%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN594-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:39 AM UTC 2025
% Result : Unsatisfiable 0.23s 0.40s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SYN594-1 : TPTP v9.0.0. Released v2.5.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 12:38:32 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.23/0.40 % SZS status Unsatisfiable
% 0.23/0.40 % SZS output start Proof
% 0.23/0.40 tff(p2_type, type, (
% 0.23/0.40 p2: ( $i * $i ) > $o)).
% 0.23/0.40 tff(f6_type, type, (
% 0.23/0.40 f6: ( $i * $i ) > $i)).
% 0.23/0.40 tff(f13_type, type, (
% 0.23/0.40 f13: ( $i * $i ) > $i)).
% 0.23/0.40 tff(f3_type, type, (
% 0.23/0.40 f3: $i > $i)).
% 0.23/0.40 tff(f5_type, type, (
% 0.23/0.40 f5: $i > $i)).
% 0.23/0.40 tff(c17_type, type, (
% 0.23/0.40 c17: $i)).
% 0.23/0.40 tff(c16_type, type, (
% 0.23/0.40 c16: $i)).
% 0.23/0.40 tff(f4_type, type, (
% 0.23/0.40 f4: $i > $i)).
% 0.23/0.40 tff(c19_type, type, (
% 0.23/0.40 c19: $i)).
% 0.23/0.40 tff(p14_type, type, (
% 0.23/0.40 p14: ( $i * $i ) > $o)).
% 0.23/0.40 tff(p15_type, type, (
% 0.23/0.40 p15: ( $i * $i ) > $o)).
% 0.23/0.40 tff(p7_type, type, (
% 0.23/0.40 p7: ( $i * $i ) > $o)).
% 0.23/0.40 tff(f8_type, type, (
% 0.23/0.40 f8: ( $i * $i ) > $i)).
% 0.23/0.40 tff(f9_type, type, (
% 0.23/0.40 f9: ( $i * $i ) > $i)).
% 0.23/0.40 tff(f10_type, type, (
% 0.23/0.40 f10: ( $i * $i ) > $i)).
% 0.23/0.40 tff(c22_type, type, (
% 0.23/0.40 c22: $i)).
% 0.23/0.40 tff(f11_type, type, (
% 0.23/0.40 f11: $i > $i)).
% 0.23/0.40 tff(f12_type, type, (
% 0.23/0.40 f12: $i > $i)).
% 0.23/0.40 tff(c20_type, type, (
% 0.23/0.40 c20: $i)).
% 0.23/0.40 tff(c21_type, type, (
% 0.23/0.40 c21: $i)).
% 0.23/0.40 tff(c18_type, type, (
% 0.23/0.40 c18: $i)).
% 0.23/0.40 tff(1,assumption,(~p2(c17, c17)), introduced(assumption)).
% 0.23/0.40 tff(2,plain,
% 0.23/0.40 (^[X10: $i] : refl(p2(X10, X10) <=> p2(X10, X10))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(3,plain,
% 0.23/0.41 (![X10: $i] : p2(X10, X10) <=> ![X10: $i] : p2(X10, X10)),
% 0.23/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.23/0.41 tff(4,plain,
% 0.23/0.41 (![X10: $i] : p2(X10, X10) <=> ![X10: $i] : p2(X10, X10)),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(5,axiom,(![X10: $i] : p2(X10, X10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_1')).
% 0.23/0.41 tff(6,plain,
% 0.23/0.41 (![X10: $i] : p2(X10, X10)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.23/0.41 tff(7,plain,(
% 0.23/0.41 ![X10: $i] : p2(X10, X10)),
% 0.23/0.41 inference(skolemize,[status(sab)],[6])).
% 0.23/0.41 tff(8,plain,
% 0.23/0.41 (![X10: $i] : p2(X10, X10)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.23/0.41 tff(9,plain,
% 0.23/0.41 ((~![X10: $i] : p2(X10, X10)) | p2(c17, c17)),
% 0.23/0.41 inference(quant_inst,[status(thm)],[])).
% 0.23/0.41 tff(10,plain,
% 0.23/0.41 ($false),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.23/0.41 tff(11,plain,(p2(c17, c17)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.41 tff(12,plain,
% 0.23/0.41 (^[X22: $i, X21: $i] : refl(((~p2(X21, X22)) | p2(f5(X21), f5(X22))) <=> ((~p2(X21, X22)) | p2(f5(X21), f5(X22))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(13,plain,
% 0.23/0.41 (![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22))) <=> ![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.23/0.41 tff(14,plain,
% 0.23/0.41 (![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22))) <=> ![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(15,plain,
% 0.23/0.41 (^[X22: $i, X21: $i] : rewrite((p2(f5(X21), f5(X22)) | (~p2(X21, X22))) <=> ((~p2(X21, X22)) | p2(f5(X21), f5(X22))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(16,plain,
% 0.23/0.41 (![X22: $i, X21: $i] : (p2(f5(X21), f5(X22)) | (~p2(X21, X22))) <=> ![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.23/0.41 tff(17,axiom,(![X22: $i, X21: $i] : (p2(f5(X21), f5(X22)) | (~p2(X21, X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_11')).
% 0.23/0.41 tff(18,plain,
% 0.23/0.41 (![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.23/0.41 tff(19,plain,
% 0.23/0.41 (![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.23/0.41 tff(20,plain,(
% 0.23/0.41 ![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22)))),
% 0.23/0.41 inference(skolemize,[status(sab)],[19])).
% 0.23/0.41 tff(21,plain,
% 0.23/0.41 (![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.23/0.41 tff(22,plain,
% 0.23/0.41 (((~![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22)))) | ((~p2(c17, c17)) | p2(f5(c17), f5(c17)))) <=> ((~![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22)))) | (~p2(c17, c17)) | p2(f5(c17), f5(c17)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(23,plain,
% 0.23/0.41 ((~![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22)))) | ((~p2(c17, c17)) | p2(f5(c17), f5(c17)))),
% 0.23/0.41 inference(quant_inst,[status(thm)],[])).
% 0.23/0.41 tff(24,plain,
% 0.23/0.41 ((~![X22: $i, X21: $i] : ((~p2(X21, X22)) | p2(f5(X21), f5(X22)))) | (~p2(c17, c17)) | p2(f5(c17), f5(c17))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.23/0.41 tff(25,plain,
% 0.23/0.41 ((~p2(c17, c17)) | p2(f5(c17), f5(c17))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.23/0.41 tff(26,plain,
% 0.23/0.41 (p2(f5(c17), f5(c17))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[25, 11])).
% 0.23/0.41 tff(27,plain,
% 0.23/0.41 (^[X20: $i, X19: $i] : refl(((~p2(X19, X20)) | p2(f4(X19), f4(X20))) <=> ((~p2(X19, X20)) | p2(f4(X19), f4(X20))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(28,plain,
% 0.23/0.41 (![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20))) <=> ![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.23/0.41 tff(29,plain,
% 0.23/0.41 (![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20))) <=> ![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(30,plain,
% 0.23/0.41 (^[X20: $i, X19: $i] : rewrite((p2(f4(X19), f4(X20)) | (~p2(X19, X20))) <=> ((~p2(X19, X20)) | p2(f4(X19), f4(X20))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(31,plain,
% 0.23/0.41 (![X20: $i, X19: $i] : (p2(f4(X19), f4(X20)) | (~p2(X19, X20))) <=> ![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.23/0.41 tff(32,axiom,(![X20: $i, X19: $i] : (p2(f4(X19), f4(X20)) | (~p2(X19, X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_10')).
% 0.23/0.41 tff(33,plain,
% 0.23/0.41 (![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.23/0.41 tff(34,plain,
% 0.23/0.41 (![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.23/0.41 tff(35,plain,(
% 0.23/0.41 ![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20)))),
% 0.23/0.41 inference(skolemize,[status(sab)],[34])).
% 0.23/0.41 tff(36,plain,
% 0.23/0.41 (![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.23/0.41 tff(37,plain,
% 0.23/0.41 (((~![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20)))) | ((~p2(f5(c17), f5(c17))) | p2(f4(f5(c17)), f4(f5(c17))))) <=> ((~![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20)))) | (~p2(f5(c17), f5(c17))) | p2(f4(f5(c17)), f4(f5(c17))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(38,plain,
% 0.23/0.41 ((~![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20)))) | ((~p2(f5(c17), f5(c17))) | p2(f4(f5(c17)), f4(f5(c17))))),
% 0.23/0.41 inference(quant_inst,[status(thm)],[])).
% 0.23/0.41 tff(39,plain,
% 0.23/0.41 ((~![X20: $i, X19: $i] : ((~p2(X19, X20)) | p2(f4(X19), f4(X20)))) | (~p2(f5(c17), f5(c17))) | p2(f4(f5(c17)), f4(f5(c17)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.23/0.41 tff(40,plain,
% 0.23/0.41 ((~p2(f5(c17), f5(c17))) | p2(f4(f5(c17)), f4(f5(c17)))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.23/0.41 tff(41,plain,
% 0.23/0.41 (p2(f4(f5(c17)), f4(f5(c17)))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[40, 26])).
% 0.23/0.41 tff(42,plain,
% 0.23/0.41 (^[X17: $i, X18: $i] : refl(((~p2(X17, X18)) | p2(f3(X17), f3(X18))) <=> ((~p2(X17, X18)) | p2(f3(X17), f3(X18))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(43,plain,
% 0.23/0.41 (![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18))) <=> ![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.23/0.41 tff(44,plain,
% 0.23/0.41 (![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18))) <=> ![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(45,plain,
% 0.23/0.41 (^[X17: $i, X18: $i] : rewrite((p2(f3(X17), f3(X18)) | (~p2(X17, X18))) <=> ((~p2(X17, X18)) | p2(f3(X17), f3(X18))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(46,plain,
% 0.23/0.41 (![X17: $i, X18: $i] : (p2(f3(X17), f3(X18)) | (~p2(X17, X18))) <=> ![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.23/0.41 tff(47,axiom,(![X17: $i, X18: $i] : (p2(f3(X17), f3(X18)) | (~p2(X17, X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_9')).
% 0.23/0.41 tff(48,plain,
% 0.23/0.41 (![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.23/0.41 tff(49,plain,
% 0.23/0.41 (![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.23/0.41 tff(50,plain,(
% 0.23/0.41 ![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18)))),
% 0.23/0.41 inference(skolemize,[status(sab)],[49])).
% 0.23/0.41 tff(51,plain,
% 0.23/0.41 (![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.23/0.41 tff(52,plain,
% 0.23/0.41 (((~![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18)))) | ((~p2(f4(f5(c17)), f4(f5(c17)))) | p2(f3(f4(f5(c17))), f3(f4(f5(c17)))))) <=> ((~![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18)))) | (~p2(f4(f5(c17)), f4(f5(c17)))) | p2(f3(f4(f5(c17))), f3(f4(f5(c17)))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(53,plain,
% 0.23/0.41 ((~![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18)))) | ((~p2(f4(f5(c17)), f4(f5(c17)))) | p2(f3(f4(f5(c17))), f3(f4(f5(c17)))))),
% 0.23/0.41 inference(quant_inst,[status(thm)],[])).
% 0.23/0.41 tff(54,plain,
% 0.23/0.41 ((~![X17: $i, X18: $i] : ((~p2(X17, X18)) | p2(f3(X17), f3(X18)))) | (~p2(f4(f5(c17)), f4(f5(c17)))) | p2(f3(f4(f5(c17))), f3(f4(f5(c17))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.23/0.41 tff(55,plain,
% 0.23/0.41 ((~p2(f4(f5(c17)), f4(f5(c17)))) | p2(f3(f4(f5(c17))), f3(f4(f5(c17))))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.23/0.41 tff(56,plain,
% 0.23/0.41 (p2(f3(f4(f5(c17))), f3(f4(f5(c17))))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[55, 41])).
% 0.23/0.41 tff(57,assumption,(~p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))), introduced(assumption)).
% 0.23/0.41 tff(58,plain,
% 0.23/0.41 ((~![X10: $i] : p2(X10, X10)) | p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))),
% 0.23/0.41 inference(quant_inst,[status(thm)],[])).
% 0.23/0.41 tff(59,plain,
% 0.23/0.41 ($false),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[58, 8, 57])).
% 0.23/0.41 tff(60,plain,(p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.41 tff(61,plain,
% 0.23/0.41 (^[X25: $i, X23: $i, X26: $i, X24: $i] : refl(((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26))) <=> ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(62,plain,
% 0.23/0.41 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26))) <=> ![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.23/0.41 tff(63,plain,
% 0.23/0.41 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26))) <=> ![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(64,plain,
% 0.23/0.41 (^[X25: $i, X23: $i, X26: $i, X24: $i] : trans(monotonicity(rewrite((p2(f6(X23, X24), f6(X25, X26)) | (~p2(X23, X25))) <=> ((~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))), (((p2(f6(X23, X24), f6(X25, X26)) | (~p2(X23, X25))) | (~p2(X24, X26))) <=> (((~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26))) | (~p2(X24, X26))))), rewrite((((~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26))) | (~p2(X24, X26))) <=> ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))), (((p2(f6(X23, X24), f6(X25, X26)) | (~p2(X23, X25))) | (~p2(X24, X26))) <=> ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(65,plain,
% 0.23/0.41 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((p2(f6(X23, X24), f6(X25, X26)) | (~p2(X23, X25))) | (~p2(X24, X26))) <=> ![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.23/0.41 tff(66,axiom,(![X25: $i, X23: $i, X26: $i, X24: $i] : ((p2(f6(X23, X24), f6(X25, X26)) | (~p2(X23, X25))) | (~p2(X24, X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_24')).
% 0.23/0.41 tff(67,plain,
% 0.23/0.41 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.23/0.41 tff(68,plain,
% 0.23/0.41 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.23/0.41 tff(69,plain,(
% 0.23/0.41 ![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))),
% 0.23/0.41 inference(skolemize,[status(sab)],[68])).
% 0.23/0.41 tff(70,plain,
% 0.23/0.41 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.23/0.41 tff(71,plain,
% 0.23/0.41 (((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))) | ((~p2(f3(f4(f5(c17))), f3(f4(f5(c17))))) | (~p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17))))))) <=> ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))) | (~p2(f3(f4(f5(c17))), f3(f4(f5(c17))))) | (~p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17))))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(72,plain,
% 0.23/0.41 (((~p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))) | (~p2(f3(f4(f5(c17))), f3(f4(f5(c17))))) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))) <=> ((~p2(f3(f4(f5(c17))), f3(f4(f5(c17))))) | (~p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17))))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(73,plain,
% 0.23/0.41 (((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))) | ((~p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))) | (~p2(f3(f4(f5(c17))), f3(f4(f5(c17))))) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17))))))) <=> ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))) | ((~p2(f3(f4(f5(c17))), f3(f4(f5(c17))))) | (~p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[72])).
% 0.23/0.41 tff(74,plain,
% 0.23/0.41 (((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))) | ((~p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))) | (~p2(f3(f4(f5(c17))), f3(f4(f5(c17))))) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17))))))) <=> ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))) | (~p2(f3(f4(f5(c17))), f3(f4(f5(c17))))) | (~p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17))))))),
% 0.23/0.41 inference(transitivity,[status(thm)],[73, 71])).
% 0.23/0.41 tff(75,plain,
% 0.23/0.41 ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))) | ((~p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))) | (~p2(f3(f4(f5(c17))), f3(f4(f5(c17))))) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17))))))),
% 0.23/0.41 inference(quant_inst,[status(thm)],[])).
% 0.23/0.41 tff(76,plain,
% 0.23/0.41 ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p2(X24, X26)) | (~p2(X23, X25)) | p2(f6(X23, X24), f6(X25, X26)))) | (~p2(f3(f4(f5(c17))), f3(f4(f5(c17))))) | (~p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.23/0.41 tff(77,plain,
% 0.23/0.41 ((~p2(f3(f4(f5(c17))), f3(f4(f5(c17))))) | (~p2(f13(c16, f3(f5(c17))), f13(c16, f3(f5(c17))))) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[76, 70])).
% 0.23/0.41 tff(78,plain,
% 0.23/0.42 (p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[77, 60, 56])).
% 0.23/0.42 tff(79,plain,
% 0.23/0.42 (p14(c19, f6(f3(f4(f5(c17))), c16)) <=> p14(c19, f6(f3(f4(f5(c17))), c16))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(80,axiom,(p14(c19, f6(f3(f4(f5(c17))), c16))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p14_7')).
% 0.23/0.42 tff(81,plain,
% 0.23/0.42 (p14(c19, f6(f3(f4(f5(c17))), c16))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.23/0.42 tff(82,plain,
% 0.23/0.42 (^[X4: $i, X5: $i] : refl(((~p14(X4, X5)) | p15(X4, X5)) <=> ((~p14(X4, X5)) | p15(X4, X5)))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(83,plain,
% 0.23/0.42 (![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5)) <=> ![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[82])).
% 0.23/0.42 tff(84,plain,
% 0.23/0.42 (![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5)) <=> ![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(85,plain,
% 0.23/0.42 (^[X4: $i, X5: $i] : rewrite((p15(X4, X5) | (~p14(X4, X5))) <=> ((~p14(X4, X5)) | p15(X4, X5)))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(86,plain,
% 0.23/0.42 (![X4: $i, X5: $i] : (p15(X4, X5) | (~p14(X4, X5))) <=> ![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[85])).
% 0.23/0.42 tff(87,axiom,(![X4: $i, X5: $i] : (p15(X4, X5) | (~p14(X4, X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p15_5')).
% 0.23/0.42 tff(88,plain,
% 0.23/0.42 (![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.23/0.42 tff(89,plain,
% 0.23/0.42 (![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.23/0.42 tff(90,plain,(
% 0.23/0.42 ![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5))),
% 0.23/0.42 inference(skolemize,[status(sab)],[89])).
% 0.23/0.42 tff(91,plain,
% 0.23/0.42 (![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.23/0.42 tff(92,plain,
% 0.23/0.42 (((~![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5))) | ((~p14(c19, f6(f3(f4(f5(c17))), c16))) | p15(c19, f6(f3(f4(f5(c17))), c16)))) <=> ((~![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5))) | (~p14(c19, f6(f3(f4(f5(c17))), c16))) | p15(c19, f6(f3(f4(f5(c17))), c16)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(93,plain,
% 0.23/0.42 ((~![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5))) | ((~p14(c19, f6(f3(f4(f5(c17))), c16))) | p15(c19, f6(f3(f4(f5(c17))), c16)))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(94,plain,
% 0.23/0.42 ((~![X4: $i, X5: $i] : ((~p14(X4, X5)) | p15(X4, X5))) | (~p14(c19, f6(f3(f4(f5(c17))), c16))) | p15(c19, f6(f3(f4(f5(c17))), c16))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.23/0.42 tff(95,plain,
% 0.23/0.42 (p15(c19, f6(f3(f4(f5(c17))), c16))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[94, 91, 81])).
% 0.23/0.42 tff(96,plain,
% 0.23/0.42 (^[X47: $i, X46: $i, X48: $i] : refl(((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47))) <=> ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(97,plain,
% 0.23/0.42 (![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47))) <=> ![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[96])).
% 0.23/0.42 tff(98,plain,
% 0.23/0.42 (![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47))) <=> ![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(99,plain,
% 0.23/0.42 (^[X47: $i, X46: $i, X48: $i] : trans(monotonicity(rewrite((((~p14(X46, f3(f4(f5(c17))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16)))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47))) <=> ((~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))), (((((~p14(X46, f3(f4(f5(c17))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16)))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47))) | (~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22))))))) <=> (((~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47))) | (~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22))))))))), rewrite((((~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47))) | (~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22))))))) <=> ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))), (((((~p14(X46, f3(f4(f5(c17))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16)))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47))) | (~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22))))))) <=> ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(100,plain,
% 0.23/0.42 (![X47: $i, X46: $i, X48: $i] : ((((~p14(X46, f3(f4(f5(c17))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16)))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47))) | (~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22))))))) <=> ![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[99])).
% 0.23/0.42 tff(101,axiom,(![X47: $i, X46: $i, X48: $i] : ((((~p14(X46, f3(f4(f5(c17))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16)))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47))) | (~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p14_27')).
% 0.23/0.42 tff(102,plain,
% 0.23/0.42 (![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.23/0.42 tff(103,plain,
% 0.23/0.43 (![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.23/0.43 tff(104,plain,(
% 0.23/0.43 ![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))),
% 0.23/0.43 inference(skolemize,[status(sab)],[103])).
% 0.23/0.43 tff(105,plain,
% 0.23/0.43 (![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.23/0.43 tff(106,plain,
% 0.23/0.43 (p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22))))) <=> p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(107,axiom,(p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_25')).
% 0.23/0.43 tff(108,plain,
% 0.23/0.43 (p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.23/0.43 tff(109,plain,
% 0.23/0.43 (p14(c18, f3(f4(f5(c17)))) <=> p14(c18, f3(f4(f5(c17))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(110,axiom,(p14(c18, f3(f4(f5(c17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p14_4')).
% 0.23/0.43 tff(111,plain,
% 0.23/0.43 (p14(c18, f3(f4(f5(c17))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.23/0.43 tff(112,plain,
% 0.23/0.43 (((~![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))) | ((~p14(c18, f3(f4(f5(c17))))) | (~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(c19, f6(f3(f4(f5(c17))), c16))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)))) <=> ((~![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))) | (~p14(c18, f3(f4(f5(c17))))) | (~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(c19, f6(f3(f4(f5(c17))), c16))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(113,plain,
% 0.23/0.43 (((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(c19, f6(f3(f4(f5(c17))), c16))) | (~p14(c18, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19))) <=> ((~p14(c18, f3(f4(f5(c17))))) | (~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(c19, f6(f3(f4(f5(c17))), c16))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(114,plain,
% 0.23/0.43 (((~![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))) | ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(c19, f6(f3(f4(f5(c17))), c16))) | (~p14(c18, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)))) <=> ((~![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))) | ((~p14(c18, f3(f4(f5(c17))))) | (~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(c19, f6(f3(f4(f5(c17))), c16))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[113])).
% 0.23/0.43 tff(115,plain,
% 0.23/0.43 (((~![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))) | ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(c19, f6(f3(f4(f5(c17))), c16))) | (~p14(c18, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)))) <=> ((~![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))) | (~p14(c18, f3(f4(f5(c17))))) | (~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(c19, f6(f3(f4(f5(c17))), c16))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)))),
% 0.23/0.43 inference(transitivity,[status(thm)],[114, 112])).
% 0.23/0.43 tff(116,plain,
% 0.23/0.43 ((~![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))) | ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(c19, f6(f3(f4(f5(c17))), c16))) | (~p14(c18, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(117,plain,
% 0.23/0.43 ((~![X47: $i, X46: $i, X48: $i] : ((~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), X46), f8(f10(f11(f3(f4(f5(c17)))), X48), f9(f11(X47), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(X47, f6(f3(f4(f5(c17))), c16))) | (~p14(X46, f3(f4(f5(c17))))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), X47)))) | (~p14(c18, f3(f4(f5(c17))))) | (~p7(c20, f8(f10(f12(f11(f3(f5(c17)))), c18), f8(f10(f11(f3(f4(f5(c17)))), c21), f9(f11(c19), f10(f11(f3(f4(f5(c17)))), c22)))))) | (~p15(c19, f6(f3(f4(f5(c17))), c16))) | (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.23/0.43 tff(118,plain,
% 0.23/0.43 (~p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[117, 111, 108, 105, 95])).
% 0.23/0.43 tff(119,plain,
% 0.23/0.43 (p15(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19) <=> p15(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(120,axiom,(p15(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p15_16')).
% 0.23/0.43 tff(121,plain,
% 0.23/0.43 (p15(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.23/0.43 tff(122,plain,
% 0.23/0.43 (^[X4: $i, X5: $i] : refl((p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5))) <=> (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(123,plain,
% 0.23/0.43 (![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5))) <=> ![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[122])).
% 0.23/0.43 tff(124,plain,
% 0.23/0.43 (![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5))) <=> ![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(125,plain,
% 0.23/0.43 (^[X4: $i, X5: $i] : rewrite(((p14(X4, X5) | p2(X4, X5)) | (~p15(X4, X5))) <=> (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(126,plain,
% 0.23/0.43 (![X4: $i, X5: $i] : ((p14(X4, X5) | p2(X4, X5)) | (~p15(X4, X5))) <=> ![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[125])).
% 0.23/0.43 tff(127,axiom,(![X4: $i, X5: $i] : ((p14(X4, X5) | p2(X4, X5)) | (~p15(X4, X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p14_13')).
% 0.23/0.43 tff(128,plain,
% 0.23/0.43 (![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.23/0.43 tff(129,plain,
% 0.23/0.43 (![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.23/0.43 tff(130,plain,(
% 0.23/0.43 ![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5)))),
% 0.23/0.43 inference(skolemize,[status(sab)],[129])).
% 0.23/0.43 tff(131,plain,
% 0.23/0.43 (![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.23/0.43 tff(132,plain,
% 0.23/0.43 (((~![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5)))) | (p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19) | (~p15(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)))) <=> ((~![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5)))) | p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19) | (~p15(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(133,plain,
% 0.23/0.43 ((~![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5)))) | (p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19) | (~p15(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(134,plain,
% 0.23/0.43 ((~![X4: $i, X5: $i] : (p14(X4, X5) | p2(X4, X5) | (~p15(X4, X5)))) | p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19) | (~p15(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.23/0.43 tff(135,plain,
% 0.23/0.43 (p14(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19) | p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[134, 131, 121])).
% 0.23/0.43 tff(136,plain,
% 0.23/0.43 (p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[135, 118])).
% 0.23/0.43 tff(137,plain,
% 0.23/0.43 ((~p2(c19, f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))) <=> (~p2(c19, f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17))))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(138,axiom,(~p2(c19, f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p2_17')).
% 0.23/0.43 tff(139,plain,
% 0.23/0.43 (~p2(c19, f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.23/0.43 tff(140,plain,
% 0.23/0.43 (^[X12: $i, X11: $i, X10: $i] : refl(((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12)) <=> ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12)))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(141,plain,
% 0.23/0.43 (![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12)) <=> ![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[140])).
% 0.23/0.43 tff(142,plain,
% 0.23/0.43 (![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12)) <=> ![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(143,plain,
% 0.23/0.44 (^[X12: $i, X11: $i, X10: $i] : trans(monotonicity(rewrite((p2(X11, X12) | (~p2(X10, X11))) <=> ((~p2(X10, X11)) | p2(X11, X12))), (((p2(X11, X12) | (~p2(X10, X11))) | (~p2(X10, X12))) <=> (((~p2(X10, X11)) | p2(X11, X12)) | (~p2(X10, X12))))), rewrite((((~p2(X10, X11)) | p2(X11, X12)) | (~p2(X10, X12))) <=> ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))), (((p2(X11, X12) | (~p2(X10, X11))) | (~p2(X10, X12))) <=> ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(144,plain,
% 0.23/0.44 (![X12: $i, X11: $i, X10: $i] : ((p2(X11, X12) | (~p2(X10, X11))) | (~p2(X10, X12))) <=> ![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[143])).
% 0.23/0.44 tff(145,axiom,(![X12: $i, X11: $i, X10: $i] : ((p2(X11, X12) | (~p2(X10, X11))) | (~p2(X10, X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_15')).
% 0.23/0.44 tff(146,plain,
% 0.23/0.44 (![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.23/0.44 tff(147,plain,
% 0.23/0.44 (![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.23/0.44 tff(148,plain,(
% 0.23/0.44 ![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))),
% 0.23/0.44 inference(skolemize,[status(sab)],[147])).
% 0.23/0.44 tff(149,plain,
% 0.23/0.44 (![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.23/0.44 tff(150,plain,
% 0.23/0.44 (((~![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))) | ((~p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)) | (~p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))) | p2(c19, f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17))))))) <=> ((~![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))) | (~p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)) | (~p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))) | p2(c19, f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(151,plain,
% 0.23/0.44 ((~![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))) | ((~p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)) | (~p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))) | p2(c19, f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17))))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(152,plain,
% 0.23/0.44 ((~![X12: $i, X11: $i, X10: $i] : ((~p2(X10, X11)) | (~p2(X10, X12)) | p2(X11, X12))) | (~p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), c19)) | (~p2(f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))), f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))) | p2(c19, f6(f3(f4(f5(c17))), f13(c16, f3(f5(c17)))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.23/0.44 tff(153,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[152, 149, 139, 136, 78])).
% 0.23/0.44 % SZS output end Proof
% 0.23/0.44 % E exiting
%------------------------------------------------------------------------------