%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE064+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE064+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n002.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 : Thu Jun 19 18:58:46 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(multiplication_type, type, (
% 0.11/0.36 multiplication: ( $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(domain_type, type, (
% 0.11/0.36 domain: $i > $i)).
% 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(addition_type, type, (
% 0.11/0.36 addition: ( $i * $i ) > $i)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 ((~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))) <=> (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 ((~![X0: $i, X1: $i] : ((addition(domain(X0), domain(X1)) = domain(X1)) => (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))) <=> (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,axiom,(~![X0: $i, X1: $i] : ((addition(domain(X0), domain(X1)) = domain(X1)) => (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), 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, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), 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, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.11/0.36 tff(8,plain,(
% 0.11/0.36 ~((~(addition(domain(X0!1), domain(X1!0)) = domain(X1!0))) | (addition(X0!1, multiplication(domain(X1!0), X0!1)) = multiplication(domain(X1!0), X0!1)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[7])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (addition(domain(X0!1), domain(X1!0)) = domain(X1!0)),
% 0.11/0.36 inference(or_elim,[status(thm)],[8])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (domain(X1!0) = addition(domain(X0!1), domain(X1!0))),
% 0.11/0.36 inference(symmetry,[status(thm)],[9])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (multiplication(domain(X1!0), X0!1) = multiplication(addition(domain(X0!1), domain(X1!0)), X0!1)),
% 0.11/0.36 inference(monotonicity,[status(thm)],[10])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (multiplication(addition(domain(X0!1), domain(X1!0)), X0!1) = multiplication(domain(X1!0), X0!1)),
% 0.11/0.36 inference(symmetry,[status(thm)],[11])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (^[A: $i, B: $i, C: $i] : refl((multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(16,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.37 tff(18,plain,(
% 0.11/0.37 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[17])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(domain(X0!1), domain(X1!0)), X0!1) = addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (multiplication(addition(domain(X0!1), domain(X1!0)), X0!1) = addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)) = multiplication(addition(domain(X0!1), domain(X1!0)), X0!1)),
% 0.11/0.37 inference(symmetry,[status(thm)],[21])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)) = multiplication(domain(X1!0), X0!1)),
% 0.11/0.37 inference(transitivity,[status(thm)],[22, 12])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(27,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain1')).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.11/0.37 tff(29,plain,(
% 0.11/0.37 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.11/0.37 inference(skolemize,[status(sab)],[28])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(X0!1, multiplication(domain(X0!1), X0!1)) = multiplication(domain(X0!1), X0!1))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (addition(X0!1, multiplication(domain(X0!1), X0!1)) = multiplication(domain(X0!1), X0!1)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (addition(addition(X0!1, multiplication(domain(X0!1), X0!1)), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))) = addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[32, 23])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (^[C: $i, B: $i, A: $i] : refl((addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> (addition(A, addition(B, C)) = addition(addition(A, B), C)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[34])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(37,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.37 tff(39,plain,(
% 0.11/0.37 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.11/0.37 inference(skolemize,[status(sab)],[38])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!1, addition(multiplication(domain(X0!1), X0!1), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)))) = addition(addition(X0!1, multiplication(domain(X0!1), X0!1)), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (addition(X0!1, addition(multiplication(domain(X0!1), X0!1), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)))) = addition(addition(X0!1, multiplication(domain(X0!1), X0!1)), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (addition(multiplication(domain(X0!1), X0!1), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))) = addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[23])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)) = addition(multiplication(domain(X0!1), X0!1), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)))),
% 0.11/0.37 inference(symmetry,[status(thm)],[43])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (multiplication(domain(X1!0), X0!1) = addition(multiplication(domain(X0!1), X0!1), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)))),
% 0.11/0.37 inference(transitivity,[status(thm)],[11, 21, 44])).
% 0.11/0.37 tff(46,plain,
% 0.11/0.37 (addition(X0!1, multiplication(domain(X1!0), X0!1)) = addition(X0!1, addition(multiplication(domain(X0!1), X0!1), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[45])).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (addition(X0!1, multiplication(domain(X1!0), X0!1)) = multiplication(domain(X1!0), X0!1)),
% 0.11/0.37 inference(transitivity,[status(thm)],[46, 42, 33, 22, 12])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (~(addition(X0!1, multiplication(domain(X1!0), X0!1)) = multiplication(domain(X1!0), X0!1))),
% 0.11/0.37 inference(or_elim,[status(thm)],[8])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------