TSTP Solution File: REL003-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : REL003-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 02:59:51 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : REL003-1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.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 : Fri Sep 2 19:43:09 EDT 2022
% 0.12/0.33 % 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(sk2_type, type, (
% 0.12/0.38 sk2: $i)).
% 0.12/0.38 tff(join_type, type, (
% 0.12/0.38 join: ( $i * $i ) > $i)).
% 0.12/0.38 tff(sk1_type, type, (
% 0.12/0.38 sk1: $i)).
% 0.12/0.38 tff(converse_type, type, (
% 0.12/0.38 converse: $i > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (![A: $i] : (converse(converse(A)) = A) <=> ![A: $i] : (converse(converse(A)) = A)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![A: $i] : (converse(converse(A)) = A) <=> ![A: $i] : (converse(converse(A)) = A)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,axiom,(![A: $i] : (converse(converse(A)) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax','converse_idempotence_8')).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![A: $i] : (converse(converse(A)) = A)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.38 tff(5,plain,(
% 0.12/0.38 ![A: $i] : (converse(converse(A)) = A)),
% 0.12/0.38 inference(skolemize,[status(sab)],[4])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![A: $i] : (converse(converse(A)) = A)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 ((~![A: $i] : (converse(converse(A)) = A)) | (converse(converse(sk2)) = sk2)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (converse(converse(sk2)) = sk2),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.12/0.38 tff(9,assumption,(~(join(converse(sk1), converse(sk2)) = converse(sk2))), introduced(assumption)).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (((join(sk1, sk2) = sk2) | (join(converse(sk1), converse(sk2)) = converse(sk2))) <=> ((join(sk1, sk2) = sk2) | (join(converse(sk1), converse(sk2)) = converse(sk2)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(11,axiom,((join(sk1, sk2) = sk2) | (join(converse(sk1), converse(sk2)) = converse(sk2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals_14')).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 ((join(sk1, sk2) = sk2) | (join(converse(sk1), converse(sk2)) = converse(sk2))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (join(sk1, sk2) = sk2),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[12, 9])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (sk2 = join(sk1, sk2)),
% 0.12/0.38 inference(symmetry,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (converse(sk2) = converse(join(sk1, sk2))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (converse(join(sk1, sk2)) = converse(sk2)),
% 0.12/0.38 inference(symmetry,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (^[B: $i, A: $i] : refl((converse(join(A, B)) = join(converse(A), converse(B))) <=> (converse(join(A, B)) = join(converse(A), converse(B))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B))) <=> ![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B))) <=> ![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(20,axiom,(![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax','converse_additivity_9')).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.38 tff(22,plain,(
% 0.12/0.38 ![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))) | (converse(join(sk1, sk2)) = join(converse(sk1), converse(sk2)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (converse(join(sk1, sk2)) = join(converse(sk1), converse(sk2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (join(converse(sk1), converse(sk2)) = converse(join(sk1, sk2))),
% 0.12/0.38 inference(symmetry,[status(thm)],[25])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (join(converse(sk1), converse(sk2)) = converse(sk2)),
% 0.12/0.38 inference(transitivity,[status(thm)],[26, 16])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[9, 27])).
% 0.12/0.38 tff(29,plain,(join(converse(sk1), converse(sk2)) = converse(sk2)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (^[B: $i, A: $i] : refl((join(A, B) = join(B, A)) <=> (join(A, B) = join(B, A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![B: $i, A: $i] : (join(A, B) = join(B, A)) <=> ![B: $i, A: $i] : (join(A, B) = join(B, A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![B: $i, A: $i] : (join(A, B) = join(B, A)) <=> ![B: $i, A: $i] : (join(A, B) = join(B, A))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(33,axiom,(![B: $i, A: $i] : (join(A, B) = join(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax','maddux1_join_commutativity_1')).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![B: $i, A: $i] : (join(A, B) = join(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.38 tff(35,plain,(
% 0.12/0.38 ![B: $i, A: $i] : (join(A, B) = join(B, A))),
% 0.12/0.38 inference(skolemize,[status(sab)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![B: $i, A: $i] : (join(A, B) = join(B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 ((~![B: $i, A: $i] : (join(A, B) = join(B, A))) | (join(converse(sk1), converse(sk2)) = join(converse(sk2), converse(sk1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (join(converse(sk1), converse(sk2)) = join(converse(sk2), converse(sk1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (join(converse(sk2), converse(sk1)) = join(converse(sk1), converse(sk2))),
% 0.12/0.38 inference(symmetry,[status(thm)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (join(converse(sk2), converse(sk1)) = converse(sk2)),
% 0.12/0.38 inference(transitivity,[status(thm)],[39, 29])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (converse(join(converse(sk2), converse(sk1))) = converse(converse(sk2))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[40])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))) | (converse(join(converse(sk2), converse(sk1))) = join(converse(converse(sk2)), converse(converse(sk1))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (converse(join(converse(sk2), converse(sk1))) = join(converse(converse(sk2)), converse(converse(sk1)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[42, 23])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (join(converse(converse(sk2)), converse(converse(sk1))) = converse(join(converse(sk2), converse(sk1)))),
% 0.12/0.38 inference(symmetry,[status(thm)],[43])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 ((~![A: $i] : (converse(converse(A)) = A)) | (converse(converse(sk1)) = sk1)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (converse(converse(sk1)) = sk1),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[45, 6])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (sk1 = converse(converse(sk1))),
% 0.12/0.38 inference(symmetry,[status(thm)],[46])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (sk2 = converse(converse(sk2))),
% 0.12/0.38 inference(symmetry,[status(thm)],[8])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (join(sk2, sk1) = join(converse(converse(sk2)), converse(converse(sk1)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[48, 47])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 ((~![B: $i, A: $i] : (join(A, B) = join(B, A))) | (join(sk1, sk2) = join(sk2, sk1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (join(sk1, sk2) = join(sk2, sk1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[50, 36])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (join(sk1, sk2) = sk2),
% 0.12/0.38 inference(transitivity,[status(thm)],[51, 49, 44, 41, 8])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (((~(join(sk1, sk2) = sk2)) | (~(join(converse(sk1), converse(sk2)) = converse(sk2)))) <=> ((~(join(sk1, sk2) = sk2)) | (~(join(converse(sk1), converse(sk2)) = converse(sk2))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(54,axiom,((~(join(sk1, sk2) = sk2)) | (~(join(converse(sk1), converse(sk2)) = converse(sk2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals_17')).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 ((~(join(sk1, sk2) = sk2)) | (~(join(converse(sk1), converse(sk2)) = converse(sk2)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (~(join(sk1, sk2) = sk2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[55, 29])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[56, 52])).
% 0.12/0.39 % SZS output end Proof
%------------------------------------------------------------------------------