%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE072+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 05:12:59 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : KLE072+1 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.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 : Thu Jun 19 18:58:46 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(addition_type, type, (
% 0.18/0.37 addition: ( $i * $i ) > $i)).
% 0.18/0.37 tff(domain_type, type, (
% 0.18/0.37 domain: $i > $i)).
% 0.18/0.37 tff(multiplication_type, type, (
% 0.18/0.37 multiplication: ( $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_X2_0_type, type, (
% 0.18/0.37 tptp_fun_X2_0: $i)).
% 0.18/0.37 tff(tptp_fun_X1_1_type, type, (
% 0.18/0.37 tptp_fun_X1_1: $i)).
% 0.18/0.37 tff(tptp_fun_X0_2_type, type, (
% 0.18/0.37 tptp_fun_X0_2: $i)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (^[X0: $i, X1: $i] : refl((domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![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)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![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)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(4,axiom,(![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax','domain5')).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.37 tff(6,plain,(
% 0.18/0.37 ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[5])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(multiplication(X0!2, domain(X2!0)), multiplication(X1!1, domain(X2!0)))) = addition(domain(multiplication(X0!2, domain(X2!0))), domain(multiplication(X1!1, domain(X2!0)))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (domain(addition(multiplication(X0!2, domain(X2!0)), multiplication(X1!1, domain(X2!0)))) = addition(domain(multiplication(X0!2, domain(X2!0))), domain(multiplication(X1!1, domain(X2!0))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (^[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))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (![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)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (![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)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(13,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.18/0.37 tff(15,plain,(
% 0.18/0.37 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[14])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!2, X1!1), domain(X2!0)) = addition(multiplication(X0!2, domain(X2!0)), multiplication(X1!1, domain(X2!0))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(18,plain,
% 0.18/0.38 (multiplication(addition(X0!2, X1!1), domain(X2!0)) = addition(multiplication(X0!2, domain(X2!0)), multiplication(X1!1, domain(X2!0)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (domain(multiplication(addition(X0!2, X1!1), domain(X2!0))) = domain(addition(multiplication(X0!2, domain(X2!0)), multiplication(X1!1, domain(X2!0))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[18])).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 (domain(multiplication(addition(X0!2, X1!1), domain(X2!0))) = addition(domain(multiplication(X0!2, domain(X2!0))), domain(multiplication(X1!1, domain(X2!0))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[19, 9])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 ((~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))) <=> (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(22,axiom,(~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.18/0.38 tff(27,plain,(
% 0.18/0.38 ~(domain(multiplication(addition(X0!2, X1!1), domain(X2!0))) = addition(domain(multiplication(X0!2, domain(X2!0))), domain(multiplication(X1!1, domain(X2!0)))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[26])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[27, 20])).
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------