TSTP Solution File: SYN200-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN200-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 23:54:10 EDT 2022
% Result : Unsatisfiable 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN200-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n025.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 02:31:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.20/0.52 % SZS status Unsatisfiable
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 tff(s1_type, type, (
% 0.20/0.52 s1: $i > $o)).
% 0.20/0.52 tff(b_type, type, (
% 0.20/0.52 b: $i)).
% 0.20/0.52 tff(p0_type, type, (
% 0.20/0.52 p0: ( $i * $i ) > $o)).
% 0.20/0.52 tff(e_type, type, (
% 0.20/0.52 e: $i)).
% 0.20/0.52 tff(q0_type, type, (
% 0.20/0.52 q0: ( $i * $i ) > $o)).
% 0.20/0.52 tff(d_type, type, (
% 0.20/0.52 d: $i)).
% 0.20/0.52 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.20/0.52 tff(2,plain,
% 0.20/0.52 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(3,plain,
% 0.20/0.52 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.52 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.52 tff(4,plain,
% 0.20/0.52 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.20/0.52 tff(6,plain,
% 0.20/0.52 (![X: $i] : p0(b, X)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.52 tff(7,plain,(
% 0.20/0.52 ![X: $i] : p0(b, X)),
% 0.20/0.52 inference(skolemize,[status(sab)],[6])).
% 0.20/0.52 tff(8,plain,
% 0.20/0.52 (![X: $i] : p0(b, X)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.52 tff(9,plain,
% 0.20/0.52 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(10,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.52 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(12,plain,
% 0.20/0.52 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(13,plain,
% 0.20/0.52 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.52 tff(14,plain,
% 0.20/0.52 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.20/0.52 tff(16,plain,
% 0.20/0.52 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.52 tff(17,plain,(
% 0.20/0.52 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[16])).
% 0.20/0.52 tff(18,plain,
% 0.20/0.52 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.52 tff(19,plain,
% 0.20/0.52 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(20,plain,
% 0.20/0.52 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(21,plain,
% 0.20/0.52 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.52 tff(22,plain,
% 0.20/0.52 (s1(b)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.20/0.52 tff(23,plain,
% 0.20/0.52 ((~s1(e)) <=> (~s1(e))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(24,axiom,(~s1(e)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.52 tff(25,plain,
% 0.20/0.52 (~s1(e)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.52 tff(26,plain,
% 0.20/0.52 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(27,plain,
% 0.20/0.52 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.52 tff(28,plain,
% 0.20/0.52 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(29,plain,
% 0.20/0.52 (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(30,plain,
% 0.20/0.52 (![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.52 tff(31,axiom,(![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_126')).
% 0.20/0.52 tff(32,plain,
% 0.20/0.52 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.52 tff(33,plain,
% 0.20/0.52 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.53 tff(34,plain,(
% 0.20/0.53 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.53 inference(skolemize,[status(sab)],[33])).
% 0.20/0.53 tff(35,plain,
% 0.20/0.53 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.53 tff(36,plain,
% 0.20/0.53 (q0(e, d) <=> q0(e, d)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(37,axiom,(q0(e, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_2')).
% 0.20/0.53 tff(38,plain,
% 0.20/0.53 (q0(e, d)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.53 tff(39,plain,
% 0.20/0.53 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~s1(b)) | s1(e) | (~q0(e, d)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~s1(b)) | s1(e) | (~q0(e, d)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(40,plain,
% 0.20/0.53 (((~q0(e, d)) | (~s1(b)) | s1(e)) <=> ((~s1(b)) | s1(e) | (~q0(e, d)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(41,plain,
% 0.20/0.53 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(e, d)) | (~s1(b)) | s1(e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~s1(b)) | s1(e) | (~q0(e, d))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.53 tff(42,plain,
% 0.20/0.53 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(e, d)) | (~s1(b)) | s1(e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~s1(b)) | s1(e) | (~q0(e, d)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[41, 39])).
% 0.20/0.53 tff(43,plain,
% 0.20/0.53 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(e, d)) | (~s1(b)) | s1(e))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(44,plain,
% 0.20/0.53 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~s1(b)) | s1(e) | (~q0(e, d))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.53 tff(45,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[44, 38, 35, 25, 22])).
% 0.20/0.53 % SZS output end Proof
%------------------------------------------------------------------------------