%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE059+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 05:12:58 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : KLE059+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 18:57:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(domain_type, type, (
% 0.12/0.38 domain: $i > $i)).
% 0.12/0.38 tff(tptp_fun_X1_0_type, type, (
% 0.12/0.38 tptp_fun_X1_0: $i)).
% 0.12/0.38 tff(addition_type, type, (
% 0.12/0.38 addition: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_X0_1_type, type, (
% 0.12/0.38 tptp_fun_X0_1: $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : ((~(addition(X0, X1) = X1)) | (addition(domain(X0), domain(X1)) = domain(X1)))) <=> (~![X0: $i, X1: $i] : ((~(addition(X0, X1) = X1)) | (addition(domain(X0), domain(X1)) = domain(X1))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : ((addition(X0, X1) = X1) => (addition(domain(X0), domain(X1)) = domain(X1)))) <=> (~![X0: $i, X1: $i] : ((~(addition(X0, X1) = X1)) | (addition(domain(X0), domain(X1)) = domain(X1))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,axiom,(~![X0: $i, X1: $i] : ((addition(X0, X1) = X1) => (addition(domain(X0), domain(X1)) = domain(X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (~![X0: $i, X1: $i] : ((~(addition(X0, X1) = X1)) | (addition(domain(X0), domain(X1)) = domain(X1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~![X0: $i, X1: $i] : ((~(addition(X0, X1) = X1)) | (addition(domain(X0), domain(X1)) = domain(X1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~![X0: $i, X1: $i] : ((~(addition(X0, X1) = X1)) | (addition(domain(X0), domain(X1)) = domain(X1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~![X0: $i, X1: $i] : ((~(addition(X0, X1) = X1)) | (addition(domain(X0), domain(X1)) = domain(X1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.38 tff(8,plain,(
% 0.12/0.38 ~((~(addition(X0!1, X1!0) = X1!0)) | (addition(domain(X0!1), domain(X1!0)) = domain(X1!0)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[7])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (addition(X0!1, X1!0) = X1!0),
% 0.12/0.38 inference(or_elim,[status(thm)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (X1!0 = addition(X0!1, X1!0)),
% 0.12/0.38 inference(symmetry,[status(thm)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (domain(X1!0) = domain(addition(X0!1, X1!0))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (domain(addition(X0!1, X1!0)) = domain(X1!0)),
% 0.12/0.38 inference(symmetry,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (^[X0: $i, X1: $i] : refl((domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(16,axiom,(![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain5')).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.38 tff(18,plain,(
% 0.12/0.38 ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(X0!1, X1!0)) = addition(domain(X0!1), domain(X1!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (domain(addition(X0!1, X1!0)) = addition(domain(X0!1), domain(X1!0))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (addition(domain(X0!1), domain(X1!0)) = domain(addition(X0!1, X1!0))),
% 0.12/0.38 inference(symmetry,[status(thm)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (addition(domain(X0!1), domain(X1!0)) = domain(X1!0)),
% 0.12/0.38 inference(transitivity,[status(thm)],[22, 12])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (~(addition(domain(X0!1), domain(X1!0)) = domain(X1!0))),
% 0.12/0.38 inference(or_elim,[status(thm)],[8])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------