TSTP Solution File: SYN189-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN189-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 23:54:07 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN189-1 : TPTP v8.1.0. Released v1.1.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 02:01:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.49 % SZS status Unsatisfiable
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 tff(r1_type, type, (
% 0.19/0.49 r1: $i > $o)).
% 0.19/0.49 tff(c_type, type, (
% 0.19/0.49 c: $i)).
% 0.19/0.49 tff(r2_type, type, (
% 0.19/0.49 r2: $i > $o)).
% 0.19/0.49 tff(l0_type, type, (
% 0.19/0.49 l0: $i > $o)).
% 0.19/0.49 tff(q1_type, type, (
% 0.19/0.49 q1: ( $i * $i * $i ) > $o)).
% 0.19/0.49 tff(d_type, type, (
% 0.19/0.49 d: $i)).
% 0.19/0.49 tff(q0_type, type, (
% 0.19/0.49 q0: ( $i * $i ) > $o)).
% 0.19/0.49 tff(s0_type, type, (
% 0.19/0.49 s0: $i > $o)).
% 0.19/0.49 tff(k0_type, type, (
% 0.19/0.49 k0: $i > $o)).
% 0.19/0.49 tff(e_type, type, (
% 0.19/0.49 e: $i)).
% 0.19/0.49 tff(1,plain,
% 0.19/0.49 ((~r2(c)) <=> (~r2(c))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(2,axiom,(~r2(c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.19/0.49 tff(3,plain,
% 0.19/0.49 (~r2(c)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.19/0.49 tff(4,plain,
% 0.19/0.49 (^[G: $i] : refl(((~l0(G)) | (~r1(G)) | r2(G)) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(5,plain,
% 0.19/0.49 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.49 tff(6,plain,
% 0.19/0.49 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(7,plain,
% 0.19/0.49 (^[G: $i] : rewrite(((r2(G) | (~r1(G))) | (~l0(G))) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(8,plain,
% 0.19/0.49 (![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G))) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.49 tff(9,axiom,(![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_188')).
% 0.19/0.49 tff(10,plain,
% 0.19/0.49 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.49 tff(11,plain,
% 0.19/0.49 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.49 tff(12,plain,(
% 0.19/0.49 ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.19/0.49 inference(skolemize,[status(sab)],[11])).
% 0.19/0.49 tff(13,plain,
% 0.19/0.49 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.49 tff(14,plain,
% 0.19/0.49 (l0(c) <=> l0(c)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(15,axiom,(l0(c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_24')).
% 0.19/0.49 tff(16,plain,
% 0.19/0.49 (l0(c)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.49 tff(17,plain,
% 0.19/0.49 (((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(c)) | r2(c) | (~r1(c)))) <=> ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(c)) | r2(c) | (~r1(c)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(18,plain,
% 0.19/0.49 (((~l0(c)) | (~r1(c)) | r2(c)) <=> ((~l0(c)) | r2(c) | (~r1(c)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(19,plain,
% 0.19/0.49 (((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(c)) | (~r1(c)) | r2(c))) <=> ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(c)) | r2(c) | (~r1(c))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.49 tff(20,plain,
% 0.19/0.49 (((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(c)) | (~r1(c)) | r2(c))) <=> ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(c)) | r2(c) | (~r1(c)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[19, 17])).
% 0.19/0.49 tff(21,plain,
% 0.19/0.49 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(c)) | (~r1(c)) | r2(c))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(22,plain,
% 0.19/0.49 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(c)) | r2(c) | (~r1(c))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.49 tff(23,plain,
% 0.19/0.49 (~r1(c)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[22, 16, 13, 3])).
% 0.19/0.49 tff(24,plain,
% 0.19/0.49 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(25,plain,
% 0.19/0.49 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.49 tff(26,plain,
% 0.19/0.49 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(27,plain,
% 0.19/0.49 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(s0(d)), (s0(d) <=> $true)), ((~s0(d)) <=> (~$true))), rewrite((~$true) <=> $false), ((~s0(d)) <=> $false)), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)))), rewrite(((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(28,plain,
% 0.19/0.49 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.49 tff(29,plain,
% 0.19/0.49 (^[D: $i, E: $i] : trans(monotonicity(rewrite(((r1(D) | (~q0(D, E))) | (~s0(d))) <=> ((~q0(D, E)) | (~s0(d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> (((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))))), rewrite((((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(30,plain,
% 0.19/0.49 (![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.49 tff(31,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 0.19/0.49 tff(32,plain,
% 0.19/0.49 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.49 tff(33,plain,
% 0.19/0.49 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.49 tff(34,plain,
% 0.19/0.49 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.19/0.49 tff(35,plain,(
% 0.19/0.49 ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.19/0.49 inference(skolemize,[status(sab)],[34])).
% 0.19/0.49 tff(36,plain,
% 0.19/0.49 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.19/0.49 tff(37,plain,
% 0.19/0.49 (q1(d, d, d) <=> q1(d, d, d)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(38,plain,
% 0.19/0.49 (($false | $false | q1(d, d, d)) <=> q1(d, d, d)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(39,plain,
% 0.19/0.49 ((~$true) <=> $false),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(40,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.19/0.49 tff(41,plain,
% 0.19/0.49 (k0(e) <=> $true),
% 0.19/0.49 inference(iff_true,[status(thm)],[40])).
% 0.19/0.49 tff(42,plain,
% 0.19/0.49 ((~k0(e)) <=> (~$true)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.49 tff(43,plain,
% 0.19/0.49 ((~k0(e)) <=> $false),
% 0.19/0.49 inference(transitivity,[status(thm)],[42, 39])).
% 0.19/0.49 tff(44,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.19/0.49 tff(45,plain,
% 0.19/0.49 (s0(d) <=> $true),
% 0.19/0.49 inference(iff_true,[status(thm)],[44])).
% 0.19/0.49 tff(46,plain,
% 0.19/0.49 ((~s0(d)) <=> (~$true)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.49 tff(47,plain,
% 0.19/0.49 ((~s0(d)) <=> $false),
% 0.19/0.49 inference(transitivity,[status(thm)],[46, 39])).
% 0.19/0.49 tff(48,plain,
% 0.19/0.49 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ($false | $false | q1(d, d, d))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[47, 43])).
% 0.19/0.49 tff(49,plain,
% 0.19/0.49 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> q1(d, d, d)),
% 0.19/0.49 inference(transitivity,[status(thm)],[48, 38])).
% 0.19/0.49 tff(50,plain,
% 0.19/0.49 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(51,plain,
% 0.19/0.49 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(52,plain,
% 0.19/0.49 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(53,plain,
% 0.19/0.49 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[52])).
% 0.19/0.49 tff(54,plain,
% 0.19/0.49 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.19/0.50 inference(transitivity,[status(thm)],[53, 51])).
% 0.19/0.50 tff(55,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 0.19/0.50 tff(56,plain,
% 0.19/0.50 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.50 tff(57,plain,
% 0.19/0.50 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[56, 50])).
% 0.19/0.50 tff(58,plain,
% 0.19/0.50 (q1(d, d, d)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[57, 49])).
% 0.19/0.50 tff(59,plain,
% 0.19/0.50 (q1(d, d, d)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[58, 37])).
% 0.19/0.50 tff(60,assumption,(~q0(c, d)), introduced(assumption)).
% 0.19/0.50 tff(61,plain,
% 0.19/0.50 (^[X: $i] : refl(q0(X, d) <=> q0(X, d))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(62,plain,
% 0.19/0.50 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.19/0.50 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.50 tff(63,plain,
% 0.19/0.50 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(64,axiom,(![X: $i] : q0(X, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_17')).
% 0.19/0.50 tff(65,plain,
% 0.19/0.50 (![X: $i] : q0(X, d)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.50 tff(66,plain,(
% 0.19/0.50 ![X: $i] : q0(X, d)),
% 0.19/0.50 inference(skolemize,[status(sab)],[65])).
% 0.19/0.50 tff(67,plain,
% 0.19/0.50 (![X: $i] : q0(X, d)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.19/0.50 tff(68,plain,
% 0.19/0.50 ((~![X: $i] : q0(X, d)) | q0(c, d)),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(69,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[68, 67, 60])).
% 0.19/0.50 tff(70,plain,(q0(c, d)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(71,plain,
% 0.19/0.50 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(c, d)) | (~q1(d, d, d)) | r1(c))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (~q0(c, d)) | (~q1(d, d, d)) | r1(c))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(72,plain,
% 0.19/0.50 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(c, d)) | (~q1(d, d, d)) | r1(c))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(73,plain,
% 0.19/0.50 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (~q0(c, d)) | (~q1(d, d, d)) | r1(c)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.50 tff(74,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[73, 70, 59, 36, 23])).
% 0.19/0.50 % SZS output end Proof
%------------------------------------------------------------------------------