TSTP Solution File: SYN034-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN034-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 23:53:13 EDT 2022
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN034-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 01:03:16 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(p_type, type, (
% 0.21/0.41 p: ( $i * $i ) > $o)).
% 0.21/0.41 tff(a_type, type, (
% 0.21/0.41 a: $i)).
% 0.21/0.41 tff(f_type, type, (
% 0.21/0.41 f: $i > $i)).
% 0.21/0.41 tff(1,assumption,(p(a, a)), introduced(assumption)).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (^[B: $i, A: $i] : refl(((~p(B, a)) | (~p(B, A)) | (~p(A, B))) <=> ((~p(B, a)) | (~p(B, A)) | (~p(A, B))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B))) <=> ![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 (![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B))) <=> ![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (^[B: $i, A: $i] : rewrite((((~p(A, B)) | (~p(B, A))) | (~p(B, a))) <=> ((~p(B, a)) | (~p(B, A)) | (~p(A, B))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 (![B: $i, A: $i] : (((~p(A, B)) | (~p(B, A))) | (~p(B, a))) <=> ![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.41 tff(7,axiom,(![B: $i, A: $i] : (((~p(A, B)) | (~p(B, A))) | (~p(B, a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem')).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.41 tff(10,plain,(
% 0.21/0.41 ![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[9])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | (~p(a, a))) <=> ((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | (~p(a, a)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (((~p(a, a)) | (~p(a, a)) | (~p(a, a))) <=> (~p(a, a))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | ((~p(a, a)) | (~p(a, a)) | (~p(a, a)))) <=> ((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | (~p(a, a)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[13])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | ((~p(a, a)) | (~p(a, a)) | (~p(a, a)))) <=> ((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | (~p(a, a)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[14, 12])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 ((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | ((~p(a, a)) | (~p(a, a)) | (~p(a, a)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 ((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | (~p(a, a))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[17, 11, 1])).
% 0.21/0.41 tff(19,plain,(~p(a, a)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (^[A: $i] : refl((p(A, a) | p(f(A), A)) <=> (p(A, a) | p(f(A), A)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (![A: $i] : (p(A, a) | p(f(A), A)) <=> ![A: $i] : (p(A, a) | p(f(A), A))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (![A: $i] : (p(A, a) | p(f(A), A)) <=> ![A: $i] : (p(A, a) | p(f(A), A))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(23,axiom,(![A: $i] : (p(A, a) | p(f(A), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (![A: $i] : (p(A, a) | p(f(A), A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.41 tff(25,plain,(
% 0.21/0.41 ![A: $i] : (p(A, a) | p(f(A), A))),
% 0.21/0.41 inference(skolemize,[status(sab)],[24])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (![A: $i] : (p(A, a) | p(f(A), A))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (((~![A: $i] : (p(A, a) | p(f(A), A))) | (p(a, a) | p(f(a), a))) <=> ((~![A: $i] : (p(A, a) | p(f(A), A))) | p(a, a) | p(f(a), a))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 ((~![A: $i] : (p(A, a) | p(f(A), A))) | (p(a, a) | p(f(a), a))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 ((~![A: $i] : (p(A, a) | p(f(A), A))) | p(a, a) | p(f(a), a)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (p(a, a) | p(f(a), a)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (p(f(a), a)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[30, 19])).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (^[A: $i] : refl((p(A, a) | p(A, f(A))) <=> (p(A, a) | p(A, f(A))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (![A: $i] : (p(A, a) | p(A, f(A))) <=> ![A: $i] : (p(A, a) | p(A, f(A)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (![A: $i] : (p(A, a) | p(A, f(A))) <=> ![A: $i] : (p(A, a) | p(A, f(A)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(35,axiom,(![A: $i] : (p(A, a) | p(A, f(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (![A: $i] : (p(A, a) | p(A, f(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.42 tff(37,plain,(
% 0.21/0.42 ![A: $i] : (p(A, a) | p(A, f(A)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[36])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (![A: $i] : (p(A, a) | p(A, f(A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (((~![A: $i] : (p(A, a) | p(A, f(A)))) | (p(a, a) | p(a, f(a)))) <=> ((~![A: $i] : (p(A, a) | p(A, f(A)))) | p(a, a) | p(a, f(a)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 ((~![A: $i] : (p(A, a) | p(A, f(A)))) | (p(a, a) | p(a, f(a)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 ((~![A: $i] : (p(A, a) | p(A, f(A)))) | p(a, a) | p(a, f(a))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (p(a, a) | p(a, f(a))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 (p(a, f(a))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[42, 19])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | ((~p(f(a), a)) | (~p(a, f(a))))) <=> ((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | (~p(f(a), a)) | (~p(a, f(a))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (((~p(f(a), a)) | (~p(f(a), a)) | (~p(a, f(a)))) <=> ((~p(f(a), a)) | (~p(a, f(a))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | ((~p(f(a), a)) | (~p(f(a), a)) | (~p(a, f(a))))) <=> ((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | ((~p(f(a), a)) | (~p(a, f(a)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[45])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | ((~p(f(a), a)) | (~p(f(a), a)) | (~p(a, f(a))))) <=> ((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | (~p(f(a), a)) | (~p(a, f(a))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[46, 44])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 ((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | ((~p(f(a), a)) | (~p(f(a), a)) | (~p(a, f(a))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 ((~![B: $i, A: $i] : ((~p(B, a)) | (~p(B, A)) | (~p(A, B)))) | (~p(f(a), a)) | (~p(a, f(a)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[49, 11, 43, 31])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------