%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE129+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:13:03 AM UTC 2025
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KLE129+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 19:00:41 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(forward_diamond_type, type, (
% 0.14/0.41 forward_diamond: ( $i * $i ) > $i)).
% 0.14/0.41 tff(domain_type, type, (
% 0.14/0.41 domain: $i > $i)).
% 0.14/0.41 tff(multiplication_type, type, (
% 0.14/0.41 multiplication: ( $i * $i ) > $i)).
% 0.14/0.41 tff(divergence_type, type, (
% 0.14/0.41 divergence: $i > $i)).
% 0.14/0.41 tff(tptp_fun_X0_0_type, type, (
% 0.14/0.41 tptp_fun_X0_0: $i)).
% 0.14/0.41 tff(addition_type, type, (
% 0.14/0.41 addition: ( $i * $i ) > $i)).
% 0.14/0.41 tff(zero_type, type, (
% 0.14/0.41 zero: $i)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 (^[X0: $i] : refl((forward_diamond(X0, divergence(X0)) = divergence(X0)) <=> (forward_diamond(X0, divergence(X0)) = divergence(X0)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0)) <=> ![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0)) <=> ![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(4,axiom,(![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+7.ax','divergence1')).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.41 tff(6,plain,(
% 0.14/0.41 ![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 0.14/0.41 inference(skolemize,[status(sab)],[5])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 ((~![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))) | (forward_diamond(X0!0, divergence(X0!0)) = divergence(X0!0))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (forward_diamond(X0!0, divergence(X0!0)) = divergence(X0!0)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (^[X0: $i, X1: $i] : refl((forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(13,axiom,(![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax','forward_diamond')).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.14/0.41 tff(15,plain,(
% 0.14/0.41 ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[14])).
% 0.14/0.41 tff(16,plain,
% 0.14/0.41 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 ((~![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))) | (forward_diamond(X0!0, divergence(X0!0)) = domain(multiplication(X0!0, domain(divergence(X0!0)))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 (forward_diamond(X0!0, divergence(X0!0)) = domain(multiplication(X0!0, domain(divergence(X0!0))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (domain(multiplication(X0!0, domain(divergence(X0!0)))) = forward_diamond(X0!0, divergence(X0!0))),
% 0.14/0.41 inference(symmetry,[status(thm)],[18])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (domain(multiplication(X0!0, domain(divergence(X0!0)))) = divergence(X0!0)),
% 0.14/0.41 inference(transitivity,[status(thm)],[19, 9])).
% 0.14/0.41 tff(21,plain,
% 0.14/0.41 (forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))) = forward_diamond(X0!0, divergence(X0!0))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[20])).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 (forward_diamond(X0!0, divergence(X0!0)) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))),
% 0.14/0.41 inference(symmetry,[status(thm)],[21])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 (divergence(X0!0) = forward_diamond(X0!0, divergence(X0!0))),
% 0.14/0.41 inference(symmetry,[status(thm)],[9])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.14/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(27,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 (![A: $i] : (addition(A, A) = A)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.14/0.41 tff(29,plain,(
% 0.14/0.41 ![A: $i] : (addition(A, A) = A)),
% 0.14/0.41 inference(skolemize,[status(sab)],[28])).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 (![A: $i] : (addition(A, A) = A)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 ((~![A: $i] : (addition(A, A) = A)) | (addition(divergence(X0!0), divergence(X0!0)) = divergence(X0!0))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 (addition(divergence(X0!0), divergence(X0!0)) = divergence(X0!0)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 (forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))) = divergence(X0!0)),
% 0.14/0.41 inference(transitivity,[status(thm)],[21, 9])).
% 0.14/0.41 tff(34,plain,
% 0.14/0.41 (addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = addition(divergence(X0!0), divergence(X0!0))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[20, 33])).
% 0.14/0.41 tff(35,plain,
% 0.14/0.41 (addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))),
% 0.14/0.41 inference(transitivity,[status(thm)],[34, 32, 23, 22])).
% 0.14/0.41 tff(36,plain,
% 0.14/0.41 ((domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero) <=> (divergence(X0!0) = zero)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[20])).
% 0.14/0.41 tff(37,plain,
% 0.14/0.41 ((divergence(X0!0) = zero) <=> (domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero)),
% 0.14/0.41 inference(symmetry,[status(thm)],[36])).
% 0.14/0.41 tff(38,plain,
% 0.14/0.41 ((~(divergence(X0!0) = zero)) <=> (~(domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.14/0.41 tff(39,plain,
% 0.14/0.41 ((![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero)) & (~(divergence(X0!0) = zero))) <=> (![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero)) & (~(divergence(X0!0) = zero)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(40,plain,
% 0.14/0.41 ((~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))) <=> (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(41,plain,
% 0.14/0.41 ((~![X0: $i] : (![X1: $i] : ((addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1))) => (domain(X1) = zero)) => (divergence(X0) = zero))) <=> (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(42,axiom,(~![X0: $i] : (![X1: $i] : ((addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1))) => (domain(X1) = zero)) => (divergence(X0) = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.14/0.41 tff(43,plain,
% 0.14/0.41 (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.14/0.41 tff(44,plain,
% 0.14/0.41 (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.14/0.41 tff(45,plain,
% 0.14/0.41 (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.14/0.41 tff(46,plain,
% 0.14/0.41 (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.14/0.41 tff(47,plain,
% 0.14/0.41 (![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero)) & (~(divergence(X0!0) = zero))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.14/0.41 tff(48,plain,
% 0.14/0.41 (~(divergence(X0!0) = zero)),
% 0.14/0.41 inference(and_elim,[status(thm)],[47])).
% 0.14/0.41 tff(49,plain,
% 0.14/0.41 (~(domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.14/0.41 tff(50,plain,
% 0.14/0.41 (^[X1: $i] : refl(((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero)) <=> ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(51,plain,
% 0.14/0.41 (![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero)) <=> ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.14/0.41 tff(52,plain,
% 0.14/0.41 (![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))),
% 0.14/0.41 inference(and_elim,[status(thm)],[47])).
% 0.14/0.41 tff(53,plain,
% 0.14/0.41 (![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.14/0.41 tff(54,plain,
% 0.14/0.41 (((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))) | ((~(addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))))) | (domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero))) <=> ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))) | (~(addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))))) | (domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(55,plain,
% 0.14/0.41 ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))) | ((~(addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))))) | (domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(56,plain,
% 0.23/0.42 ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))) | (~(addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))))) | (domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero)),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.23/0.42 tff(57,plain,
% 0.23/0.42 ((~(addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))))) | (domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.23/0.42 tff(58,plain,
% 0.23/0.42 (~(addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[57, 49])).
% 0.23/0.42 tff(59,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[58, 35])).
% 0.23/0.42 % SZS output end Proof
% 0.23/0.42 % E exiting
%------------------------------------------------------------------------------