%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : REL003-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:23:37 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : REL003-1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n001.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 02:52:49 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.36 % SZS status Unsatisfiable
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(sk2_type, type, (
% 0.12/0.36 sk2: $i)).
% 0.12/0.36 tff(join_type, type, (
% 0.12/0.36 join: ( $i * $i ) > $i)).
% 0.12/0.36 tff(sk1_type, type, (
% 0.12/0.36 sk1: $i)).
% 0.12/0.36 tff(converse_type, type, (
% 0.12/0.36 converse: $i > $i)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 (![A: $i] : (converse(converse(A)) = A) <=> ![A: $i] : (converse(converse(A)) = A)),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (![A: $i] : (converse(converse(A)) = A) <=> ![A: $i] : (converse(converse(A)) = A)),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(3,axiom,(![A: $i] : (converse(converse(A)) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax','converse_idempotence_8')).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (![A: $i] : (converse(converse(A)) = A)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.36 tff(5,plain,(
% 0.12/0.36 ![A: $i] : (converse(converse(A)) = A)),
% 0.12/0.36 inference(skolemize,[status(sab)],[4])).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 (![A: $i] : (converse(converse(A)) = A)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 ((~![A: $i] : (converse(converse(A)) = A)) | (converse(converse(sk2)) = sk2)),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (converse(converse(sk2)) = sk2),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.12/0.36 tff(9,assumption,(~(join(converse(sk1), converse(sk2)) = converse(sk2))), introduced(assumption)).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (((join(sk1, sk2) = sk2) | (join(converse(sk1), converse(sk2)) = converse(sk2))) <=> ((join(sk1, sk2) = sk2) | (join(converse(sk1), converse(sk2)) = converse(sk2)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(11,axiom,((join(sk1, sk2) = sk2) | (join(converse(sk1), converse(sk2)) = converse(sk2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals_14')).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 ((join(sk1, sk2) = sk2) | (join(converse(sk1), converse(sk2)) = converse(sk2))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 (join(sk1, sk2) = sk2),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[12, 9])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 (sk2 = join(sk1, sk2)),
% 0.12/0.36 inference(symmetry,[status(thm)],[13])).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 (converse(sk2) = converse(join(sk1, sk2))),
% 0.12/0.36 inference(monotonicity,[status(thm)],[14])).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 (converse(join(sk1, sk2)) = converse(sk2)),
% 0.12/0.36 inference(symmetry,[status(thm)],[15])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 (^[B: $i, A: $i] : refl((converse(join(A, B)) = join(converse(A), converse(B))) <=> (converse(join(A, B)) = join(converse(A), converse(B))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 (![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)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 (![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)))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 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')).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 (![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.36 tff(22,plain,(
% 0.12/0.36 ![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))),
% 0.12/0.36 inference(skolemize,[status(sab)],[21])).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 (![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.12/0.36 tff(24,plain,
% 0.12/0.36 ((~![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))) | (converse(join(sk1, sk2)) = join(converse(sk1), converse(sk2)))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(25,plain,
% 0.12/0.36 (converse(join(sk1, sk2)) = join(converse(sk1), converse(sk2))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.12/0.36 tff(26,plain,
% 0.12/0.36 (join(converse(sk1), converse(sk2)) = converse(join(sk1, sk2))),
% 0.12/0.36 inference(symmetry,[status(thm)],[25])).
% 0.12/0.36 tff(27,plain,
% 0.12/0.36 (join(converse(sk1), converse(sk2)) = converse(sk2)),
% 0.12/0.36 inference(transitivity,[status(thm)],[26, 16])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[9, 27])).
% 0.12/0.37 tff(29,plain,(join(converse(sk1), converse(sk2)) = converse(sk2)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (converse(join(converse(sk1), converse(sk2))) = converse(converse(sk2))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[29])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 ((~![B: $i, A: $i] : (converse(join(A, B)) = join(converse(A), converse(B)))) | (converse(join(converse(sk1), converse(sk2))) = join(converse(converse(sk1)), converse(converse(sk2))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (converse(join(converse(sk1), converse(sk2))) = join(converse(converse(sk1)), converse(converse(sk2)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[31, 23])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (join(converse(converse(sk1)), converse(converse(sk2))) = converse(join(converse(sk1), converse(sk2)))),
% 0.12/0.37 inference(symmetry,[status(thm)],[32])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (sk2 = converse(converse(sk2))),
% 0.12/0.37 inference(symmetry,[status(thm)],[8])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 ((~![A: $i] : (converse(converse(A)) = A)) | (converse(converse(sk1)) = sk1)),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (converse(converse(sk1)) = sk1),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[35, 6])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (sk1 = converse(converse(sk1))),
% 0.12/0.37 inference(symmetry,[status(thm)],[36])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (join(sk1, sk2) = join(converse(converse(sk1)), converse(converse(sk2)))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[37, 34])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (join(sk1, sk2) = sk2),
% 0.12/0.37 inference(transitivity,[status(thm)],[38, 33, 30, 8])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 (((~(join(sk1, sk2) = sk2)) | (~(join(converse(sk1), converse(sk2)) = converse(sk2)))) <=> ((~(join(sk1, sk2) = sk2)) | (~(join(converse(sk1), converse(sk2)) = converse(sk2))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(41,axiom,((~(join(sk1, sk2) = sk2)) | (~(join(converse(sk1), converse(sk2)) = converse(sk2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals_17')).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 ((~(join(sk1, sk2) = sk2)) | (~(join(converse(sk1), converse(sk2)) = converse(sk2)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (~(join(sk1, sk2) = sk2)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[42, 29])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[43, 39])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------