TSTP Solution File: SYN049+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN049+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 23:53:20 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SYN049+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 01:24:10 EDT 2022
% 0.13/0.34 % 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.
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(big_p_type, type, (
% 0.13/0.38 big_p: $i > $o)).
% 0.13/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.38 tptp_fun_Y_1: $i > $i)).
% 0.13/0.38 tff(tptp_fun_Z_0_type, type, (
% 0.13/0.38 tptp_fun_Z_0: $i > $i)).
% 0.13/0.38 tff(elem_2_type, type, (
% 0.13/0.38 elem_2: $i)).
% 0.13/0.38 tff(big_q_type, type, (
% 0.13/0.38 big_q: $i > $o)).
% 0.13/0.38 tff(1,assumption,(big_q(tptp_fun_Y_1(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Y_1(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Y_1(elem!2))))))), introduced(assumption)).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (^[X: $i] : refl((~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X))))))) <=> (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X))))))) <=> ![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 ((~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 ((~?[X: $i] : ![Y: $i, Z: $i] : ((big_p(Y) => big_q(Z)) => (big_p(X) => big_q(X)))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(6,axiom,(~?[X: $i] : ![Y: $i, Z: $i] : ((big_p(Y) => big_q(Z)) => (big_p(X) => big_q(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel19')).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (^[X: $i] : sk($oeq((~![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))), (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(15,plain,(
% 0.13/0.38 ![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))),
% 0.13/0.38 inference(nnf-neg,[status(sab)],[13, 14])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[15, 3])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 ((~![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))) | (~(big_q(tptp_fun_Y_1(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Y_1(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Y_1(elem!2))))))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[17, 16, 1])).
% 0.13/0.38 tff(19,plain,(~(big_q(tptp_fun_Y_1(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Y_1(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Y_1(elem!2)))))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 ((big_q(tptp_fun_Y_1(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Y_1(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Y_1(elem!2))))))) | big_p(tptp_fun_Y_1(elem!2))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (big_p(tptp_fun_Y_1(elem!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ((~![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))) | (~(big_q(elem!2) | (~big_p(elem!2)) | (~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (~(big_q(elem!2) | (~big_p(elem!2)) | (~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ((big_q(elem!2) | (~big_p(elem!2)) | (~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))))) | (big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))))) | big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (big_q(tptp_fun_Z_0(elem!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[27, 21])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Z_0(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_q(tptp_fun_Z_0(elem!2)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Z_0(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 ((~![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))) | (~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Z_0(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[31, 16, 30])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------