7(c13, c11))) | (~p2(f7(c13, c12), f7(c13, c12))) | p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((~![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))) | ((~p2(f7(c13, c11), f7(c13, c11))) | (~p2(f7(c13, c12), f7(c13, c12))) | p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 ((~![X22: $i, X21: $i, X20: $i, X19: $i] : ((~p2(X20, X22)) | (~p2(X19, X21)) | p2(f5(X19, X20), f5(X21, X22)))) | (~p2(f7(c13, c11), f7(c13, c11))) | (~p2(f7(c13, c12), f7(c13, c12))) | p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 ((~p2(f7(c13, c11), f7(c13, c11))) | (~p2(f7(c13, c12), f7(c13, c12))) | p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[55, 41, 11])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15)) <=> p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(58,axiom,(p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_15')).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (^[X6: $i, X7: $i, X8: $i] : refl(((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8)) <=> ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8)) <=> ![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8)) <=> ![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (^[X6: $i, X7: $i, X8: $i] : trans(monotonicity(rewrite((p2(X7, X8) | (~p2(X6, X7))) <=> ((~p2(X6, X7)) | p2(X7, X8))), (((p2(X7, X8) | (~p2(X6, X7))) | (~p2(X6, X8))) <=> (((~p2(X6, X7)) | p2(X7, X8)) | (~p2(X6, X8))))), rewrite((((~p2(X6, X7)) | p2(X7, X8)) | (~p2(X6, X8))) <=> ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))), (((p2(X7, X8) | (~p2(X6, X7))) | (~p2(X6, X8))) <=> ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (![X6: $i, X7: $i, X8: $i] : ((p2(X7, X8) | (~p2(X6, X7))) | (~p2(X6, X8))) <=> ![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.39 tff(65,axiom,(![X6: $i, X7: $i, X8: $i] : ((p2(X7, X8) | (~p2(X6, X7))) | (~p2(X6, X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_10')).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.39 tff(68,plain,(
% 0.20/0.39 ![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))),
% 0.20/0.39 inference(skolemize,[status(sab)],[67])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (((~![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))) | ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))) | p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))))) <=> ((~![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))) | p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (((~p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))) | p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11)))) <=> ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))) | p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (((~![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))) | ((~p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))) | p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))))) <=> ((~![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))) | ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))) | p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (((~![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))) | ((~p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))) | p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))))) <=> ((~![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))) | p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 ((~![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))) | ((~p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))) | p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 ((~![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), c15))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f5(f7(c13, c12), f7(c13, c11)))) | p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[75, 69, 59, 56])).
% 0.20/0.39 tff(77,assumption,(~p2(f5(c12, c11), f5(c12, c11))), introduced(assumption)).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 ((~![X6: $i] : p2(X6, X6)) | p2(f5(c12, c11), f5(c12, c11))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[78, 8, 77])).
% 0.20/0.39 tff(80,plain,(p2(f5(c12, c11), f5(c12, c11))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (^[X4: $i, X5: $i] : refl(((~p8(X4, X5)) | p10(X4, X5)) <=> ((~p8(X4, X5)) | p10(X4, X5)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5)) <=> ![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 (![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5)) <=> ![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 (^[X4: $i, X5: $i] : rewrite((p10(X4, X5) | (~p8(X4, X5))) <=> ((~p8(X4, X5)) | p10(X4, X5)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 (![X4: $i, X5: $i] : (p10(X4, X5) | (~p8(X4, X5))) <=> ![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.39 tff(86,axiom,(![X4: $i, X5: $i] : (p10(X4, X5) | (~p8(X4, X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_7')).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 (![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.39 tff(89,plain,(
% 0.20/0.39 ![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))),
% 0.20/0.39 inference(skolemize,[status(sab)],[88])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 (![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 (p8(c11, c14) <=> p8(c11, c14)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(92,axiom,(p8(c11, c14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_5')).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 (p8(c11, c14)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 (((~![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))) | ((~p8(c11, c14)) | p10(c11, c14))) <=> ((~![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))) | (~p8(c11, c14)) | p10(c11, c14))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 ((~![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))) | ((~p8(c11, c14)) | p10(c11, c14))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 ((~![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))) | (~p8(c11, c14)) | p10(c11, c14)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 (p10(c11, c14)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[96, 93, 90])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 (p8(c14, c12) <=> p8(c14, c12)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(99,axiom,(p8(c14, c12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_3')).
% 0.20/0.39 tff(100,plain,
% 0.20/0.39 (p8(c14, c12)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (((~![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))) | ((~p8(c14, c12)) | p10(c14, c12))) <=> ((~![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))) | (~p8(c14, c12)) | p10(c14, c12))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 ((~![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))) | ((~p8(c14, c12)) | p10(c14, c12))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(103,plain,
% 0.20/0.40 ((~![X4: $i, X5: $i] : ((~p8(X4, X5)) | p10(X4, X5))) | (~p8(c14, c12)) | p10(c14, c12)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.40 tff(104,plain,
% 0.20/0.40 (p10(c14, c12)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[103, 100, 90])).
% 0.20/0.40 tff(105,plain,
% 0.20/0.40 (^[X40: $i] : refl(((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40)) <=> ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(106,plain,
% 0.20/0.40 (![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40)) <=> ![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.40 tff(107,plain,
% 0.20/0.40 (![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40)) <=> ![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(108,plain,
% 0.20/0.40 (^[X40: $i] : trans(monotonicity(rewrite((p9(c13, f3(X40), X40) | (~p10(X40, c12))) <=> ((~p10(X40, c12)) | p9(c13, f3(X40), X40))), (((p9(c13, f3(X40), X40) | (~p10(X40, c12))) | (~p10(c11, X40))) <=> (((~p10(X40, c12)) | p9(c13, f3(X40), X40)) | (~p10(c11, X40))))), rewrite((((~p10(X40, c12)) | p9(c13, f3(X40), X40)) | (~p10(c11, X40))) <=> ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))), (((p9(c13, f3(X40), X40) | (~p10(X40, c12))) | (~p10(c11, X40))) <=> ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(109,plain,
% 0.20/0.40 (![X40: $i] : ((p9(c13, f3(X40), X40) | (~p10(X40, c12))) | (~p10(c11, X40))) <=> ![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[108])).
% 0.20/0.40 tff(110,axiom,(![X40: $i] : ((p9(c13, f3(X40), X40) | (~p10(X40, c12))) | (~p10(c11, X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_12')).
% 0.20/0.40 tff(111,plain,
% 0.20/0.40 (![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.40 tff(112,plain,
% 0.20/0.40 (![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.20/0.40 tff(113,plain,(
% 0.20/0.40 ![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))),
% 0.20/0.40 inference(skolemize,[status(sab)],[112])).
% 0.20/0.40 tff(114,plain,
% 0.20/0.40 (![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.20/0.40 tff(115,plain,
% 0.20/0.40 (((~![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))) | ((~p10(c11, c14)) | (~p10(c14, c12)) | p9(c13, f3(c14), c14))) <=> ((~![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))) | (~p10(c11, c14)) | (~p10(c14, c12)) | p9(c13, f3(c14), c14))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(116,plain,
% 0.20/0.40 ((~![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))) | ((~p10(c11, c14)) | (~p10(c14, c12)) | p9(c13, f3(c14), c14))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(117,plain,
% 0.20/0.40 ((~![X40: $i] : ((~p10(c11, X40)) | (~p10(X40, c12)) | p9(c13, f3(X40), X40))) | (~p10(c11, c14)) | (~p10(c14, c12)) | p9(c13, f3(c14), c14)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.40 tff(118,plain,
% 0.20/0.40 (p9(c13, f3(c14), c14)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[117, 114, 104, 97])).
% 0.20/0.40 tff(119,plain,
% 0.20/0.40 (^[X9: $i, X12: $i, X11: $i, X10: $i] : refl(((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10)) <=> ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(120,plain,
% 0.20/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.40 tff(121,plain,
% 0.20/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(122,plain,
% 0.20/0.40 (^[X9: $i, X12: $i, X11: $i, X10: $i] : trans(monotonicity(rewrite((p2(X9, X10) | (~p9(X11, X9, X12))) <=> ((~p9(X11, X9, X12)) | p2(X9, X10))), (((p2(X9, X10) | (~p9(X11, X9, X12))) | (~p9(X11, X10, X12))) <=> (((~p9(X11, X9, X12)) | p2(X9, X10)) | (~p9(X11, X10, X12))))), rewrite((((~p9(X11, X9, X12)) | p2(X9, X10)) | (~p9(X11, X10, X12))) <=> ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))), (((p2(X9, X10) | (~p9(X11, X9, X12))) | (~p9(X11, X10, X12))) <=> ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(123,plain,
% 0.20/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((p2(X9, X10) | (~p9(X11, X9, X12))) | (~p9(X11, X10, X12))) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.40 tff(124,axiom,(![X9: $i, X12: $i, X11: $i, X10: $i] : ((p2(X9, X10) | (~p9(X11, X9, X12))) | (~p9(X11, X10, X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_11')).
% 0.20/0.40 tff(125,plain,
% 0.20/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.40 tff(126,plain,
% 0.20/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.20/0.40 tff(127,plain,(
% 0.20/0.40 ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))),
% 0.20/0.40 inference(skolemize,[status(sab)],[126])).
% 0.20/0.40 tff(128,plain,
% 0.20/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.20/0.40 tff(129,plain,
% 0.20/0.40 (p9(c13, c15, c14) <=> p9(c13, c15, c14)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(130,axiom,(p9(c13, c15, c14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_6')).
% 0.20/0.40 tff(131,plain,
% 0.20/0.40 (p9(c13, c15, c14)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.40 tff(132,plain,
% 0.20/0.40 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))) | ((~p9(c13, c15, c14)) | p2(c15, f3(c14)) | (~p9(c13, f3(c14), c14)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))) | (~p9(c13, c15, c14)) | p2(c15, f3(c14)) | (~p9(c13, f3(c14), c14)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(133,plain,
% 0.20/0.40 (((~p9(c13, f3(c14), c14)) | (~p9(c13, c15, c14)) | p2(c15, f3(c14))) <=> ((~p9(c13, c15, c14)) | p2(c15, f3(c14)) | (~p9(c13, f3(c14), c14)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(134,plain,
% 0.20/0.40 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))) | ((~p9(c13, f3(c14), c14)) | (~p9(c13, c15, c14)) | p2(c15, f3(c14)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))) | ((~p9(c13, c15, c14)) | p2(c15, f3(c14)) | (~p9(c13, f3(c14), c14))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[133])).
% 0.20/0.40 tff(135,plain,
% 0.20/0.40 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))) | ((~p9(c13, f3(c14), c14)) | (~p9(c13, c15, c14)) | p2(c15, f3(c14)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))) | (~p9(c13, c15, c14)) | p2(c15, f3(c14)) | (~p9(c13, f3(c14), c14)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[134, 132])).
% 0.20/0.40 tff(136,plain,
% 0.20/0.40 ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))) | ((~p9(c13, f3(c14), c14)) | (~p9(c13, c15, c14)) | p2(c15, f3(c14)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(137,plain,
% 0.20/0.40 ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p9(X11, X10, X12)) | (~p9(X11, X9, X12)) | p2(X9, X10))) | (~p9(c13, c15, c14)) | p2(c15, f3(c14)) | (~p9(c13, f3(c14), c14))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.40 tff(138,plain,
% 0.20/0.40 (p2(c15, f3(c14))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[137, 131, 128, 118])).
% 0.20/0.40 tff(139,plain,
% 0.20/0.40 (^[X17: $i, X16: $i, X18: $i, X15: $i] : refl(((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18))) <=> ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(140,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18))) <=> ![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.40 tff(141,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18))) <=> ![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(142,plain,
% 0.20/0.40 (^[X17: $i, X16: $i, X18: $i, X15: $i] : trans(monotonicity(rewrite((p2(f4(X15, X16), f4(X17, X18)) | (~p2(X15, X17))) <=> ((~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))), (((p2(f4(X15, X16), f4(X17, X18)) | (~p2(X15, X17))) | (~p2(X16, X18))) <=> (((~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18))) | (~p2(X16, X18))))), rewrite((((~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18))) | (~p2(X16, X18))) <=> ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))), (((p2(f4(X15, X16), f4(X17, X18)) | (~p2(X15, X17))) | (~p2(X16, X18))) <=> ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(143,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X15: $i] : ((p2(f4(X15, X16), f4(X17, X18)) | (~p2(X15, X17))) | (~p2(X16, X18))) <=> ![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[142])).
% 0.20/0.40 tff(144,axiom,(![X17: $i, X16: $i, X18: $i, X15: $i] : ((p2(f4(X15, X16), f4(X17, X18)) | (~p2(X15, X17))) | (~p2(X16, X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_16')).
% 0.20/0.40 tff(145,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.40 tff(146,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.20/0.40 tff(147,plain,(
% 0.20/0.40 ![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[146])).
% 0.20/0.40 tff(148,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.20/0.40 tff(149,plain,
% 0.20/0.40 (((~![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))) | ((~p2(c15, f3(c14))) | (~p2(f5(c12, c11), f5(c12, c11))) | p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))))) <=> ((~![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))) | (~p2(c15, f3(c14))) | (~p2(f5(c12, c11), f5(c12, c11))) | p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(150,plain,
% 0.20/0.40 ((~![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))) | ((~p2(c15, f3(c14))) | (~p2(f5(c12, c11), f5(c12, c11))) | p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(151,plain,
% 0.20/0.40 ((~![X17: $i, X16: $i, X18: $i, X15: $i] : ((~p2(X16, X18)) | (~p2(X15, X17)) | p2(f4(X15, X16), f4(X17, X18)))) | (~p2(c15, f3(c14))) | (~p2(f5(c12, c11), f5(c12, c11))) | p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.40 tff(152,plain,
% 0.20/0.40 ((~p2(c15, f3(c14))) | (~p2(f5(c12, c11), f5(c12, c11))) | p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[151, 148])).
% 0.20/0.41 tff(153,plain,
% 0.20/0.41 ((~p2(f5(c12, c11), f5(c12, c11))) | p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[152, 138])).
% 0.20/0.41 tff(154,plain,
% 0.20/0.41 (p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[153, 80])).
% 0.20/0.41 tff(155,plain,
% 0.20/0.41 (^[X41: $i] : refl(((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41))) <=> ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(156,plain,
% 0.20/0.41 (![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41))) <=> ![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[155])).
% 0.20/0.41 tff(157,plain,
% 0.20/0.41 (![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41))) <=> ![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(158,plain,
% 0.20/0.41 (^[X41: $i] : trans(monotonicity(rewrite(((~p8(X41, c12)) | (~p8(c11, X41))) <=> ((~p8(X41, c12)) | (~p8(c11, X41)))), ((((~p8(X41, c12)) | (~p8(c11, X41))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41))))) <=> (((~p8(X41, c12)) | (~p8(c11, X41))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41))))))), rewrite((((~p8(X41, c12)) | (~p8(c11, X41))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41))))) <=> ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))), ((((~p8(X41, c12)) | (~p8(c11, X41))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41))))) <=> ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(159,plain,
% 0.20/0.41 (![X41: $i] : (((~p8(X41, c12)) | (~p8(c11, X41))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41))))) <=> ![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[158])).
% 0.20/0.41 tff(160,axiom,(![X41: $i] : (((~p8(X41, c12)) | (~p8(c11, X41))) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p8_20')).
% 0.20/0.41 tff(161,plain,
% 0.20/0.41 (![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.41 tff(162,plain,
% 0.20/0.41 (![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.20/0.41 tff(163,plain,(
% 0.20/0.41 ![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[162])).
% 0.20/0.41 tff(164,plain,
% 0.20/0.41 (![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.20/0.41 tff(165,plain,
% 0.20/0.41 (((~![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))) | ((~p8(c14, c12)) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14)))) | (~p8(c11, c14)))) <=> ((~![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))) | (~p8(c14, c12)) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14)))) | (~p8(c11, c14)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(166,plain,
% 0.20/0.41 (((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14)))) | (~p8(c14, c12)) | (~p8(c11, c14))) <=> ((~p8(c14, c12)) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14)))) | (~p8(c11, c14)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(167,plain,
% 0.20/0.41 (((~![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))) | ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14)))) | (~p8(c14, c12)) | (~p8(c11, c14)))) <=> ((~![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))) | ((~p8(c14, c12)) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14)))) | (~p8(c11, c14))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[166])).
% 0.20/0.41 tff(168,plain,
% 0.20/0.41 (((~![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))) | ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14)))) | (~p8(c14, c12)) | (~p8(c11, c14)))) <=> ((~![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))) | (~p8(c14, c12)) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14)))) | (~p8(c11, c14)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[167, 165])).
% 0.20/0.41 tff(169,plain,
% 0.20/0.41 ((~![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))) | ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14)))) | (~p8(c14, c12)) | (~p8(c11, c14)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(170,plain,
% 0.20/0.41 ((~![X41: $i] : ((~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(X41)))) | (~p8(X41, c12)) | (~p8(c11, X41)))) | (~p8(c14, c12)) | (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14)))) | (~p8(c11, c14))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.41 tff(171,plain,
% 0.20/0.41 (~p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[170, 100, 93, 164])).
% 0.20/0.41 tff(172,plain,
% 0.20/0.41 (((~![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))) | ((~p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14)))) | (~p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11)))) | p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))))) <=> ((~![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))) | (~p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14)))) | (~p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11)))) | p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(173,plain,
% 0.20/0.41 ((~![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))) | ((~p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14)))) | (~p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11)))) | p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(174,plain,
% 0.20/0.41 ((~![X6: $i, X7: $i, X8: $i] : ((~p2(X6, X8)) | (~p2(X6, X7)) | p2(X7, X8))) | (~p2(f4(f5(c12, c11), c15), f4(f5(c12, c11), f3(c14)))) | (~p2(f4(f5(c12, c11), c15), f5(f7(c13, c12), f7(c13, c11)))) | p2(f5(f7(c13, c12), f7(c13, c11)), f4(f5(c12, c11), f3(c14)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.41 tff(175,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[174, 69, 171, 154, 76])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------