TSTP Solution File: KLE083+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE083+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 Sep 17 17:24:07 EDT 2022
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE083+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 08:19:27 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(multiplication_type, type, (
% 0.21/0.43 multiplication: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_X0_0_type, type, (
% 0.21/0.43 tptp_fun_X0_0: $i)).
% 0.21/0.43 tff(domain_type, type, (
% 0.21/0.43 domain: $i > $i)).
% 0.21/0.43 tff(addition_type, type, (
% 0.21/0.43 addition: ( $i * $i ) > $i)).
% 0.21/0.43 tff(zero_type, type, (
% 0.21/0.43 zero: $i)).
% 0.21/0.43 tff(antidomain_type, type, (
% 0.21/0.43 antidomain: $i > $i)).
% 0.21/0.43 tff(one_type, type, (
% 0.21/0.43 one: $i)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.21/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(4,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (![A: $i] : (addition(A, zero) = A)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.43 tff(6,plain,(
% 0.21/0.43 ![A: $i] : (addition(A, zero) = A)),
% 0.21/0.43 inference(skolemize,[status(sab)],[5])).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (![A: $i] : (addition(A, zero) = A)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(domain(X0!0), X0!0), zero) = multiplication(domain(X0!0), X0!0))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 (addition(multiplication(domain(X0!0), X0!0), zero) = multiplication(domain(X0!0), X0!0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (^[X0: $i] : refl((multiplication(antidomain(X0), X0) = zero) <=> (multiplication(antidomain(X0), X0) = zero))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.21/0.43 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(13,axiom,(![X0: $i] : (multiplication(antidomain(X0), X0) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax','domain1')).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.43 tff(15,plain,(
% 0.21/0.43 ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.21/0.43 inference(skolemize,[status(sab)],[14])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 ((~![X0: $i] : (multiplication(antidomain(X0), X0) = zero)) | (multiplication(antidomain(X0!0), X0!0) = zero)),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (multiplication(antidomain(X0!0), X0!0) = zero),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (zero = multiplication(antidomain(X0!0), X0!0)),
% 0.21/0.43 inference(symmetry,[status(thm)],[18])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (^[X0: $i] : refl((domain(X0) = antidomain(antidomain(X0))) <=> (domain(X0) = antidomain(antidomain(X0))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(23,axiom,(![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax','domain4')).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.43 tff(25,plain,(
% 0.21/0.43 ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[24])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.44 tff(27,plain,
% 0.21/0.44 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(X0!0) = antidomain(antidomain(X0!0)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 (domain(X0!0) = antidomain(antidomain(X0!0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (antidomain(antidomain(X0!0)) = domain(X0!0)),
% 0.21/0.44 inference(symmetry,[status(thm)],[28])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (multiplication(antidomain(antidomain(X0!0)), X0!0) = multiplication(domain(X0!0), X0!0)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[29])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (multiplication(domain(X0!0), X0!0) = multiplication(antidomain(antidomain(X0!0)), X0!0)),
% 0.21/0.44 inference(symmetry,[status(thm)],[30])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (addition(multiplication(domain(X0!0), X0!0), zero) = addition(multiplication(antidomain(antidomain(X0!0)), X0!0), multiplication(antidomain(X0!0), X0!0))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[31, 19])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (addition(multiplication(antidomain(antidomain(X0!0)), X0!0), multiplication(antidomain(X0!0), X0!0)) = addition(multiplication(domain(X0!0), X0!0), zero)),
% 0.21/0.44 inference(symmetry,[status(thm)],[32])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(37,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')).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.44 tff(39,plain,(
% 0.21/0.44 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[38])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(antidomain(antidomain(X0!0)), antidomain(X0!0)), X0!0) = addition(multiplication(antidomain(antidomain(X0!0)), X0!0), multiplication(antidomain(X0!0), X0!0)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (multiplication(addition(antidomain(antidomain(X0!0)), antidomain(X0!0)), X0!0) = addition(multiplication(antidomain(antidomain(X0!0)), X0!0), multiplication(antidomain(X0!0), X0!0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (^[X0: $i] : refl((addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> (addition(antidomain(antidomain(X0)), antidomain(X0)) = one))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one) <=> ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(46,axiom,(![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax','domain3')).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.44 tff(48,plain,(
% 0.21/0.44 ![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.21/0.44 inference(skolemize,[status(sab)],[47])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 (![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 ((~![X0: $i] : (addition(antidomain(antidomain(X0)), antidomain(X0)) = one)) | (addition(antidomain(antidomain(X0!0)), antidomain(X0!0)) = one)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (addition(antidomain(antidomain(X0!0)), antidomain(X0!0)) = one),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (multiplication(addition(antidomain(antidomain(X0!0)), antidomain(X0!0)), X0!0) = multiplication(one, X0!0)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[51])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (multiplication(one, X0!0) = multiplication(addition(antidomain(antidomain(X0!0)), antidomain(X0!0)), X0!0)),
% 0.21/0.44 inference(symmetry,[status(thm)],[52])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(57,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (![A: $i] : (multiplication(one, A) = A)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.44 tff(59,plain,(
% 0.21/0.44 ![A: $i] : (multiplication(one, A) = A)),
% 0.21/0.44 inference(skolemize,[status(sab)],[58])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 (![A: $i] : (multiplication(one, A) = A)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!0) = X0!0)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (multiplication(one, X0!0) = X0!0),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (X0!0 = multiplication(one, X0!0)),
% 0.21/0.44 inference(symmetry,[status(thm)],[62])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (X0!0 = multiplication(domain(X0!0), X0!0)),
% 0.21/0.44 inference(transitivity,[status(thm)],[63, 53, 42, 33, 9])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 ((~![X0: $i] : (X0 = multiplication(domain(X0), X0))) <=> (~![X0: $i] : (X0 = multiplication(domain(X0), X0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(66,axiom,(~![X0: $i] : (X0 = multiplication(domain(X0), X0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (~![X0: $i] : (X0 = multiplication(domain(X0), X0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (~![X0: $i] : (X0 = multiplication(domain(X0), X0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[67, 65])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (~![X0: $i] : (X0 = multiplication(domain(X0), X0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 (~![X0: $i] : (X0 = multiplication(domain(X0), X0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 (~![X0: $i] : (X0 = multiplication(domain(X0), X0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[70, 65])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (~![X0: $i] : (X0 = multiplication(domain(X0), X0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[71, 65])).
% 0.21/0.44 tff(73,plain,
% 0.21/0.44 (~![X0: $i] : (X0 = multiplication(domain(X0), X0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.21/0.44 tff(74,plain,(
% 0.21/0.44 ~(X0!0 = multiplication(domain(X0!0), X0!0))),
% 0.21/0.44 inference(skolemize,[status(sab)],[73])).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[74, 64])).
% 0.21/0.44 % SZS output end Proof
%------------------------------------------------------------------------------