%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN603-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:39:40 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN603-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:37:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(p2_type, type, (
% 0.18/0.37 p2: ( $i * $i ) > $o)).
% 0.18/0.37 tff(f7_type, type, (
% 0.18/0.37 f7: ( $i * $i ) > $i)).
% 0.18/0.37 tff(c20_type, type, (
% 0.18/0.37 c20: $i)).
% 0.18/0.37 tff(f8_type, type, (
% 0.18/0.37 f8: ( $i * $i ) > $i)).
% 0.18/0.37 tff(c22_type, type, (
% 0.18/0.37 c22: $i)).
% 0.18/0.37 tff(c21_type, type, (
% 0.18/0.37 c21: $i)).
% 0.18/0.37 tff(f6_type, type, (
% 0.18/0.37 f6: ( $i * $i ) > $i)).
% 0.18/0.37 tff(f3_type, type, (
% 0.18/0.37 f3: $i > $i)).
% 0.18/0.37 tff(f4_type, type, (
% 0.18/0.37 f4: $i > $i)).
% 0.18/0.37 tff(c16_type, type, (
% 0.18/0.37 c16: $i)).
% 0.18/0.37 tff(f5_type, type, (
% 0.18/0.37 f5: $i > $i)).
% 0.18/0.37 tff(c17_type, type, (
% 0.18/0.37 c17: $i)).
% 0.18/0.37 tff(p15_type, type, (
% 0.18/0.37 p15: ( $i * $i ) > $o)).
% 0.18/0.37 tff(f9_type, type, (
% 0.18/0.37 f9: ( $i * $i ) > $i)).
% 0.18/0.37 tff(c23_type, type, (
% 0.18/0.37 c23: $i)).
% 0.18/0.37 tff(1,assumption,(~p2(f5(f4(c16)), f5(f4(c16)))), introduced(assumption)).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (^[X18: $i] : refl(p2(X18, X18) <=> p2(X18, X18))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![X18: $i] : p2(X18, X18) <=> ![X18: $i] : p2(X18, X18)),
% 0.18/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![X18: $i] : p2(X18, X18) <=> ![X18: $i] : p2(X18, X18)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(5,axiom,(![X18: $i] : p2(X18, X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_2')).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (![X18: $i] : p2(X18, X18)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.37 tff(7,plain,(
% 0.18/0.37 ![X18: $i] : p2(X18, X18)),
% 0.18/0.37 inference(skolemize,[status(sab)],[6])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (![X18: $i] : p2(X18, X18)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 ((~![X18: $i] : p2(X18, X18)) | p2(f5(f4(c16)), f5(f4(c16)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.37 tff(11,plain,(p2(f5(f4(c16)), f5(f4(c16)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (^[X39: $i, X38: $i, X37: $i, X40: $i] : refl(((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40))) <=> ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40))) <=> ![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40))) <=> ![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (^[X39: $i, X38: $i, X37: $i, X40: $i] : trans(monotonicity(rewrite((p2(f6(X37, X38), f6(X39, X40)) | (~p2(X37, X39))) <=> ((~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))), (((p2(f6(X37, X38), f6(X39, X40)) | (~p2(X37, X39))) | (~p2(X38, X40))) <=> (((~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40))) | (~p2(X38, X40))))), rewrite((((~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40))) | (~p2(X38, X40))) <=> ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))), (((p2(f6(X37, X38), f6(X39, X40)) | (~p2(X37, X39))) | (~p2(X38, X40))) <=> ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (![X39: $i, X38: $i, X37: $i, X40: $i] : ((p2(f6(X37, X38), f6(X39, X40)) | (~p2(X37, X39))) | (~p2(X38, X40))) <=> ![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.37 tff(17,axiom,(![X39: $i, X38: $i, X37: $i, X40: $i] : ((p2(f6(X37, X38), f6(X39, X40)) | (~p2(X37, X39))) | (~p2(X38, X40)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_21')).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 (![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.38 tff(20,plain,(
% 0.18/0.38 ![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[19])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (p2(f3(f4(c16)), c17) <=> p2(f3(f4(c16)), c17)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(23,axiom,(p2(f3(f4(c16)), c17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_6')).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (p2(f3(f4(c16)), c17)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (((~![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))) | ((~p2(f3(f4(c16)), c17)) | (~p2(f5(f4(c16)), f5(f4(c16)))) | p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17)))) <=> ((~![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))) | (~p2(f3(f4(c16)), c17)) | (~p2(f5(f4(c16)), f5(f4(c16)))) | p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 ((~![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))) | ((~p2(f3(f4(c16)), c17)) | (~p2(f5(f4(c16)), f5(f4(c16)))) | p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 ((~![X39: $i, X38: $i, X37: $i, X40: $i] : ((~p2(X38, X40)) | (~p2(X37, X39)) | p2(f6(X37, X38), f6(X39, X40)))) | (~p2(f3(f4(c16)), c17)) | (~p2(f5(f4(c16)), f5(f4(c16)))) | p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 ((~p2(f5(f4(c16)), f5(f4(c16)))) | p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[27, 24, 21])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 (p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[28, 11])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (^[X53: $i, X54: $i] : refl(((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21))) <=> ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21))) <=> ![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 (![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21))) <=> ![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 (^[X53: $i, X54: $i] : rewrite((((~p15(X53, c21)) | (~p2(X53, f9(c20, X54)))) | (~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17)))) <=> ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 (![X53: $i, X54: $i] : (((~p15(X53, c21)) | (~p2(X53, f9(c20, X54)))) | (~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17)))) <=> ![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.38 tff(35,axiom,(![X53: $i, X54: $i] : (((~p15(X53, c21)) | (~p2(X53, f9(c20, X54)))) | (~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p15_26')).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 (![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.18/0.38 tff(38,plain,(
% 0.18/0.38 ![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[37])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 (![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (p2(c22, f9(c20, c23)) <=> p2(c22, f9(c20, c23))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(41,axiom,(p2(c22, f9(c20, c23))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_5')).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (p2(c22, f9(c20, c23))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (p15(c22, c21) <=> p15(c22, c21)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(44,axiom,(p15(c22, c21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p15_3')).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (p15(c22, c21)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (((~![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))) | ((~p15(c22, c21)) | (~p2(c22, f9(c20, c23))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17))))) <=> ((~![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))) | (~p15(c22, c21)) | (~p2(c22, f9(c20, c23))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (((~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17))) | (~p2(c22, f9(c20, c23))) | (~p15(c22, c21))) <=> ((~p15(c22, c21)) | (~p2(c22, f9(c20, c23))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (((~![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))) | ((~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17))) | (~p2(c22, f9(c20, c23))) | (~p15(c22, c21)))) <=> ((~![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))) | ((~p15(c22, c21)) | (~p2(c22, f9(c20, c23))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17)))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[47])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 (((~![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))) | ((~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17))) | (~p2(c22, f9(c20, c23))) | (~p15(c22, c21)))) <=> ((~![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))) | (~p15(c22, c21)) | (~p2(c22, f9(c20, c23))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[48, 46])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 ((~![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))) | ((~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17))) | (~p2(c22, f9(c20, c23))) | (~p15(c22, c21)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 ((~![X53: $i, X54: $i] : ((~p2(f7(f8(c21, X53), c20), f6(f5(f4(c16)), c17))) | (~p2(X53, f9(c20, X54))) | (~p15(X53, c21)))) | (~p15(c22, c21)) | (~p2(c22, f9(c20, c23))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[51, 45, 42, 39])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 (^[X18: $i, X20: $i, X19: $i] : refl((p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(54,plain,
% 0.18/0.38 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (^[X18: $i, X20: $i, X19: $i] : trans(monotonicity(rewrite((p2(X19, X20) | (~p2(X18, X19))) <=> (p2(X19, X20) | (~p2(X18, X19)))), (((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))))), rewrite(((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))), (((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (![X18: $i, X20: $i, X19: $i] : ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.18/0.39 tff(58,axiom,(![X18: $i, X20: $i, X19: $i] : ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_14')).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.18/0.39 tff(61,plain,(
% 0.18/0.39 ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[60])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17)) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20))) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17)) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20))) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 ((p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17)) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17))) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20)))) <=> (p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17)) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20))) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17)) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17))) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17)) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20))) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[64])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17)) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17))) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17)) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20))) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[65, 63])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17)) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17))) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), c17)) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20))) | (~p2(f6(f5(f4(c16)), f3(f4(c16))), f6(f5(f4(c16)), c17)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 (~p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[68, 62, 52, 29])).
% 0.18/0.39 tff(70,assumption,(~p2(c21, c21)), introduced(assumption)).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 ((~![X18: $i] : p2(X18, X18)) | p2(c21, c21)),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[71, 8, 70])).
% 0.18/0.39 tff(73,plain,(p2(c21, c21)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 (^[X22: $i, X21: $i, X23: $i] : refl(((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22)) <=> ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 (![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22)) <=> ![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[74])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22)) <=> ![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (^[X22: $i, X21: $i, X23: $i] : trans(monotonicity(trans(monotonicity(rewrite((p2(X21, c22) | (~p15(X21, c21))) <=> ((~p15(X21, c21)) | p2(X21, c22))), (((p2(X21, c22) | (~p15(X21, c21))) | (~p2(X21, f9(c20, X22)))) <=> (((~p15(X21, c21)) | p2(X21, c22)) | (~p2(X21, f9(c20, X22)))))), rewrite((((~p15(X21, c21)) | p2(X21, c22)) | (~p2(X21, f9(c20, X22)))) <=> ((~p15(X21, c21)) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))), (((p2(X21, c22) | (~p15(X21, c21))) | (~p2(X21, f9(c20, X22)))) <=> ((~p15(X21, c21)) | (~p2(X21, f9(c20, X22))) | p2(X21, c22)))), ((((p2(X21, c22) | (~p15(X21, c21))) | (~p2(X21, f9(c20, X22)))) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23)))) <=> (((~p15(X21, c21)) | (~p2(X21, f9(c20, X22))) | p2(X21, c22)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23)))))), rewrite((((~p15(X21, c21)) | (~p2(X21, f9(c20, X22))) | p2(X21, c22)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23)))) <=> ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))), ((((p2(X21, c22) | (~p15(X21, c21))) | (~p2(X21, f9(c20, X22)))) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23)))) <=> ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (![X22: $i, X21: $i, X23: $i] : (((p2(X21, c22) | (~p15(X21, c21))) | (~p2(X21, f9(c20, X22)))) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23)))) <=> ![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[77])).
% 0.18/0.39 tff(79,axiom,(![X22: $i, X21: $i, X23: $i] : (((p2(X21, c22) | (~p15(X21, c21))) | (~p2(X21, f9(c20, X22)))) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_27')).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 (![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.18/0.39 tff(81,plain,
% 0.18/0.39 (![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.18/0.39 tff(82,plain,(
% 0.18/0.39 ![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))),
% 0.18/0.39 inference(skolemize,[status(sab)],[81])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 (![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.18/0.39 tff(84,plain,
% 0.18/0.39 (p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16)))) <=> p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(85,axiom,(p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_19')).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 (p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 (((~![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))) | ((~p15(c22, c21)) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))) | (~p2(c22, f9(c20, c23))) | p2(c22, c22))) <=> ((~![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))) | (~p15(c22, c21)) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))) | (~p2(c22, f9(c20, c23))) | p2(c22, c22))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(88,plain,
% 0.18/0.39 ((~![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))) | ((~p15(c22, c21)) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))) | (~p2(c22, f9(c20, c23))) | p2(c22, c22))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 ((~![X22: $i, X21: $i, X23: $i] : ((~p15(X21, c21)) | (~p2(f7(f8(c21, X21), c20), f6(f5(f4(c16)), X23))) | (~p2(X21, f9(c20, X22))) | p2(X21, c22))) | (~p15(c22, c21)) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))) | (~p2(c22, f9(c20, c23))) | p2(c22, c22)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 (p2(c22, c22)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[89, 45, 42, 86, 83])).
% 0.18/0.39 tff(91,plain,
% 0.18/0.39 (^[X47: $i, X45: $i, X46: $i, X48: $i] : refl(((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48))) <=> ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 (![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48))) <=> ![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[91])).
% 0.18/0.39 tff(93,plain,
% 0.18/0.39 (![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48))) <=> ![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(94,plain,
% 0.18/0.39 (^[X47: $i, X45: $i, X46: $i, X48: $i] : trans(monotonicity(rewrite((p2(f8(X45, X46), f8(X47, X48)) | (~p2(X45, X47))) <=> ((~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))), (((p2(f8(X45, X46), f8(X47, X48)) | (~p2(X45, X47))) | (~p2(X46, X48))) <=> (((~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48))) | (~p2(X46, X48))))), rewrite((((~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48))) | (~p2(X46, X48))) <=> ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))), (((p2(f8(X45, X46), f8(X47, X48)) | (~p2(X45, X47))) | (~p2(X46, X48))) <=> ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 (![X47: $i, X45: $i, X46: $i, X48: $i] : ((p2(f8(X45, X46), f8(X47, X48)) | (~p2(X45, X47))) | (~p2(X46, X48))) <=> ![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[94])).
% 0.18/0.40 tff(96,axiom,(![X47: $i, X45: $i, X46: $i, X48: $i] : ((p2(f8(X45, X46), f8(X47, X48)) | (~p2(X45, X47))) | (~p2(X46, X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_23')).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.18/0.40 tff(99,plain,(
% 0.18/0.40 ![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[98])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 (![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 (((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))) | (p2(f8(c21, c22), f8(c21, c22)) | (~p2(c22, c22)) | (~p2(c21, c21)))) <=> ((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))) | p2(f8(c21, c22), f8(c21, c22)) | (~p2(c22, c22)) | (~p2(c21, c21)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (((~p2(c22, c22)) | (~p2(c21, c21)) | p2(f8(c21, c22), f8(c21, c22))) <=> (p2(f8(c21, c22), f8(c21, c22)) | (~p2(c22, c22)) | (~p2(c21, c21)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 (((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))) | ((~p2(c22, c22)) | (~p2(c21, c21)) | p2(f8(c21, c22), f8(c21, c22)))) <=> ((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))) | (p2(f8(c21, c22), f8(c21, c22)) | (~p2(c22, c22)) | (~p2(c21, c21))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[102])).
% 0.18/0.40 tff(104,plain,
% 0.18/0.40 (((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))) | ((~p2(c22, c22)) | (~p2(c21, c21)) | p2(f8(c21, c22), f8(c21, c22)))) <=> ((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))) | p2(f8(c21, c22), f8(c21, c22)) | (~p2(c22, c22)) | (~p2(c21, c21)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[103, 101])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 ((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))) | ((~p2(c22, c22)) | (~p2(c21, c21)) | p2(f8(c21, c22), f8(c21, c22)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 ((~![X47: $i, X45: $i, X46: $i, X48: $i] : ((~p2(X46, X48)) | (~p2(X45, X47)) | p2(f8(X45, X46), f8(X47, X48)))) | p2(f8(c21, c22), f8(c21, c22)) | (~p2(c22, c22)) | (~p2(c21, c21))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.18/0.40 tff(107,plain,
% 0.18/0.40 (p2(f8(c21, c22), f8(c21, c22)) | (~p2(c21, c21))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[106, 100, 90])).
% 0.18/0.40 tff(108,plain,
% 0.18/0.40 (p2(f8(c21, c22), f8(c21, c22))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[107, 73])).
% 0.18/0.40 tff(109,assumption,(~p2(c20, c20)), introduced(assumption)).
% 0.18/0.40 tff(110,plain,
% 0.18/0.40 ((~![X18: $i] : p2(X18, X18)) | p2(c20, c20)),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(111,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[110, 8, 109])).
% 0.18/0.40 tff(112,plain,(p2(c20, c20)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(113,plain,
% 0.18/0.40 (^[X43: $i, X42: $i, X44: $i, X41: $i] : refl(((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44))) <=> ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(114,plain,
% 0.18/0.40 (![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44))) <=> ![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[113])).
% 0.18/0.40 tff(115,plain,
% 0.18/0.40 (![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44))) <=> ![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(116,plain,
% 0.18/0.40 (^[X43: $i, X42: $i, X44: $i, X41: $i] : trans(monotonicity(rewrite((p2(f7(X41, X42), f7(X43, X44)) | (~p2(X41, X43))) <=> ((~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))), (((p2(f7(X41, X42), f7(X43, X44)) | (~p2(X41, X43))) | (~p2(X42, X44))) <=> (((~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44))) | (~p2(X42, X44))))), rewrite((((~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44))) | (~p2(X42, X44))) <=> ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))), (((p2(f7(X41, X42), f7(X43, X44)) | (~p2(X41, X43))) | (~p2(X42, X44))) <=> ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(117,plain,
% 0.18/0.40 (![X43: $i, X42: $i, X44: $i, X41: $i] : ((p2(f7(X41, X42), f7(X43, X44)) | (~p2(X41, X43))) | (~p2(X42, X44))) <=> ![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[116])).
% 0.18/0.40 tff(118,axiom,(![X43: $i, X42: $i, X44: $i, X41: $i] : ((p2(f7(X41, X42), f7(X43, X44)) | (~p2(X41, X43))) | (~p2(X42, X44)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_22')).
% 0.18/0.40 tff(119,plain,
% 0.18/0.40 (![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.18/0.40 tff(120,plain,
% 0.18/0.40 (![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.18/0.40 tff(121,plain,(
% 0.18/0.40 ![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[120])).
% 0.18/0.40 tff(122,plain,
% 0.18/0.40 (![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.18/0.40 tff(123,plain,
% 0.18/0.40 (((~![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))) | ((~p2(c20, c20)) | (~p2(f8(c21, c22), f8(c21, c22))) | p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20)))) <=> ((~![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))) | (~p2(c20, c20)) | (~p2(f8(c21, c22), f8(c21, c22))) | p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(124,plain,
% 0.18/0.40 ((~![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))) | ((~p2(c20, c20)) | (~p2(f8(c21, c22), f8(c21, c22))) | p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(125,plain,
% 0.18/0.40 ((~![X43: $i, X42: $i, X44: $i, X41: $i] : ((~p2(X42, X44)) | (~p2(X41, X43)) | p2(f7(X41, X42), f7(X43, X44)))) | (~p2(c20, c20)) | (~p2(f8(c21, c22), f8(c21, c22))) | p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.40 tff(126,plain,
% 0.18/0.40 ((~p2(c20, c20)) | (~p2(f8(c21, c22), f8(c21, c22))) | p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[125, 122])).
% 0.18/0.40 tff(127,plain,
% 0.18/0.40 ((~p2(f8(c21, c22), f8(c21, c22))) | p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[126, 112])).
% 0.18/0.40 tff(128,plain,
% 0.18/0.40 (p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[127, 108])).
% 0.18/0.41 tff(129,plain,
% 0.18/0.41 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | ((~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))) | p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20)) | (~p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))) | p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20)) | (~p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(130,plain,
% 0.18/0.41 ((p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20)) | (~p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16)))))) <=> ((~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))) | p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20)) | (~p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20)) | (~p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | ((~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))) | p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20)) | (~p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[130])).
% 0.18/0.41 tff(132,plain,
% 0.18/0.41 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20)) | (~p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))) | p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20)) | (~p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[131, 129])).
% 0.18/0.41 tff(133,plain,
% 0.18/0.41 ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20)) | (~p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (~p2(f7(f8(c21, c22), c20), f6(f5(f4(c16)), f3(f4(c16))))) | p2(f6(f5(f4(c16)), f3(f4(c16))), f7(f8(c21, c22), c20)) | (~p2(f7(f8(c21, c22), c20), f7(f8(c21, c22), c20)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.18/0.41 tff(135,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[134, 62, 86, 128, 69])).
% 0.18/0.41 % SZS output end Proof
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------