%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE085+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:13:00 AM UTC 2025
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE085+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 19:02:34 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(one_type, type, (
% 0.14/0.39 one: $i)).
% 0.14/0.39 tff(addition_type, type, (
% 0.14/0.39 addition: ( $i * $i ) > $i)).
% 0.14/0.39 tff(domain_type, type, (
% 0.14/0.39 domain: $i > $i)).
% 0.14/0.39 tff(tptp_fun_X0_0_type, type, (
% 0.14/0.39 tptp_fun_X0_0: $i)).
% 0.14/0.39 tff(antidomain_type, type, (
% 0.14/0.39 antidomain: $i > $i)).
% 0.14/0.39 tff(1,plain,
% 0.14/0.39 (^[X0: $i] : refl((addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> (addition(antidomain(antidomain(X0)), antidomain(X0)) = one))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(2,plain,
% 0.14/0.39 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.14/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.39 tff(3,plain,
% 0.14/0.39 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(4,axiom,(![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax','domain3')).
% 0.14/0.39 tff(5,plain,
% 0.14/0.39 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.39 tff(6,plain,(
% 0.14/0.39 ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.14/0.39 inference(skolemize,[status(sab)],[5])).
% 0.14/0.39 tff(7,plain,
% 0.14/0.39 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(X0!0)), antidomain(X0!0)) = one)),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (addition(antidomain(antidomain(X0!0)), antidomain(X0!0)) = one),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(11,plain,
% 0.14/0.39 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.14/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(13,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.14/0.39 tff(14,plain,
% 0.14/0.39 (![A: $i] : (addition(A, A) = A)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.14/0.39 tff(15,plain,(
% 0.14/0.39 ![A: $i] : (addition(A, A) = A)),
% 0.14/0.39 inference(skolemize,[status(sab)],[14])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (![A: $i] : (addition(A, A) = A)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.14/0.39 tff(17,plain,
% 0.14/0.39 ((~![A: $i] : (addition(A, A) = A)) | (addition(antidomain(antidomain(X0!0)), antidomain(antidomain(X0!0))) = antidomain(antidomain(X0!0)))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(18,plain,
% 0.14/0.39 (addition(antidomain(antidomain(X0!0)), antidomain(antidomain(X0!0))) = antidomain(antidomain(X0!0))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.14/0.39 tff(19,plain,
% 0.14/0.39 (antidomain(antidomain(X0!0)) = addition(antidomain(antidomain(X0!0)), antidomain(antidomain(X0!0)))),
% 0.14/0.39 inference(symmetry,[status(thm)],[18])).
% 0.14/0.39 tff(20,plain,
% 0.14/0.39 (addition(antidomain(antidomain(X0!0)), antidomain(X0!0)) = addition(addition(antidomain(antidomain(X0!0)), antidomain(antidomain(X0!0))), antidomain(X0!0))),
% 0.14/0.39 inference(monotonicity,[status(thm)],[19])).
% 0.14/0.39 tff(21,plain,
% 0.14/0.39 (addition(addition(antidomain(antidomain(X0!0)), antidomain(antidomain(X0!0))), antidomain(X0!0)) = addition(antidomain(antidomain(X0!0)), antidomain(X0!0))),
% 0.14/0.39 inference(symmetry,[status(thm)],[20])).
% 0.14/0.39 tff(22,plain,
% 0.14/0.39 (^[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)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(23,plain,
% 0.14/0.39 (![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))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.14/0.39 tff(24,plain,
% 0.14/0.39 (![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))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(25,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')).
% 0.14/0.39 tff(26,plain,
% 0.14/0.39 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.14/0.39 tff(27,plain,(
% 0.14/0.39 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.14/0.39 inference(skolemize,[status(sab)],[26])).
% 0.14/0.39 tff(28,plain,
% 0.14/0.39 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.14/0.39 tff(29,plain,
% 0.14/0.39 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(antidomain(antidomain(X0!0)), addition(antidomain(antidomain(X0!0)), antidomain(X0!0))) = addition(addition(antidomain(antidomain(X0!0)), antidomain(antidomain(X0!0))), antidomain(X0!0)))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(30,plain,
% 0.14/0.39 (addition(antidomain(antidomain(X0!0)), addition(antidomain(antidomain(X0!0)), antidomain(X0!0))) = addition(addition(antidomain(antidomain(X0!0)), antidomain(antidomain(X0!0))), antidomain(X0!0))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.14/0.39 tff(31,plain,
% 0.14/0.39 (^[X0: $i] : refl((domain(X0) = antidomain(antidomain(X0))) <=> (domain(X0) = antidomain(antidomain(X0))))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(32,plain,
% 0.14/0.39 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.14/0.39 tff(33,plain,
% 0.14/0.39 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(34,axiom,(![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax','domain4')).
% 0.14/0.39 tff(35,plain,
% 0.14/0.39 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.14/0.39 tff(36,plain,(
% 0.14/0.39 ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.14/0.39 inference(skolemize,[status(sab)],[35])).
% 0.14/0.39 tff(37,plain,
% 0.14/0.39 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.14/0.39 tff(38,plain,
% 0.14/0.39 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(X0!0) = antidomain(antidomain(X0!0)))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(39,plain,
% 0.14/0.39 (domain(X0!0) = antidomain(antidomain(X0!0))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.14/0.39 tff(40,plain,
% 0.14/0.39 (antidomain(antidomain(X0!0)) = domain(X0!0)),
% 0.14/0.39 inference(symmetry,[status(thm)],[39])).
% 0.14/0.39 tff(41,plain,
% 0.14/0.39 (addition(antidomain(antidomain(X0!0)), addition(antidomain(antidomain(X0!0)), antidomain(X0!0))) = addition(domain(X0!0), one)),
% 0.14/0.39 inference(monotonicity,[status(thm)],[40, 9])).
% 0.14/0.39 tff(42,plain,
% 0.14/0.39 (addition(domain(X0!0), one) = addition(antidomain(antidomain(X0!0)), addition(antidomain(antidomain(X0!0)), antidomain(X0!0)))),
% 0.14/0.39 inference(symmetry,[status(thm)],[41])).
% 0.14/0.39 tff(43,plain,
% 0.14/0.39 (addition(domain(X0!0), one) = one),
% 0.14/0.39 inference(transitivity,[status(thm)],[42, 30, 21, 9])).
% 0.14/0.39 tff(44,plain,
% 0.14/0.39 ((~![X0: $i] : (addition(domain(X0), one) = one)) <=> (~![X0: $i] : (addition(domain(X0), one) = one))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(45,axiom,(~![X0: $i] : (addition(domain(X0), one) = one)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.14/0.39 tff(46,plain,
% 0.14/0.39 (~![X0: $i] : (addition(domain(X0), one) = one)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.14/0.39 tff(47,plain,
% 0.14/0.39 (~![X0: $i] : (addition(domain(X0), one) = one)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[46, 44])).
% 0.14/0.39 tff(48,plain,
% 0.14/0.39 (~![X0: $i] : (addition(domain(X0), one) = one)),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[47, 44])).
% 0.22/0.39 tff(49,plain,
% 0.22/0.39 (~![X0: $i] : (addition(domain(X0), one) = one)),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.22/0.39 tff(50,plain,(
% 0.22/0.39 ~(addition(domain(X0!0), one) = one)),
% 0.22/0.39 inference(skolemize,[status(sab)],[49])).
% 0.22/0.39 tff(51,plain,
% 0.22/0.39 ($false),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[50, 43])).
% 0.22/0.39 % SZS output end Proof
% 0.22/0.39 % E exiting
%------------------------------------------------------------------------------