TSTP Solution File: SYN613-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN613-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Thu Sep 29 23:56:38 EDT 2022
% Result : Unsatisfiable 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN613-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 06:07:43 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.52 % SZS status Unsatisfiable
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 tff(p11_type, type, (
% 0.20/0.52 p11: ( $i * $i ) > $o)).
% 0.20/0.52 tff(c23_type, type, (
% 0.20/0.52 c23: $i)).
% 0.20/0.52 tff(f12_type, type, (
% 0.20/0.52 f12: $i > $i)).
% 0.20/0.52 tff(f9_type, type, (
% 0.20/0.52 f9: $i > $i)).
% 0.20/0.52 tff(c21_type, type, (
% 0.20/0.52 c21: $i)).
% 0.20/0.52 tff(p17_type, type, (
% 0.20/0.52 p17: ( $i * $i * $i ) > $o)).
% 0.20/0.52 tff(f4_type, type, (
% 0.20/0.52 f4: $i > $i)).
% 0.20/0.52 tff(f7_type, type, (
% 0.20/0.52 f7: ( $i * $i ) > $i)).
% 0.20/0.52 tff(f8_type, type, (
% 0.20/0.52 f8: ( $i * $i ) > $i)).
% 0.20/0.52 tff(c22_type, type, (
% 0.20/0.52 c22: $i)).
% 0.20/0.52 tff(f10_type, type, (
% 0.20/0.52 f10: $i > $i)).
% 0.20/0.52 tff(c20_type, type, (
% 0.20/0.52 c20: $i)).
% 0.20/0.52 tff(c19_type, type, (
% 0.20/0.52 c19: $i)).
% 0.20/0.52 tff(p3_type, type, (
% 0.20/0.52 p3: ( $i * $i ) > $o)).
% 0.20/0.52 tff(p2_type, type, (
% 0.20/0.52 p2: ( $i * $i ) > $o)).
% 0.20/0.52 tff(p16_type, type, (
% 0.20/0.52 p16: ( $i * $i ) > $o)).
% 0.20/0.52 tff(c24_type, type, (
% 0.20/0.52 c24: $i)).
% 0.20/0.52 tff(1,plain,
% 0.20/0.52 (^[X29: $i] : refl(p2(X29, X29) <=> p2(X29, X29))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(2,plain,
% 0.20/0.52 (![X29: $i] : p2(X29, X29) <=> ![X29: $i] : p2(X29, X29)),
% 0.20/0.52 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.52 tff(3,plain,
% 0.20/0.52 (![X29: $i] : p2(X29, X29) <=> ![X29: $i] : p2(X29, X29)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(4,axiom,(![X29: $i] : p2(X29, X29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_5')).
% 0.20/0.52 tff(5,plain,
% 0.20/0.52 (![X29: $i] : p2(X29, X29)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.52 tff(6,plain,(
% 0.20/0.52 ![X29: $i] : p2(X29, X29)),
% 0.20/0.52 inference(skolemize,[status(sab)],[5])).
% 0.20/0.52 tff(7,plain,
% 0.20/0.52 (![X29: $i] : p2(X29, X29)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.52 tff(8,plain,
% 0.20/0.52 ((~![X29: $i] : p2(X29, X29)) | p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(9,plain,
% 0.20/0.52 (p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.52 tff(10,plain,
% 0.20/0.52 (^[X39: $i, X40: $i] : refl(((~p2(X39, X40)) | p3(f4(X39), f4(X40))) <=> ((~p2(X39, X40)) | p3(f4(X39), f4(X40))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(11,plain,
% 0.20/0.52 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40))) <=> ![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.52 tff(12,plain,
% 0.20/0.52 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40))) <=> ![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(13,plain,
% 0.20/0.52 (^[X39: $i, X40: $i] : rewrite((p3(f4(X39), f4(X40)) | (~p2(X39, X40))) <=> ((~p2(X39, X40)) | p3(f4(X39), f4(X40))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(14,plain,
% 0.20/0.52 (![X39: $i, X40: $i] : (p3(f4(X39), f4(X40)) | (~p2(X39, X40))) <=> ![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.52 tff(15,axiom,(![X39: $i, X40: $i] : (p3(f4(X39), f4(X40)) | (~p2(X39, X40)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_13')).
% 0.20/0.52 tff(16,plain,
% 0.20/0.52 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.52 tff(17,plain,
% 0.20/0.52 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.52 tff(18,plain,(
% 0.20/0.52 ![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[17])).
% 0.20/0.52 tff(19,plain,
% 0.20/0.52 (![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.52 tff(20,plain,
% 0.20/0.52 (((~![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))) | ((~p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))) | p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22)))))) <=> ((~![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))) | (~p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))) | p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(21,plain,
% 0.20/0.52 ((~![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))) | ((~p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))) | p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(22,plain,
% 0.20/0.52 ((~![X39: $i, X40: $i] : ((~p2(X39, X40)) | p3(f4(X39), f4(X40)))) | (~p2(f7(f10(c20), f8(f9(c21), c22)), f7(f10(c20), f8(f9(c21), c22)))) | p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.52 tff(23,plain,
% 0.20/0.52 (p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.20/0.52 tff(24,assumption,(~p16(c19, c19)), introduced(assumption)).
% 0.20/0.52 tff(25,plain,
% 0.20/0.52 (^[X14: $i] : refl(p16(X14, X14) <=> p16(X14, X14))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(26,plain,
% 0.20/0.52 (![X14: $i] : p16(X14, X14) <=> ![X14: $i] : p16(X14, X14)),
% 0.20/0.52 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.52 tff(27,plain,
% 0.20/0.52 (![X14: $i] : p16(X14, X14) <=> ![X14: $i] : p16(X14, X14)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(28,axiom,(![X14: $i] : p16(X14, X14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p16_6')).
% 0.20/0.52 tff(29,plain,
% 0.20/0.52 (![X14: $i] : p16(X14, X14)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.52 tff(30,plain,(
% 0.20/0.52 ![X14: $i] : p16(X14, X14)),
% 0.20/0.52 inference(skolemize,[status(sab)],[29])).
% 0.20/0.52 tff(31,plain,
% 0.20/0.52 (![X14: $i] : p16(X14, X14)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.52 tff(32,plain,
% 0.20/0.52 ((~![X14: $i] : p16(X14, X14)) | p16(c19, c19)),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(33,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[32, 31, 24])).
% 0.20/0.52 tff(34,plain,(p16(c19, c19)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(35,plain,
% 0.20/0.52 (^[X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : refl(((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) <=> ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(36,plain,
% 0.20/0.52 (![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) <=> ![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.52 tff(37,plain,
% 0.20/0.52 (![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) <=> ![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(38,plain,
% 0.20/0.52 (^[X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p17(X17, X18, X19) | (~p3(X22, X18))) <=> ((~p3(X22, X18)) | p17(X17, X18, X19))), (((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) <=> (((~p3(X22, X18)) | p17(X17, X18, X19)) | (~p16(X21, X17))))), rewrite((((~p3(X22, X18)) | p17(X17, X18, X19)) | (~p16(X21, X17))) <=> ((~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))), (((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) <=> ((~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)))), ((((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) | (~p11(X20, X19))) <=> (((~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) | (~p11(X20, X19))))), rewrite((((~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) | (~p11(X20, X19))) <=> ((~p11(X20, X19)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))), ((((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) | (~p11(X20, X19))) <=> ((~p11(X20, X19)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)))), (((((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) | (~p11(X20, X19))) | (~p17(X21, X22, X20))) <=> (((~p11(X20, X19)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) | (~p17(X21, X22, X20))))), rewrite((((~p11(X20, X19)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19)) | (~p17(X21, X22, X20))) <=> ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))), (((((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) | (~p11(X20, X19))) | (~p17(X21, X22, X20))) <=> ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(39,plain,
% 0.20/0.52 (![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) | (~p11(X20, X19))) | (~p17(X21, X22, X20))) <=> ![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.52 tff(40,axiom,(![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((((p17(X17, X18, X19) | (~p3(X22, X18))) | (~p16(X21, X17))) | (~p11(X20, X19))) | (~p17(X21, X22, X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p17_29')).
% 0.20/0.52 tff(41,plain,
% 0.20/0.52 (![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.52 tff(42,plain,
% 0.20/0.52 (![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.52 tff(43,plain,(
% 0.20/0.52 ![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.20/0.52 inference(skolemize,[status(sab)],[42])).
% 0.20/0.52 tff(44,plain,
% 0.20/0.52 (![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.52 tff(45,plain,
% 0.20/0.52 (p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24) <=> p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(46,axiom,(p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p17_21')).
% 0.20/0.52 tff(47,plain,
% 0.20/0.52 (p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.52 tff(48,plain,
% 0.20/0.52 (p11(c24, f12(f9(c21))) <=> p11(c24, f12(f9(c21)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(49,axiom,(p11(c24, f12(f9(c21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_8')).
% 0.20/0.52 tff(50,plain,
% 0.20/0.52 (p11(c24, f12(f9(c21)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.52 tff(51,plain,
% 0.20/0.52 (((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | ((~p11(c24, f12(f9(c21)))) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21))))) <=> ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | (~p11(c24, f12(f9(c21)))) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(52,plain,
% 0.20/0.52 ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | ((~p11(c24, f12(f9(c21)))) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(53,plain,
% 0.20/0.52 ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | (~p11(c24, f12(f9(c21)))) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.52 tff(54,plain,
% 0.20/0.52 (p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[53, 50, 47, 44, 34, 23])).
% 0.20/0.52 tff(55,plain,
% 0.20/0.52 ((~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)) <=> (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(56,axiom,(~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p17_22')).
% 0.20/0.52 tff(57,plain,
% 0.20/0.52 (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.52 tff(58,plain,
% 0.20/0.52 (((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | (p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | (~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))))) <=> ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | (~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(59,plain,
% 0.20/0.52 (((~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)) <=> (p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | (~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(60,plain,
% 0.20/0.52 (((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | ((~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23))) <=> ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | (p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | (~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.52 tff(61,plain,
% 0.20/0.52 (((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | ((~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23))) <=> ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | (~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[60, 58])).
% 0.20/0.53 tff(62,plain,
% 0.20/0.53 ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | ((~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21)))) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(63,plain,
% 0.20/0.53 ((~![X22: $i, X21: $i, X17: $i, X18: $i, X20: $i, X19: $i] : ((~p11(X20, X19)) | (~p17(X21, X22, X20)) | (~p16(X21, X17)) | (~p3(X22, X18)) | p17(X17, X18, X19))) | p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) | (~p16(c19, c19)) | (~p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22))))) | (~p11(f12(f9(c21)), c23)) | (~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), f12(f9(c21))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.53 tff(64,plain,
% 0.20/0.53 (~p11(f12(f9(c21)), c23)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[63, 57, 44, 34, 23, 54])).
% 0.20/0.53 tff(65,plain,
% 0.20/0.53 (^[X0: $i] : refl(p11(X0, X0) <=> p11(X0, X0))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(66,plain,
% 0.20/0.53 (![X0: $i] : p11(X0, X0) <=> ![X0: $i] : p11(X0, X0)),
% 0.20/0.53 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.53 tff(67,plain,
% 0.20/0.53 (![X0: $i] : p11(X0, X0) <=> ![X0: $i] : p11(X0, X0)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(68,axiom,(![X0: $i] : p11(X0, X0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_1')).
% 0.20/0.53 tff(69,plain,
% 0.20/0.53 (![X0: $i] : p11(X0, X0)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.53 tff(70,plain,(
% 0.20/0.53 ![X0: $i] : p11(X0, X0)),
% 0.20/0.53 inference(skolemize,[status(sab)],[69])).
% 0.20/0.53 tff(71,plain,
% 0.20/0.53 (![X0: $i] : p11(X0, X0)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.20/0.53 tff(72,plain,
% 0.20/0.53 ((~![X0: $i] : p11(X0, X0)) | p11(c23, c23)),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(73,plain,
% 0.20/0.53 (p11(c23, c23)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.53 tff(74,plain,
% 0.20/0.53 (^[X0: $i, X2: $i, X1: $i] : refl((p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1))) <=> (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(75,plain,
% 0.20/0.53 (![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.53 tff(76,plain,
% 0.20/0.53 (![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(77,plain,
% 0.20/0.53 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p11(X1, X2) | (~p11(X0, X1))) <=> (p11(X1, X2) | (~p11(X0, X1)))), (((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))) <=> ((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))))), rewrite(((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))) <=> (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))), (((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))) <=> (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(78,plain,
% 0.20/0.53 (![X0: $i, X2: $i, X1: $i] : ((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))) <=> ![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.53 tff(79,axiom,(![X0: $i, X2: $i, X1: $i] : ((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_15')).
% 0.20/0.53 tff(80,plain,
% 0.20/0.53 (![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.53 tff(81,plain,
% 0.20/0.53 (![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.53 tff(82,plain,(
% 0.20/0.53 ![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[81])).
% 0.20/0.53 tff(83,plain,
% 0.20/0.53 (![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.53 tff(84,plain,
% 0.20/0.53 (p11(c23, f12(f9(c21))) <=> p11(c23, f12(f9(c21)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(85,axiom,(p11(c23, f12(f9(c21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_7')).
% 0.20/0.53 tff(86,plain,
% 0.20/0.53 (p11(c23, f12(f9(c21)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.53 tff(87,plain,
% 0.20/0.53 (((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | ((~p11(c23, f12(f9(c21)))) | p11(f12(f9(c21)), c23) | (~p11(c23, c23)))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | (~p11(c23, f12(f9(c21)))) | p11(f12(f9(c21)), c23) | (~p11(c23, c23)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(88,plain,
% 0.20/0.53 ((p11(f12(f9(c21)), c23) | (~p11(c23, c23)) | (~p11(c23, f12(f9(c21))))) <=> ((~p11(c23, f12(f9(c21)))) | p11(f12(f9(c21)), c23) | (~p11(c23, c23)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(89,plain,
% 0.20/0.53 (((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | (p11(f12(f9(c21)), c23) | (~p11(c23, c23)) | (~p11(c23, f12(f9(c21)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | ((~p11(c23, f12(f9(c21)))) | p11(f12(f9(c21)), c23) | (~p11(c23, c23))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.53 tff(90,plain,
% 0.20/0.53 (((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | (p11(f12(f9(c21)), c23) | (~p11(c23, c23)) | (~p11(c23, f12(f9(c21)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | (~p11(c23, f12(f9(c21)))) | p11(f12(f9(c21)), c23) | (~p11(c23, c23)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.53 tff(91,plain,
% 0.20/0.53 ((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | (p11(f12(f9(c21)), c23) | (~p11(c23, c23)) | (~p11(c23, f12(f9(c21)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(92,plain,
% 0.20/0.53 ((~![X0: $i, X2: $i, X1: $i] : (p11(X1, X2) | (~p11(X0, X2)) | (~p11(X0, X1)))) | (~p11(c23, f12(f9(c21)))) | p11(f12(f9(c21)), c23) | (~p11(c23, c23))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.53 tff(93,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[92, 86, 83, 73, 64])).
% 0.20/0.53 % SZS output end Proof
%------------------------------------------------------------------------------