TSTP Solution File: SYN382+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN382+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 23:55:04 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN382+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 02:59:38 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.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(big_p_type, type, (
% 0.13/0.40 big_p: ( $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.40 tptp_fun_Y_1: $i)).
% 0.13/0.40 tff(tptp_fun_X_0_type, type, (
% 0.13/0.40 tptp_fun_X_0: $i > $i)).
% 0.13/0.40 tff(big_q_type, type, (
% 0.13/0.40 big_q: ( $i * $i ) > $o)).
% 0.13/0.40 tff(1,assumption,(big_p(tptp_fun_X_0(Y!1), Y!1) | big_q(tptp_fun_X_0(Y!1), Y!1)), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (^[X: $i] : refl((~(big_p(X, Y!1) | big_q(X, Y!1))) <=> (~(big_p(X, Y!1) | big_q(X, Y!1))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![X: $i] : (~(big_p(X, Y!1) | big_q(X, Y!1))) <=> ![X: $i] : (~(big_p(X, Y!1) | big_q(X, Y!1)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 ((~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))) <=> (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 ((~(![Z: $i] : ?[X: $i] : (![Y: $i] : big_p(X, Y) | big_q(X, Z)) => ![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y)))) <=> (~((~![Z: $i] : ?[X: $i] : (big_q(X, Z) | ![Y: $i] : big_p(X, Y))) | ![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(6,axiom,(~(![Z: $i] : ?[X: $i] : (![Y: $i] : big_p(X, Y) | big_q(X, Z)) => ![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2134')).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (~((~![Z: $i] : ?[X: $i] : (big_q(X, Z) | ![Y: $i] : big_p(X, Y))) | ![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))),
% 0.13/0.40 inference(or_elim,[status(thm)],[7])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.13/0.40 tff(15,plain,(
% 0.13/0.40 $oeq((~?[X: $i] : (big_p(X, Y!1) | big_q(X, Y!1))), ![X: $i] : (~(big_p(X, Y!1) | big_q(X, Y!1))))),
% 0.13/0.40 inference(transitivity,[status(sab)],[14])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![X: $i] : (~(big_p(X, Y!1) | big_q(X, Y!1)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 3])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 ((~![X: $i] : (~(big_p(X, Y!1) | big_q(X, Y!1)))) | (~(big_p(tptp_fun_X_0(Y!1), Y!1) | big_q(tptp_fun_X_0(Y!1), Y!1)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[17, 16, 1])).
% 0.13/0.40 tff(19,plain,(~(big_p(tptp_fun_X_0(Y!1), Y!1) | big_q(tptp_fun_X_0(Y!1), Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 ((big_p(tptp_fun_X_0(Y!1), Y!1) | big_q(tptp_fun_X_0(Y!1), Y!1)) | (~big_p(tptp_fun_X_0(Y!1), Y!1))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (~big_p(tptp_fun_X_0(Y!1), Y!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 ((big_p(tptp_fun_X_0(Y!1), Y!1) | big_q(tptp_fun_X_0(Y!1), Y!1)) | (~big_q(tptp_fun_X_0(Y!1), Y!1))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (~big_q(tptp_fun_X_0(Y!1), Y!1)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[22, 19])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![Z: $i] : ?[X: $i] : (big_q(X, Z) | ![Y: $i] : big_p(X, Y)) <=> ![Z: $i] : ?[X: $i] : (big_q(X, Z) | ![Y: $i] : big_p(X, Y))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![Z: $i] : ?[X: $i] : (big_q(X, Z) | ![Y: $i] : big_p(X, Y))),
% 0.13/0.40 inference(or_elim,[status(thm)],[7])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (![Z: $i] : ?[X: $i] : (big_q(X, Z) | ![Y: $i] : big_p(X, Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.13/0.40 tff(27,plain,(
% 0.13/0.41 ![Z: $i] : (big_q(tptp_fun_X_0(Z), Z) | ![Y: $i] : big_p(tptp_fun_X_0(Z), Y))),
% 0.13/0.41 inference(skolemize,[status(sab)],[26])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (((~![Z: $i] : (big_q(tptp_fun_X_0(Z), Z) | ![Y: $i] : big_p(tptp_fun_X_0(Z), Y))) | (big_q(tptp_fun_X_0(Y!1), Y!1) | ![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y))) <=> ((~![Z: $i] : (big_q(tptp_fun_X_0(Z), Z) | ![Y: $i] : big_p(tptp_fun_X_0(Z), Y))) | big_q(tptp_fun_X_0(Y!1), Y!1) | ![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 ((~![Z: $i] : (big_q(tptp_fun_X_0(Z), Z) | ![Y: $i] : big_p(tptp_fun_X_0(Z), Y))) | (big_q(tptp_fun_X_0(Y!1), Y!1) | ![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 ((~![Z: $i] : (big_q(tptp_fun_X_0(Z), Z) | ![Y: $i] : big_p(tptp_fun_X_0(Z), Y))) | big_q(tptp_fun_X_0(Y!1), Y!1) | ![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (big_q(tptp_fun_X_0(Y!1), Y!1) | ![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[30, 27])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 (![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[31, 23])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 ((~![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y)) | big_p(tptp_fun_X_0(Y!1), Y!1)),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[33, 32, 21])).
% 0.13/0.41 % SZS output end Proof
%------------------------------------------------------------------------------