TSTP Solution File: SYN341+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN341+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 23:54:51 EDT 2022
% Result : Theorem 1.58s 1.32s
% Output : Proof 1.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN341+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 02:47:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 1.58/1.32 % SZS status Theorem
% 1.58/1.32 % SZS output start Proof
% 1.58/1.32 tff(big_f_type, type, (
% 1.58/1.32 big_f: ( $i * $i * $i ) > $o)).
% 1.58/1.32 tff(tptp_fun_X4_1_type, type, (
% 1.58/1.32 tptp_fun_X4_1: ( $i * $i ) > $i)).
% 1.58/1.32 tff(tptp_fun_X2_0_type, type, (
% 1.58/1.32 tptp_fun_X2_0: $i > $i)).
% 1.58/1.32 tff(elem_2_type, type, (
% 1.58/1.32 elem_2: $i)).
% 1.58/1.32 tff(1,plain,
% 1.58/1.32 (![X1: $i] : ![X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1)))) <=> ![X1: $i, X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))),
% 1.58/1.32 inference(pull_quant,[status(thm)],[])).
% 1.58/1.32 tff(2,plain,
% 1.58/1.32 ((~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))) <=> (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4)))),
% 1.58/1.32 inference(rewrite,[status(thm)],[])).
% 1.58/1.32 tff(3,plain,
% 1.58/1.32 ((~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : (big_f(X1, X2, X3) => big_f(X2, X3, X4))) <=> (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4)))),
% 1.58/1.32 inference(rewrite,[status(thm)],[])).
% 1.58/1.32 tff(4,axiom,(~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : (big_f(X1, X2, X3) => big_f(X2, X3, X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_15_6')).
% 1.58/1.32 tff(5,plain,
% 1.58/1.32 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))),
% 1.58/1.32 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.58/1.32 tff(6,plain,
% 1.58/1.32 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))),
% 1.58/1.32 inference(modus_ponens,[status(thm)],[5, 2])).
% 1.58/1.32 tff(7,plain,
% 1.58/1.32 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))),
% 1.58/1.32 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.58/1.32 tff(8,plain,
% 1.58/1.32 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))),
% 1.58/1.32 inference(modus_ponens,[status(thm)],[7, 2])).
% 1.58/1.32 tff(9,plain,
% 1.58/1.32 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))),
% 1.58/1.32 inference(modus_ponens,[status(thm)],[8, 2])).
% 1.58/1.32 tff(10,plain,
% 1.58/1.32 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))),
% 1.58/1.32 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.58/1.32 tff(11,plain,
% 1.58/1.32 (~?[X1: $i] : ![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))),
% 1.58/1.32 inference(modus_ponens,[status(thm)],[10, 2])).
% 1.58/1.32 tff(12,plain,
% 1.58/1.32 (^[X1: $i] : trans(sk($oeq((~![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))), (~?[X3: $i] : ![X4: $i] : ((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, X4))))), nnf_neg(proof_bind(^[X3: $i] : sk($oeq((~![X4: $i] : ((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, X4))), (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))))), $oeq((~?[X3: $i] : ![X4: $i] : ((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, X4))), ![X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1)))))), $oeq((~![X2: $i] : ?[X3: $i] : ![X4: $i] : ((~big_f(X1, X2, X3)) | big_f(X2, X3, X4))), ![X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))))),
% 1.58/1.32 inference(bind,[status(th)],[])).
% 1.58/1.32 tff(13,plain,(
% 1.58/1.32 ![X1: $i] : ![X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))),
% 1.58/1.32 inference(nnf-neg,[status(sab)],[11, 12])).
% 1.58/1.32 tff(14,plain,
% 1.58/1.32 (![X1: $i, X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))),
% 1.58/1.32 inference(modus_ponens,[status(thm)],[13, 1])).
% 1.58/1.32 tff(15,plain,
% 1.58/1.32 ((~![X1: $i, X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))) | (~((~big_f(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))))),
% 1.58/1.32 inference(quant_inst,[status(thm)],[])).
% 1.58/1.32 tff(16,plain,
% 1.58/1.32 (~((~big_f(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))),
% 1.58/1.32 inference(unit_resolution,[status(thm)],[15, 14])).
% 1.58/1.32 tff(17,plain,
% 1.58/1.32 (((~big_f(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))) | (~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))),
% 1.58/1.32 inference(tautology,[status(thm)],[])).
% 1.58/1.32 tff(18,plain,
% 1.58/1.32 (~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))),
% 1.58/1.32 inference(unit_resolution,[status(thm)],[17, 16])).
% 1.58/1.32 tff(19,plain,
% 1.58/1.32 (((~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X4_1(tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))),
% 1.58/1.32 inference(tautology,[status(thm)],[])).
% 1.58/1.32 tff(20,plain,
% 1.58/1.32 ((~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X4_1(tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))),
% 1.58/1.32 inference(unit_resolution,[status(thm)],[19, 18])).
% 1.58/1.32 tff(21,plain,
% 1.58/1.32 ((~![X1: $i, X3: $i] : (~((~big_f(X1, tptp_fun_X2_0(X1), X3)) | big_f(tptp_fun_X2_0(X1), X3, tptp_fun_X4_1(X3, X1))))) | (~((~big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))))) | big_f(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X4_1(tptp_fun_X4_1(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))), tptp_fun_X2_0(tptp_fun_X2_0(elem!2))), tptp_fun_X2_0(tptp_fun_X2_0(tptp_fun_X2_0(elem!2)))))))),
% 1.58/1.32 inference(quant_inst,[status(thm)],[])).
% 1.58/1.32 tff(22,plain,
% 1.58/1.32 ($false),
% 1.58/1.32 inference(unit_resolution,[status(thm)],[21, 14, 20])).
% 1.58/1.32 % SZS output end Proof
%------------------------------------------------------------------------------