%------------------------------------------------------------------------------
% 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 : n012.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 : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL003+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 02:47:55 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(tptp_fun_X1_0_type, type, (
% 0.11/0.36 tptp_fun_X1_0: $i)).
% 0.11/0.36 tff(join_type, type, (
% 0.11/0.36 join: ( $i * $i ) > $i)).
% 0.11/0.36 tff(tptp_fun_X0_1_type, type, (
% 0.11/0.36 tptp_fun_X0_1: $i)).
% 0.11/0.36 tff(converse_type, type, (
% 0.11/0.36 converse: $i > $i)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 (![X0: $i] : (converse(converse(X0)) = X0) <=> ![X0: $i] : (converse(converse(X0)) = X0)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (![X0: $i] : (converse(converse(X0)) = X0) <=> ![X0: $i] : (converse(converse(X0)) = X0)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,axiom,(![X0: $i] : (converse(converse(X0)) = X0)), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','converse_idempotence')).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (![X0: $i] : (converse(converse(X0)) = X0)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.11/0.36 tff(5,plain,(
% 0.11/0.36 ![X0: $i] : (converse(converse(X0)) = X0)),
% 0.11/0.36 inference(skolemize,[status(sab)],[4])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (![X0: $i] : (converse(converse(X0)) = X0)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 ((~![X0: $i] : (converse(converse(X0)) = X0)) | (converse(converse(X1!0)) = X1!0)),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (converse(converse(X1!0)) = X1!0),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.11/0.36 tff(9,assumption,(~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))), introduced(assumption)).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 ((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 ((~(~((~((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0)))) | (~((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0)))))) <=> ((~((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0)))) | (~((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 ((((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0))) & ((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0))) <=> (~((~((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0)))) | (~((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 ((~(((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0))) & ((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0)))) <=> (~(~((~((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0)))) | (~((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0))))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[13])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 ((~(((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0))) & ((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0)))) <=> ((~((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0)))) | (~((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[14, 12])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 ((~![X0: $i, X1: $i] : (((~(join(X0, X1) = X1)) | (join(converse(X0), converse(X1)) = converse(X1))) & ((~(join(converse(X0), converse(X1)) = converse(X1))) | (join(X0, X1) = X1)))) <=> (~![X0: $i, X1: $i] : (((~(join(X0, X1) = X1)) | (join(converse(X0), converse(X1)) = converse(X1))) & ((~(join(converse(X0), converse(X1)) = converse(X1))) | (join(X0, X1) = X1))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 ((~![X0: $i, X1: $i] : (((join(X0, X1) = X1) => (join(converse(X0), converse(X1)) = converse(X1))) & ((join(converse(X0), converse(X1)) = converse(X1)) => (join(X0, X1) = X1)))) <=> (~![X0: $i, X1: $i] : (((~(join(X0, X1) = X1)) | (join(converse(X0), converse(X1)) = converse(X1))) & ((~(join(converse(X0), converse(X1)) = converse(X1))) | (join(X0, X1) = X1))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(18,axiom,(~![X0: $i, X1: $i] : (((join(X0, X1) = X1) => (join(converse(X0), converse(X1)) = converse(X1))) & ((join(converse(X0), converse(X1)) = converse(X1)) => (join(X0, X1) = X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (~![X0: $i, X1: $i] : (((~(join(X0, X1) = X1)) | (join(converse(X0), converse(X1)) = converse(X1))) & ((~(join(converse(X0), converse(X1)) = converse(X1))) | (join(X0, X1) = X1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (~![X0: $i, X1: $i] : (((~(join(X0, X1) = X1)) | (join(converse(X0), converse(X1)) = converse(X1))) & ((~(join(converse(X0), converse(X1)) = converse(X1))) | (join(X0, X1) = X1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (~![X0: $i, X1: $i] : (((~(join(X0, X1) = X1)) | (join(converse(X0), converse(X1)) = converse(X1))) & ((~(join(converse(X0), converse(X1)) = converse(X1))) | (join(X0, X1) = X1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (~![X0: $i, X1: $i] : (((~(join(X0, X1) = X1)) | (join(converse(X0), converse(X1)) = converse(X1))) & ((~(join(converse(X0), converse(X1)) = converse(X1))) | (join(X0, X1) = X1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.11/0.37 tff(23,plain,(
% 0.11/0.37 ~(((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0))) & ((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[22])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 ((~((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0)))) | (~((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (~((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[24, 11])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (join(X0!1, X1!0) = X1!0),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (X1!0 = join(X0!1, X1!0)),
% 0.11/0.37 inference(symmetry,[status(thm)],[27])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (converse(X1!0) = converse(join(X0!1, X1!0))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[28])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (converse(join(X0!1, X1!0)) = converse(X1!0)),
% 0.11/0.37 inference(symmetry,[status(thm)],[29])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (^[X0: $i, X1: $i] : refl((converse(join(X0, X1)) = join(converse(X0), converse(X1))) <=> (converse(join(X0, X1)) = join(converse(X0), converse(X1))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1))) <=> ![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1))) <=> ![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(34,axiom,(![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','converse_additivity')).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.11/0.37 tff(36,plain,(
% 0.11/0.37 ![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[35])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 ((~![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))) | (converse(join(X0!1, X1!0)) = join(converse(X0!1), converse(X1!0)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (converse(join(X0!1, X1!0)) = join(converse(X0!1), converse(X1!0))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (join(converse(X0!1), converse(X1!0)) = converse(join(X0!1, X1!0))),
% 0.11/0.37 inference(symmetry,[status(thm)],[39])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (join(converse(X0!1), converse(X1!0)) = converse(X1!0)),
% 0.11/0.37 inference(transitivity,[status(thm)],[40, 30])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[9, 41])).
% 0.11/0.37 tff(43,plain,(join(converse(X0!1), converse(X1!0)) = converse(X1!0)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (converse(join(converse(X0!1), converse(X1!0))) = converse(converse(X1!0))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[43])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 ((~![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))) | (converse(join(converse(X0!1), converse(X1!0))) = join(converse(converse(X0!1)), converse(converse(X1!0))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(46,plain,
% 0.11/0.37 (converse(join(converse(X0!1), converse(X1!0))) = join(converse(converse(X0!1)), converse(converse(X1!0)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[45, 37])).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (join(converse(converse(X0!1)), converse(converse(X1!0))) = converse(join(converse(X0!1), converse(X1!0)))),
% 0.11/0.37 inference(symmetry,[status(thm)],[46])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (X1!0 = converse(converse(X1!0))),
% 0.11/0.37 inference(symmetry,[status(thm)],[8])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 ((~![X0: $i] : (converse(converse(X0)) = X0)) | (converse(converse(X0!1)) = X0!1)),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 (converse(converse(X0!1)) = X0!1),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[49, 6])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 (X0!1 = converse(converse(X0!1))),
% 0.11/0.37 inference(symmetry,[status(thm)],[50])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 (join(X0!1, X1!0) = join(converse(converse(X0!1)), converse(converse(X1!0)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[51, 48])).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 (join(X0!1, X1!0) = X1!0),
% 0.11/0.37 inference(transitivity,[status(thm)],[52, 47, 44, 8])).
% 0.11/0.37 tff(54,plain,
% 0.11/0.37 (((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (~(join(converse(X0!1), converse(X1!0)) = converse(X1!0)))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(55,plain,
% 0.11/0.37 ((~(join(X0!1, X1!0) = X1!0)) | (join(converse(X0!1), converse(X1!0)) = converse(X1!0))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[54, 43])).
% 0.11/0.37 tff(56,plain,
% 0.11/0.37 (~((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[24, 55])).
% 0.11/0.37 tff(57,plain,
% 0.11/0.37 (((~(join(converse(X0!1), converse(X1!0)) = converse(X1!0))) | (join(X0!1, X1!0) = X1!0)) | (~(join(X0!1, X1!0) = X1!0))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(58,plain,
% 0.11/0.37 (~(join(X0!1, X1!0) = X1!0)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.11/0.37 tff(59,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[58, 53])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------