%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : REL046+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:23:49 AM UTC 2025
% Result : Theorem 5.05s 5.26s
% Output : Proof 5.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL046+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 03:03:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 5.05/5.26 % SZS status Theorem
% 5.05/5.26 % SZS output start Proof
% 5.05/5.26 tff(tptp_fun_X1_1_type, type, (
% 5.05/5.26 tptp_fun_X1_1: $i)).
% 5.05/5.26 tff(join_type, type, (
% 5.05/5.26 join: ( $i * $i ) > $i)).
% 5.05/5.26 tff(tptp_fun_X0_2_type, type, (
% 5.05/5.26 tptp_fun_X0_2: $i)).
% 5.05/5.26 tff(complement_type, type, (
% 5.05/5.26 complement: $i > $i)).
% 5.05/5.26 tff(tptp_fun_X2_0_type, type, (
% 5.05/5.26 tptp_fun_X2_0: $i)).
% 5.05/5.26 tff(meet_type, type, (
% 5.05/5.26 meet: ( $i * $i ) > $i)).
% 5.05/5.26 tff(1,plain,
% 5.05/5.26 (^[X0: $i, X1: $i] : refl((X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1)))) <=> (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1)))))),
% 5.05/5.26 inference(bind,[status(th)],[])).
% 5.05/5.26 tff(2,plain,
% 5.05/5.26 (![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1)))) <=> ![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 5.05/5.26 inference(quant_intro,[status(thm)],[1])).
% 5.05/5.26 tff(3,plain,
% 5.05/5.26 (![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1)))) <=> ![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 5.05/5.26 inference(rewrite,[status(thm)],[])).
% 5.05/5.26 tff(4,axiom,(![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','maddux3_a_kind_of_de_Morgan')).
% 5.05/5.26 tff(5,plain,
% 5.05/5.26 (![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[4, 3])).
% 5.05/5.26 tff(6,plain,(
% 5.05/5.26 ![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 5.05/5.26 inference(skolemize,[status(sab)],[5])).
% 5.05/5.26 tff(7,plain,
% 5.05/5.26 (![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[6, 2])).
% 5.05/5.26 tff(8,plain,
% 5.05/5.26 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (X1!1 = join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))))),
% 5.05/5.26 inference(quant_inst,[status(thm)],[])).
% 5.05/5.26 tff(9,plain,
% 5.05/5.26 (X1!1 = join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))),
% 5.05/5.26 inference(unit_resolution,[status(thm)],[8, 7])).
% 5.05/5.26 tff(10,plain,
% 5.05/5.26 (join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))) = X1!1),
% 5.05/5.26 inference(symmetry,[status(thm)],[9])).
% 5.05/5.26 tff(11,plain,
% 5.05/5.26 (^[X0: $i, X1: $i] : refl((meet(X0, X1) = complement(join(complement(X0), complement(X1)))) <=> (meet(X0, X1) = complement(join(complement(X0), complement(X1)))))),
% 5.05/5.26 inference(bind,[status(th)],[])).
% 5.05/5.26 tff(12,plain,
% 5.05/5.26 (![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1)))) <=> ![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 5.05/5.26 inference(quant_intro,[status(thm)],[11])).
% 5.05/5.26 tff(13,plain,
% 5.05/5.26 (![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1)))) <=> ![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 5.05/5.26 inference(rewrite,[status(thm)],[])).
% 5.05/5.26 tff(14,axiom,(![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','maddux4_definiton_of_meet')).
% 5.05/5.26 tff(15,plain,
% 5.05/5.26 (![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[14, 13])).
% 5.05/5.26 tff(16,plain,(
% 5.05/5.26 ![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 5.05/5.26 inference(skolemize,[status(sab)],[15])).
% 5.05/5.26 tff(17,plain,
% 5.05/5.26 (![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[16, 12])).
% 5.05/5.26 tff(18,plain,
% 5.05/5.26 ((~![X0: $i, X1: $i] : (meet(X0, X1) = complement(join(complement(X0), complement(X1))))) | (meet(X1!1, X2!0) = complement(join(complement(X1!1), complement(X2!0))))),
% 5.05/5.26 inference(quant_inst,[status(thm)],[])).
% 5.05/5.26 tff(19,plain,
% 5.05/5.26 (meet(X1!1, X2!0) = complement(join(complement(X1!1), complement(X2!0)))),
% 5.05/5.26 inference(unit_resolution,[status(thm)],[18, 17])).
% 5.05/5.26 tff(20,plain,
% 5.05/5.26 ((~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2))))),
% 5.05/5.26 inference(rewrite,[status(thm)],[])).
% 5.05/5.26 tff(21,plain,
% 5.05/5.26 ((~![X0: $i, X1: $i, X2: $i] : ((join(X0, meet(X1, X2)) = meet(X1, X2)) => ((join(X0, X1) = X1) & (join(X0, X2) = X2)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2))))),
% 5.05/5.26 inference(rewrite,[status(thm)],[])).
% 5.05/5.26 tff(22,axiom,(~![X0: $i, X1: $i, X2: $i] : ((join(X0, meet(X1, X2)) = meet(X1, X2)) => ((join(X0, X1) = X1) & (join(X0, X2) = X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 5.05/5.26 tff(23,plain,
% 5.05/5.26 (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[22, 21])).
% 5.05/5.26 tff(24,plain,
% 5.05/5.26 (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[23, 20])).
% 5.05/5.26 tff(25,plain,
% 5.05/5.26 (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[24, 20])).
% 5.05/5.26 tff(26,plain,
% 5.05/5.26 (~![X0: $i, X1: $i, X2: $i] : ((~(join(X0, meet(X1, X2)) = meet(X1, X2))) | ((join(X0, X1) = X1) & (join(X0, X2) = X2)))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[25, 20])).
% 5.05/5.26 tff(27,plain,(
% 5.05/5.26 ~((~(join(X0!2, meet(X1!1, X2!0)) = meet(X1!1, X2!0))) | ((join(X0!2, X1!1) = X1!1) & (join(X0!2, X2!0) = X2!0)))),
% 5.05/5.26 inference(skolemize,[status(sab)],[26])).
% 5.05/5.26 tff(28,plain,
% 5.05/5.26 (join(X0!2, meet(X1!1, X2!0)) = meet(X1!1, X2!0)),
% 5.05/5.26 inference(or_elim,[status(thm)],[27])).
% 5.05/5.26 tff(29,plain,
% 5.05/5.26 (join(X0!2, meet(X1!1, X2!0)) = complement(join(complement(X1!1), complement(X2!0)))),
% 5.05/5.26 inference(transitivity,[status(thm)],[28, 19])).
% 5.05/5.26 tff(30,plain,
% 5.05/5.26 (join(join(X0!2, meet(X1!1, X2!0)), complement(join(complement(X1!1), X2!0))) = join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))),
% 5.05/5.26 inference(monotonicity,[status(thm)],[29])).
% 5.05/5.26 tff(31,plain,
% 5.05/5.26 (^[X0: $i, X1: $i, X2: $i] : refl((join(X0, join(X1, X2)) = join(join(X0, X1), X2)) <=> (join(X0, join(X1, X2)) = join(join(X0, X1), X2)))),
% 5.05/5.26 inference(bind,[status(th)],[])).
% 5.05/5.26 tff(32,plain,
% 5.05/5.26 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2)) <=> ![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 5.05/5.26 inference(quant_intro,[status(thm)],[31])).
% 5.05/5.26 tff(33,plain,
% 5.05/5.26 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2)) <=> ![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 5.05/5.26 inference(rewrite,[status(thm)],[])).
% 5.05/5.26 tff(34,axiom,(![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','maddux2_join_associativity')).
% 5.05/5.26 tff(35,plain,
% 5.05/5.26 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[34, 33])).
% 5.05/5.26 tff(36,plain,(
% 5.05/5.26 ![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 5.05/5.26 inference(skolemize,[status(sab)],[35])).
% 5.05/5.26 tff(37,plain,
% 5.05/5.26 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[36, 32])).
% 5.05/5.26 tff(38,plain,
% 5.05/5.26 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(X0!2, join(meet(X1!1, X2!0), complement(join(complement(X1!1), X2!0)))) = join(join(X0!2, meet(X1!1, X2!0)), complement(join(complement(X1!1), X2!0))))),
% 5.05/5.26 inference(quant_inst,[status(thm)],[])).
% 5.05/5.26 tff(39,plain,
% 5.05/5.26 (join(X0!2, join(meet(X1!1, X2!0), complement(join(complement(X1!1), X2!0)))) = join(join(X0!2, meet(X1!1, X2!0)), complement(join(complement(X1!1), X2!0)))),
% 5.05/5.26 inference(unit_resolution,[status(thm)],[38, 37])).
% 5.05/5.26 tff(40,plain,
% 5.05/5.26 (join(meet(X1!1, X2!0), complement(join(complement(X1!1), X2!0))) = join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0)))),
% 5.05/5.26 inference(monotonicity,[status(thm)],[19])).
% 5.05/5.26 tff(41,plain,
% 5.05/5.26 (join(complement(join(complement(X1!1), complement(X2!0))), complement(join(complement(X1!1), X2!0))) = join(meet(X1!1, X2!0), complement(join(complement(X1!1), X2!0)))),
% 5.05/5.26 inference(symmetry,[status(thm)],[40])).
% 5.05/5.26 tff(42,plain,
% 5.05/5.26 (X1!1 = join(meet(X1!1, X2!0), complement(join(complement(X1!1), X2!0)))),
% 5.05/5.26 inference(transitivity,[status(thm)],[9, 41])).
% 5.05/5.26 tff(43,plain,
% 5.05/5.26 (join(X0!2, X1!1) = join(X0!2, join(meet(X1!1, X2!0), complement(join(complement(X1!1), X2!0))))),
% 5.05/5.26 inference(monotonicity,[status(thm)],[42])).
% 5.05/5.26 tff(44,plain,
% 5.05/5.26 (join(X0!2, X1!1) = X1!1),
% 5.05/5.26 inference(transitivity,[status(thm)],[43, 39, 30, 10])).
% 5.05/5.26 tff(45,plain,
% 5.05/5.26 ((~![X0: $i, X1: $i] : (X0 = join(complement(join(complement(X0), complement(X1))), complement(join(complement(X0), X1))))) | (X2!0 = join(complement(join(complement(X2!0), complement(X1!1))), complement(join(complement(X2!0), X1!1))))),
% 5.05/5.26 inference(quant_inst,[status(thm)],[])).
% 5.05/5.26 tff(46,plain,
% 5.05/5.26 (X2!0 = join(complement(join(complement(X2!0), complement(X1!1))), complement(join(complement(X2!0), X1!1)))),
% 5.05/5.26 inference(unit_resolution,[status(thm)],[45, 7])).
% 5.05/5.26 tff(47,plain,
% 5.05/5.26 (join(complement(join(complement(X2!0), complement(X1!1))), complement(join(complement(X2!0), X1!1))) = X2!0),
% 5.05/5.26 inference(symmetry,[status(thm)],[46])).
% 5.05/5.26 tff(48,plain,
% 5.05/5.26 (^[X0: $i, X1: $i] : refl((join(X0, X1) = join(X1, X0)) <=> (join(X0, X1) = join(X1, X0)))),
% 5.05/5.26 inference(bind,[status(th)],[])).
% 5.05/5.26 tff(49,plain,
% 5.05/5.26 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0)) <=> ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 5.05/5.26 inference(quant_intro,[status(thm)],[48])).
% 5.05/5.26 tff(50,plain,
% 5.05/5.26 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0)) <=> ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 5.05/5.26 inference(rewrite,[status(thm)],[])).
% 5.05/5.26 tff(51,axiom,(![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax','maddux1_join_commutativity')).
% 5.05/5.26 tff(52,plain,
% 5.05/5.26 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[51, 50])).
% 5.05/5.26 tff(53,plain,(
% 5.05/5.26 ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 5.05/5.26 inference(skolemize,[status(sab)],[52])).
% 5.05/5.26 tff(54,plain,
% 5.05/5.26 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 5.05/5.26 inference(modus_ponens,[status(thm)],[53, 49])).
% 5.05/5.26 tff(55,plain,
% 5.05/5.26 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(complement(X1!1), complement(X2!0)) = join(complement(X2!0), complement(X1!1)))),
% 5.05/5.26 inference(quant_inst,[status(thm)],[])).
% 5.05/5.26 tff(56,plain,
% 5.05/5.26 (join(complement(X1!1), complement(X2!0)) = join(complement(X2!0), complement(X1!1))),
% 5.05/5.26 inference(unit_resolution,[status(thm)],[55, 54])).
% 5.05/5.26 tff(57,plain,
% 5.05/5.26 (join(complement(X2!0), complement(X1!1)) = join(complement(X1!1), complement(X2!0))),
% 5.05/5.26 inference(symmetry,[status(thm)],[56])).
% 5.05/5.26 tff(58,plain,
% 5.05/5.26 (complement(join(complement(X2!0), complement(X1!1))) = complement(join(complement(X1!1), complement(X2!0)))),
% 5.05/5.26 inference(monotonicity,[status(thm)],[57])).
% 5.05/5.26 tff(59,plain,
% 5.05/5.26 (complement(join(complement(X1!1), complement(X2!0))) = complement(join(complement(X2!0), complement(X1!1)))),
% 5.05/5.26 inference(symmetry,[status(thm)],[58])).
% 5.05/5.26 tff(60,plain,
% 5.05/5.26 (join(X0!2, meet(X1!1, X2!0)) = complement(join(complement(X2!0), complement(X1!1)))),
% 5.05/5.26 inference(transitivity,[status(thm)],[28, 19, 59])).
% 5.05/5.26 tff(61,plain,
% 5.05/5.26 (join(join(X0!2, meet(X1!1, X2!0)), complement(join(complement(X2!0), X1!1))) = join(complement(join(complement(X2!0), complement(X1!1))), complement(join(complement(X2!0), X1!1)))),
% 5.12/5.29 inference(monotonicity,[status(thm)],[60])).
% 5.12/5.29 tff(62,plain,
% 5.12/5.29 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(X0!2, join(meet(X1!1, X2!0), complement(join(complement(X2!0), X1!1)))) = join(join(X0!2, meet(X1!1, X2!0)), complement(join(complement(X2!0), X1!1))))),
% 5.12/5.29 inference(quant_inst,[status(thm)],[])).
% 5.12/5.29 tff(63,plain,
% 5.12/5.29 (join(X0!2, join(meet(X1!1, X2!0), complement(join(complement(X2!0), X1!1)))) = join(join(X0!2, meet(X1!1, X2!0)), complement(join(complement(X2!0), X1!1)))),
% 5.12/5.29 inference(unit_resolution,[status(thm)],[62, 37])).
% 5.12/5.29 tff(64,plain,
% 5.12/5.29 (meet(X1!1, X2!0) = complement(join(complement(X2!0), complement(X1!1)))),
% 5.12/5.29 inference(transitivity,[status(thm)],[19, 59])).
% 5.12/5.29 tff(65,plain,
% 5.12/5.29 (join(meet(X1!1, X2!0), complement(join(complement(X2!0), X1!1))) = join(complement(join(complement(X2!0), complement(X1!1))), complement(join(complement(X2!0), X1!1)))),
% 5.12/5.29 inference(monotonicity,[status(thm)],[64])).
% 5.12/5.29 tff(66,plain,
% 5.12/5.29 (join(complement(join(complement(X2!0), complement(X1!1))), complement(join(complement(X2!0), X1!1))) = join(meet(X1!1, X2!0), complement(join(complement(X2!0), X1!1)))),
% 5.12/5.29 inference(symmetry,[status(thm)],[65])).
% 5.12/5.29 tff(67,plain,
% 5.12/5.29 (X2!0 = join(meet(X1!1, X2!0), complement(join(complement(X2!0), X1!1)))),
% 5.12/5.29 inference(transitivity,[status(thm)],[46, 66])).
% 5.12/5.29 tff(68,plain,
% 5.12/5.29 (join(X0!2, X2!0) = join(X0!2, join(meet(X1!1, X2!0), complement(join(complement(X2!0), X1!1))))),
% 5.12/5.29 inference(monotonicity,[status(thm)],[67])).
% 5.12/5.29 tff(69,plain,
% 5.12/5.29 (join(X0!2, X2!0) = X2!0),
% 5.12/5.29 inference(transitivity,[status(thm)],[68, 63, 61, 47])).
% 5.12/5.29 tff(70,plain,
% 5.12/5.29 ((~(~((~(join(X0!2, X1!1) = X1!1)) | (~(join(X0!2, X2!0) = X2!0))))) <=> ((~(join(X0!2, X1!1) = X1!1)) | (~(join(X0!2, X2!0) = X2!0)))),
% 5.12/5.29 inference(rewrite,[status(thm)],[])).
% 5.12/5.29 tff(71,plain,
% 5.12/5.29 (((join(X0!2, X1!1) = X1!1) & (join(X0!2, X2!0) = X2!0)) <=> (~((~(join(X0!2, X1!1) = X1!1)) | (~(join(X0!2, X2!0) = X2!0))))),
% 5.12/5.29 inference(rewrite,[status(thm)],[])).
% 5.12/5.29 tff(72,plain,
% 5.12/5.29 ((~((join(X0!2, X1!1) = X1!1) & (join(X0!2, X2!0) = X2!0))) <=> (~(~((~(join(X0!2, X1!1) = X1!1)) | (~(join(X0!2, X2!0) = X2!0)))))),
% 5.12/5.29 inference(monotonicity,[status(thm)],[71])).
% 5.12/5.29 tff(73,plain,
% 5.12/5.29 ((~((join(X0!2, X1!1) = X1!1) & (join(X0!2, X2!0) = X2!0))) <=> ((~(join(X0!2, X1!1) = X1!1)) | (~(join(X0!2, X2!0) = X2!0)))),
% 5.12/5.29 inference(transitivity,[status(thm)],[72, 70])).
% 5.12/5.29 tff(74,plain,
% 5.12/5.29 (~((join(X0!2, X1!1) = X1!1) & (join(X0!2, X2!0) = X2!0))),
% 5.12/5.29 inference(or_elim,[status(thm)],[27])).
% 5.12/5.29 tff(75,plain,
% 5.12/5.29 ((~(join(X0!2, X1!1) = X1!1)) | (~(join(X0!2, X2!0) = X2!0))),
% 5.12/5.29 inference(modus_ponens,[status(thm)],[74, 73])).
% 5.12/5.29 tff(76,plain,
% 5.12/5.29 ($false),
% 5.12/5.29 inference(unit_resolution,[status(thm)],[75, 69, 44])).
% 5.12/5.29 % SZS output end Proof
% 5.12/5.29 % E exiting
%------------------------------------------------------------------------------