TSTP Solution File: SYN031-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN031-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 23:53:12 EDT 2022
% Result : Unsatisfiable 0.43s 0.52s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN031-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.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 01:08:50 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.
% 0.43/0.52 % SZS status Unsatisfiable
% 0.43/0.52 % SZS output start Proof
% 0.43/0.52 tff(g_type, type, (
% 0.43/0.52 g: ( $i * $i ) > $o)).
% 0.43/0.52 tff(f_type, type, (
% 0.43/0.52 f: $i > $i)).
% 0.43/0.52 tff(a_type, type, (
% 0.43/0.52 a: $i)).
% 0.43/0.52 tff(1,assumption,(g(a, a)), introduced(assumption)).
% 0.43/0.52 tff(2,plain,
% 0.43/0.52 (^[B: $i, A: $i] : refl(((~g(A, B)) | (~g(B, a))) <=> ((~g(A, B)) | (~g(B, a))))),
% 0.43/0.52 inference(bind,[status(th)],[])).
% 0.43/0.52 tff(3,plain,
% 0.43/0.52 (![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a))) <=> ![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))),
% 0.43/0.52 inference(quant_intro,[status(thm)],[2])).
% 0.43/0.52 tff(4,plain,
% 0.43/0.52 (![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a))) <=> ![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))),
% 0.43/0.52 inference(rewrite,[status(thm)],[])).
% 0.43/0.52 tff(5,axiom,(![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','theorem')).
% 0.43/0.52 tff(6,plain,
% 0.43/0.52 (![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))),
% 0.43/0.52 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.43/0.52 tff(7,plain,(
% 0.43/0.52 ![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))),
% 0.43/0.52 inference(skolemize,[status(sab)],[6])).
% 0.43/0.52 tff(8,plain,
% 0.43/0.52 (![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))),
% 0.43/0.52 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.43/0.52 tff(9,plain,
% 0.43/0.52 (((~![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))) | (~g(a, a))) <=> ((~![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))) | (~g(a, a)))),
% 0.43/0.52 inference(rewrite,[status(thm)],[])).
% 0.43/0.52 tff(10,plain,
% 0.43/0.52 (((~g(a, a)) | (~g(a, a))) <=> (~g(a, a))),
% 0.43/0.52 inference(rewrite,[status(thm)],[])).
% 0.43/0.52 tff(11,plain,
% 0.43/0.52 (((~![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))) | ((~g(a, a)) | (~g(a, a)))) <=> ((~![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))) | (~g(a, a)))),
% 0.43/0.52 inference(monotonicity,[status(thm)],[10])).
% 0.43/0.52 tff(12,plain,
% 0.43/0.52 (((~![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))) | ((~g(a, a)) | (~g(a, a)))) <=> ((~![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))) | (~g(a, a)))),
% 0.43/0.52 inference(transitivity,[status(thm)],[11, 9])).
% 0.43/0.52 tff(13,plain,
% 0.43/0.52 ((~![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))) | ((~g(a, a)) | (~g(a, a)))),
% 0.43/0.52 inference(quant_inst,[status(thm)],[])).
% 0.43/0.52 tff(14,plain,
% 0.43/0.52 ((~![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))) | (~g(a, a))),
% 0.43/0.52 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.43/0.52 tff(15,plain,
% 0.43/0.52 ($false),
% 0.43/0.52 inference(unit_resolution,[status(thm)],[14, 8, 1])).
% 0.43/0.52 tff(16,plain,(~g(a, a)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.52 tff(17,plain,
% 0.43/0.52 (^[A: $i] : refl((g(A, a) | g(A, f(A))) <=> (g(A, a) | g(A, f(A))))),
% 0.43/0.52 inference(bind,[status(th)],[])).
% 0.43/0.52 tff(18,plain,
% 0.43/0.52 (![A: $i] : (g(A, a) | g(A, f(A))) <=> ![A: $i] : (g(A, a) | g(A, f(A)))),
% 0.43/0.52 inference(quant_intro,[status(thm)],[17])).
% 0.43/0.52 tff(19,plain,
% 0.43/0.52 (![A: $i] : (g(A, a) | g(A, f(A))) <=> ![A: $i] : (g(A, a) | g(A, f(A)))),
% 0.43/0.52 inference(rewrite,[status(thm)],[])).
% 0.43/0.52 tff(20,axiom,(![A: $i] : (g(A, a) | g(A, f(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 0.43/0.52 tff(21,plain,
% 0.43/0.52 (![A: $i] : (g(A, a) | g(A, f(A)))),
% 0.43/0.52 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.43/0.52 tff(22,plain,(
% 0.43/0.52 ![A: $i] : (g(A, a) | g(A, f(A)))),
% 0.43/0.52 inference(skolemize,[status(sab)],[21])).
% 0.43/0.52 tff(23,plain,
% 0.43/0.52 (![A: $i] : (g(A, a) | g(A, f(A)))),
% 0.43/0.52 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.43/0.52 tff(24,plain,
% 0.43/0.52 (((~![A: $i] : (g(A, a) | g(A, f(A)))) | (g(a, a) | g(a, f(a)))) <=> ((~![A: $i] : (g(A, a) | g(A, f(A)))) | g(a, a) | g(a, f(a)))),
% 0.43/0.52 inference(rewrite,[status(thm)],[])).
% 0.43/0.52 tff(25,plain,
% 0.43/0.52 ((~![A: $i] : (g(A, a) | g(A, f(A)))) | (g(a, a) | g(a, f(a)))),
% 0.43/0.52 inference(quant_inst,[status(thm)],[])).
% 0.43/0.52 tff(26,plain,
% 0.43/0.52 ((~![A: $i] : (g(A, a) | g(A, f(A)))) | g(a, a) | g(a, f(a))),
% 0.43/0.52 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.43/0.52 tff(27,plain,
% 0.43/0.52 (g(a, a) | g(a, f(a))),
% 0.43/0.52 inference(unit_resolution,[status(thm)],[26, 23])).
% 0.43/0.52 tff(28,plain,
% 0.43/0.52 (g(a, f(a))),
% 0.43/0.52 inference(unit_resolution,[status(thm)],[27, 16])).
% 0.43/0.52 tff(29,plain,
% 0.43/0.52 (^[A: $i] : refl((g(A, a) | g(f(A), A)) <=> (g(A, a) | g(f(A), A)))),
% 0.43/0.52 inference(bind,[status(th)],[])).
% 0.43/0.52 tff(30,plain,
% 0.43/0.52 (![A: $i] : (g(A, a) | g(f(A), A)) <=> ![A: $i] : (g(A, a) | g(f(A), A))),
% 0.43/0.52 inference(quant_intro,[status(thm)],[29])).
% 0.43/0.52 tff(31,plain,
% 0.43/0.52 (![A: $i] : (g(A, a) | g(f(A), A)) <=> ![A: $i] : (g(A, a) | g(f(A), A))),
% 0.43/0.52 inference(rewrite,[status(thm)],[])).
% 0.43/0.52 tff(32,axiom,(![A: $i] : (g(A, a) | g(f(A), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.43/0.52 tff(33,plain,
% 0.43/0.52 (![A: $i] : (g(A, a) | g(f(A), A))),
% 0.43/0.52 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.43/0.52 tff(34,plain,(
% 0.43/0.52 ![A: $i] : (g(A, a) | g(f(A), A))),
% 0.43/0.52 inference(skolemize,[status(sab)],[33])).
% 0.43/0.52 tff(35,plain,
% 0.43/0.52 (![A: $i] : (g(A, a) | g(f(A), A))),
% 0.43/0.52 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.43/0.52 tff(36,plain,
% 0.43/0.52 (((~![A: $i] : (g(A, a) | g(f(A), A))) | (g(a, a) | g(f(a), a))) <=> ((~![A: $i] : (g(A, a) | g(f(A), A))) | g(a, a) | g(f(a), a))),
% 0.43/0.52 inference(rewrite,[status(thm)],[])).
% 0.43/0.52 tff(37,plain,
% 0.43/0.52 ((~![A: $i] : (g(A, a) | g(f(A), A))) | (g(a, a) | g(f(a), a))),
% 0.43/0.52 inference(quant_inst,[status(thm)],[])).
% 0.43/0.52 tff(38,plain,
% 0.43/0.52 ((~![A: $i] : (g(A, a) | g(f(A), A))) | g(a, a) | g(f(a), a)),
% 0.43/0.52 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.43/0.52 tff(39,plain,
% 0.43/0.52 (g(a, a) | g(f(a), a)),
% 0.43/0.52 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.43/0.52 tff(40,plain,
% 0.43/0.52 (g(f(a), a)),
% 0.43/0.52 inference(unit_resolution,[status(thm)],[39, 16])).
% 0.43/0.52 tff(41,plain,
% 0.43/0.52 (((~![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))) | ((~g(a, f(a))) | (~g(f(a), a)))) <=> ((~![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))) | (~g(a, f(a))) | (~g(f(a), a)))),
% 0.43/0.52 inference(rewrite,[status(thm)],[])).
% 0.43/0.52 tff(42,plain,
% 0.43/0.52 ((~![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))) | ((~g(a, f(a))) | (~g(f(a), a)))),
% 0.43/0.52 inference(quant_inst,[status(thm)],[])).
% 0.43/0.52 tff(43,plain,
% 0.43/0.52 ((~![B: $i, A: $i] : ((~g(A, B)) | (~g(B, a)))) | (~g(a, f(a))) | (~g(f(a), a))),
% 0.43/0.52 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.43/0.52 tff(44,plain,
% 0.43/0.52 ($false),
% 0.43/0.52 inference(unit_resolution,[status(thm)],[43, 8, 40, 28])).
% 0.43/0.52 % SZS output end Proof
%------------------------------------------------------------------------------