TSTP Solution File: SYN406+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN406+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 23:55:11 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN406+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 02:34:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(g_type, type, (
% 0.13/0.39 g: $i > $o)).
% 0.13/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.13/0.39 tptp_fun_Y_0: $i)).
% 0.13/0.39 tff(f_type, type, (
% 0.13/0.39 f: $i > $o)).
% 0.13/0.39 tff(h_type, type, (
% 0.13/0.39 h: $i > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (?[Y: $i] : (f(Y) & h(Y)) <=> ?[Y: $i] : (f(Y) & h(Y))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~((![X: $i] : (f(X) => g(X)) & ?[Y: $i] : (f(Y) & h(Y))) => ?[Z: $i] : (g(Z) & h(Z)))) <=> (~((~(![X: $i] : (g(X) | (~f(X))) & ?[Y: $i] : (f(Y) & h(Y)))) | ?[Z: $i] : (g(Z) & h(Z))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,axiom,(~((![X: $i] : (f(X) => g(X)) & ?[Y: $i] : (f(Y) & h(Y))) => ?[Z: $i] : (g(Z) & h(Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','kalish240')).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (~((~(![X: $i] : (g(X) | (~f(X))) & ?[Y: $i] : (f(Y) & h(Y)))) | ?[Z: $i] : (g(Z) & h(Z)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![X: $i] : (g(X) | (~f(X))) & ?[Y: $i] : (f(Y) & h(Y))),
% 0.13/0.39 inference(or_elim,[status(thm)],[4])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (?[Y: $i] : (f(Y) & h(Y))),
% 0.13/0.39 inference(and_elim,[status(thm)],[5])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (?[Y: $i] : (f(Y) & h(Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.39 tff(8,plain,(
% 0.13/0.39 f(Y!0) & h(Y!0)),
% 0.13/0.39 inference(skolemize,[status(sab)],[7])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (f(Y!0)),
% 0.13/0.39 inference(and_elim,[status(thm)],[8])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (^[X: $i] : refl((g(X) | (~f(X))) <=> (g(X) | (~f(X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (![X: $i] : (g(X) | (~f(X))) <=> ![X: $i] : (g(X) | (~f(X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (![X: $i] : (g(X) | (~f(X))) <=> ![X: $i] : (g(X) | (~f(X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![X: $i] : (g(X) | (~f(X)))),
% 0.13/0.39 inference(and_elim,[status(thm)],[5])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (![X: $i] : (g(X) | (~f(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.39 tff(15,plain,(
% 0.13/0.39 ![X: $i] : (g(X) | (~f(X)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[14])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![X: $i] : (g(X) | (~f(X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (((~![X: $i] : (g(X) | (~f(X)))) | (g(Y!0) | (~f(Y!0)))) <=> ((~![X: $i] : (g(X) | (~f(X)))) | g(Y!0) | (~f(Y!0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 ((~![X: $i] : (g(X) | (~f(X)))) | (g(Y!0) | (~f(Y!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 ((~![X: $i] : (g(X) | (~f(X)))) | g(Y!0) | (~f(Y!0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (g(Y!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (^[Z: $i] : refl(((~g(Z)) | (~h(Z))) <=> ((~g(Z)) | (~h(Z))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![Z: $i] : ((~g(Z)) | (~h(Z))) <=> ![Z: $i] : ((~g(Z)) | (~h(Z)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (^[Z: $i] : trans(monotonicity(rewrite((g(Z) & h(Z)) <=> (~((~g(Z)) | (~h(Z))))), ((~(g(Z) & h(Z))) <=> (~(~((~g(Z)) | (~h(Z))))))), rewrite((~(~((~g(Z)) | (~h(Z))))) <=> ((~g(Z)) | (~h(Z)))), ((~(g(Z) & h(Z))) <=> ((~g(Z)) | (~h(Z)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![Z: $i] : (~(g(Z) & h(Z))) <=> ![Z: $i] : ((~g(Z)) | (~h(Z)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ((~?[Z: $i] : (g(Z) & h(Z))) <=> (~?[Z: $i] : (g(Z) & h(Z)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (~?[Z: $i] : (g(Z) & h(Z))),
% 0.13/0.39 inference(or_elim,[status(thm)],[4])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~?[Z: $i] : (g(Z) & h(Z))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (~?[Z: $i] : (g(Z) & h(Z))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 25])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (~?[Z: $i] : (g(Z) & h(Z))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (~?[Z: $i] : (g(Z) & h(Z))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (~?[Z: $i] : (g(Z) & h(Z))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (~?[Z: $i] : (g(Z) & h(Z))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (^[Z: $i] : refl($oeq((~(g(Z) & h(Z))), (~(g(Z) & h(Z)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(34,plain,(
% 0.13/0.39 ![Z: $i] : (~(g(Z) & h(Z)))),
% 0.13/0.39 inference(nnf-neg,[status(sab)],[32, 33])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (![Z: $i] : ((~g(Z)) | (~h(Z)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![Z: $i] : ((~g(Z)) | (~h(Z)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[35, 22])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (h(Y!0)),
% 0.13/0.39 inference(and_elim,[status(thm)],[8])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (((~![Z: $i] : ((~g(Z)) | (~h(Z)))) | ((~g(Y!0)) | (~h(Y!0)))) <=> ((~![Z: $i] : ((~g(Z)) | (~h(Z)))) | (~g(Y!0)) | (~h(Y!0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 ((~![Z: $i] : ((~g(Z)) | (~h(Z)))) | ((~g(Y!0)) | (~h(Y!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 ((~![Z: $i] : ((~g(Z)) | (~h(Z)))) | (~g(Y!0)) | (~h(Y!0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[40, 37, 36, 20])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------