TSTP Solution File: SET786-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET786-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Tue Sep 20 05:08:00 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET786-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n019.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 : Sat Sep 3 08:01:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(element_type, type, (
% 0.12/0.38 element: ( $i * $i ) > $o)).
% 0.12/0.38 tff(sk1_type, type, (
% 0.12/0.38 sk1: $i)).
% 0.12/0.38 tff(sk2_type, type, (
% 0.12/0.38 sk2: $i > $i)).
% 0.12/0.38 tff(1,assumption,(element(sk1, sk1)), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[B: $i, A: $i] : refl(((~element(A, sk1)) | (~element(A, B)) | (~element(B, A))) <=> ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A))) <=> ![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A))) <=> ![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (^[B: $i, A: $i] : trans(monotonicity(rewrite(((~element(B, A)) | (~element(A, B))) <=> ((~element(A, B)) | (~element(B, A)))), ((((~element(B, A)) | (~element(A, B))) | (~element(A, sk1))) <=> (((~element(A, B)) | (~element(B, A))) | (~element(A, sk1))))), rewrite((((~element(A, B)) | (~element(B, A))) | (~element(A, sk1))) <=> ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))), ((((~element(B, A)) | (~element(A, B))) | (~element(A, sk1))) <=> ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![B: $i, A: $i] : (((~element(B, A)) | (~element(A, B))) | (~element(A, sk1))) <=> ![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.12/0.38 tff(7,axiom,(![B: $i, A: $i] : (((~element(B, A)) | (~element(A, B))) | (~element(A, sk1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm25_1')).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.38 tff(10,plain,(
% 0.12/0.38 ![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | (~element(sk1, sk1))) <=> ((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | (~element(sk1, sk1)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (((~element(sk1, sk1)) | (~element(sk1, sk1)) | (~element(sk1, sk1))) <=> (~element(sk1, sk1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | ((~element(sk1, sk1)) | (~element(sk1, sk1)) | (~element(sk1, sk1)))) <=> ((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | (~element(sk1, sk1)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | ((~element(sk1, sk1)) | (~element(sk1, sk1)) | (~element(sk1, sk1)))) <=> ((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | (~element(sk1, sk1)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[14, 12])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 ((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | ((~element(sk1, sk1)) | (~element(sk1, sk1)) | (~element(sk1, sk1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | (~element(sk1, sk1))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[17, 11, 1])).
% 0.12/0.38 tff(19,plain,(~element(sk1, sk1)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (^[A: $i] : refl((element(A, sk1) | element(sk2(A), A)) <=> (element(A, sk1) | element(sk2(A), A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![A: $i] : (element(A, sk1) | element(sk2(A), A)) <=> ![A: $i] : (element(A, sk1) | element(sk2(A), A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![A: $i] : (element(A, sk1) | element(sk2(A), A)) <=> ![A: $i] : (element(A, sk1) | element(sk2(A), A))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,axiom,(![A: $i] : (element(A, sk1) | element(sk2(A), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm25_3')).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![A: $i] : (element(A, sk1) | element(sk2(A), A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,plain,(
% 0.12/0.38 ![A: $i] : (element(A, sk1) | element(sk2(A), A))),
% 0.12/0.38 inference(skolemize,[status(sab)],[24])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![A: $i] : (element(A, sk1) | element(sk2(A), A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (((~![A: $i] : (element(A, sk1) | element(sk2(A), A))) | (element(sk1, sk1) | element(sk2(sk1), sk1))) <=> ((~![A: $i] : (element(A, sk1) | element(sk2(A), A))) | element(sk1, sk1) | element(sk2(sk1), sk1))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ((~![A: $i] : (element(A, sk1) | element(sk2(A), A))) | (element(sk1, sk1) | element(sk2(sk1), sk1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 ((~![A: $i] : (element(A, sk1) | element(sk2(A), A))) | element(sk1, sk1) | element(sk2(sk1), sk1)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (element(sk1, sk1) | element(sk2(sk1), sk1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (element(sk2(sk1), sk1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[30, 19])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (^[A: $i] : refl((element(A, sk1) | element(A, sk2(A))) <=> (element(A, sk1) | element(A, sk2(A))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![A: $i] : (element(A, sk1) | element(A, sk2(A))) <=> ![A: $i] : (element(A, sk1) | element(A, sk2(A)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![A: $i] : (element(A, sk1) | element(A, sk2(A))) <=> ![A: $i] : (element(A, sk1) | element(A, sk2(A)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(35,axiom,(![A: $i] : (element(A, sk1) | element(A, sk2(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm25_2')).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![A: $i] : (element(A, sk1) | element(A, sk2(A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.12/0.38 tff(37,plain,(
% 0.12/0.38 ![A: $i] : (element(A, sk1) | element(A, sk2(A)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[36])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![A: $i] : (element(A, sk1) | element(A, sk2(A)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (((~![A: $i] : (element(A, sk1) | element(A, sk2(A)))) | (element(sk1, sk1) | element(sk1, sk2(sk1)))) <=> ((~![A: $i] : (element(A, sk1) | element(A, sk2(A)))) | element(sk1, sk1) | element(sk1, sk2(sk1)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 ((~![A: $i] : (element(A, sk1) | element(A, sk2(A)))) | (element(sk1, sk1) | element(sk1, sk2(sk1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ((~![A: $i] : (element(A, sk1) | element(A, sk2(A)))) | element(sk1, sk1) | element(sk1, sk2(sk1))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (element(sk1, sk1) | element(sk1, sk2(sk1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (element(sk1, sk2(sk1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[42, 19])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | ((~element(sk1, sk2(sk1))) | (~element(sk2(sk1), sk1)))) <=> ((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | (~element(sk1, sk2(sk1))) | (~element(sk2(sk1), sk1)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (((~element(sk2(sk1), sk1)) | (~element(sk2(sk1), sk1)) | (~element(sk1, sk2(sk1)))) <=> ((~element(sk1, sk2(sk1))) | (~element(sk2(sk1), sk1)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | ((~element(sk2(sk1), sk1)) | (~element(sk2(sk1), sk1)) | (~element(sk1, sk2(sk1))))) <=> ((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | ((~element(sk1, sk2(sk1))) | (~element(sk2(sk1), sk1))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[45])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | ((~element(sk2(sk1), sk1)) | (~element(sk2(sk1), sk1)) | (~element(sk1, sk2(sk1))))) <=> ((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | (~element(sk1, sk2(sk1))) | (~element(sk2(sk1), sk1)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[46, 44])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 ((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | ((~element(sk2(sk1), sk1)) | (~element(sk2(sk1), sk1)) | (~element(sk1, sk2(sk1))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 ((~![B: $i, A: $i] : ((~element(A, sk1)) | (~element(A, B)) | (~element(B, A)))) | (~element(sk1, sk2(sk1))) | (~element(sk2(sk1), sk1))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[49, 11, 43, 31])).
% 0.18/0.38 % SZS output end Proof
%------------------------------------------------------------------------------