%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : REL049+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : REL049+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri Jun 20 03:04:02 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(tptp_fun_X1_1_type, type, (
% 0.13/0.39 tptp_fun_X1_1: $i)).
% 0.13/0.39 tff(join_type, type, (
% 0.13/0.39 join: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_X2_0_type, type, (
% 0.13/0.39 tptp_fun_X2_0: $i)).
% 0.13/0.39 tff(tptp_fun_X0_2_type, type, (
% 0.13/0.39 tptp_fun_X0_2: $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((~![X0: $i, X1: $i, X2: $i] : ((~((join(X0, X1) = X1) & (join(X2, X1) = X1))) | (join(join(X0, X2), X1) = X1))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~((join(X0, X1) = X1) & (join(X2, X1) = X1))) | (join(join(X0, X2), X1) = X1)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~![X0: $i, X1: $i, X2: $i] : (((join(X0, X1) = X1) & (join(X2, X1) = X1)) => (join(join(X0, X2), X1) = X1))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~((join(X0, X1) = X1) & (join(X2, X1) = X1))) | (join(join(X0, X2), X1) = X1)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,axiom,(~![X0: $i, X1: $i, X2: $i] : (((join(X0, X1) = X1) & (join(X2, X1) = X1)) => (join(join(X0, X2), X1) = X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (~![X0: $i, X1: $i, X2: $i] : ((~((join(X0, X1) = X1) & (join(X2, X1) = X1))) | (join(join(X0, X2), X1) = X1))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~![X0: $i, X1: $i, X2: $i] : ((~((join(X0, X1) = X1) & (join(X2, X1) = X1))) | (join(join(X0, X2), X1) = X1))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![X0: $i, X1: $i, X2: $i] : ((~((join(X0, X1) = X1) & (join(X2, X1) = X1))) | (join(join(X0, X2), X1) = X1))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~![X0: $i, X1: $i, X2: $i] : ((~((join(X0, X1) = X1) & (join(X2, X1) = X1))) | (join(join(X0, X2), X1) = X1))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.39 tff(8,plain,(
% 0.13/0.39 ~((~((join(X0!2, X1!1) = X1!1) & (join(X2!0, X1!1) = X1!1))) | (join(join(X0!2, X2!0), X1!1) = X1!1))),
% 0.13/0.39 inference(skolemize,[status(sab)],[7])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 ((join(X0!2, X1!1) = X1!1) & (join(X2!0, X1!1) = X1!1)),
% 0.13/0.39 inference(or_elim,[status(thm)],[8])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (join(X0!2, X1!1) = X1!1),
% 0.13/0.39 inference(and_elim,[status(thm)],[9])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (join(X2!0, X1!1) = X1!1),
% 0.13/0.39 inference(and_elim,[status(thm)],[9])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (join(X0!2, join(X2!0, X1!1)) = join(X0!2, X1!1)),
% 0.13/0.39 inference(monotonicity,[status(thm)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (^[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)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (![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))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (![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))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(16,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')).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.39 tff(18,plain,(
% 0.13/0.39 ![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 0.13/0.39 inference(skolemize,[status(sab)],[17])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((~![X0: $i, X1: $i, X2: $i] : (join(X0, join(X1, X2)) = join(join(X0, X1), X2))) | (join(X0!2, join(X2!0, X1!1)) = join(join(X0!2, X2!0), X1!1))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (join(X0!2, join(X2!0, X1!1)) = join(join(X0!2, X2!0), X1!1)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (join(join(X0!2, X2!0), X1!1) = join(X0!2, join(X2!0, X1!1))),
% 0.13/0.39 inference(symmetry,[status(thm)],[21])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (join(join(X0!2, X2!0), X1!1) = X1!1),
% 0.13/0.40 inference(transitivity,[status(thm)],[22, 12, 10])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (~(join(join(X0!2, X2!0), X1!1) = X1!1)),
% 0.13/0.40 inference(or_elim,[status(thm)],[8])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.13/0.40 % SZS output end Proof
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------