TSTP Solution File: KLE056+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE056+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 17:24:03 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE056+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 08:19:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(zero_type, type, (
% 0.19/0.39 zero: $i)).
% 0.19/0.39 tff(tptp_fun_X0_0_type, type, (
% 0.19/0.39 tptp_fun_X0_0: $i)).
% 0.19/0.39 tff(addition_type, type, (
% 0.19/0.39 addition: ( $i * $i ) > $i)).
% 0.19/0.39 tff(multiplication_type, type, (
% 0.19/0.39 multiplication: ( $i * $i ) > $i)).
% 0.19/0.39 tff(domain_type, type, (
% 0.19/0.39 domain: $i > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![A: $i] : (addition(A, zero) = A)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![A: $i] : (addition(A, zero) = A)),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![A: $i] : (addition(A, zero) = A)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![A: $i] : (addition(A, zero) = A)) | (addition(addition(X0!0, X0!0), zero) = addition(X0!0, X0!0))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (addition(addition(X0!0, X0!0), zero) = addition(X0!0, X0!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (addition(X0!0, X0!0) = addition(addition(X0!0, X0!0), zero)),
% 0.19/0.39 inference(symmetry,[status(thm)],[9])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(14,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![A: $i] : (addition(A, A) = A)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.39 tff(16,plain,(
% 0.19/0.39 ![A: $i] : (addition(A, A) = A)),
% 0.19/0.39 inference(skolemize,[status(sab)],[15])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![A: $i] : (addition(A, A) = A)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!0, X0!0) = X0!0)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (addition(X0!0, X0!0) = X0!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (X0!0 = addition(X0!0, X0!0)),
% 0.19/0.39 inference(symmetry,[status(thm)],[19])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (X0!0 = addition(addition(X0!0, X0!0), zero)),
% 0.19/0.39 inference(transitivity,[status(thm)],[20, 10])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 ((X0!0 = zero) <=> (addition(addition(X0!0, X0!0), zero) = zero)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ((addition(addition(X0!0, X0!0), zero) = zero) <=> (X0!0 = zero)),
% 0.19/0.39 inference(symmetry,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(27,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.39 tff(29,plain,(
% 0.19/0.39 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.19/0.39 inference(skolemize,[status(sab)],[28])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, X0!0) = zero)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (multiplication(zero, X0!0) = zero),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 ((~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))) <=> (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![X0: $i] : ((domain(X0) = zero) => (X0 = zero))) <=> (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(35,axiom,(~![X0: $i] : ((domain(X0) = zero) => (X0 = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (~![X0: $i] : ((~(domain(X0) = zero)) | (X0 = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.19/0.39 tff(43,plain,(
% 0.19/0.39 ~((~(domain(X0!0) = zero)) | (X0!0 = zero))),
% 0.19/0.39 inference(skolemize,[status(sab)],[42])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (domain(X0!0) = zero),
% 0.19/0.39 inference(or_elim,[status(thm)],[43])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (multiplication(domain(X0!0), X0!0) = multiplication(zero, X0!0)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain1')).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,(
% 0.19/0.39 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.19/0.39 inference(skolemize,[status(sab)],[50])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(X0!0, multiplication(domain(X0!0), X0!0)) = multiplication(domain(X0!0), X0!0))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (addition(X0!0, multiplication(domain(X0!0), X0!0)) = multiplication(domain(X0!0), X0!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (addition(X0!0, addition(X0!0, multiplication(domain(X0!0), X0!0))) = addition(X0!0, multiplication(domain(X0!0), X0!0))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (^[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)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (![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))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (![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))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(59,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')).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.39 tff(61,plain,(
% 0.19/0.39 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.39 inference(skolemize,[status(sab)],[60])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!0, addition(X0!0, multiplication(domain(X0!0), X0!0))) = addition(addition(X0!0, X0!0), multiplication(domain(X0!0), X0!0)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (addition(X0!0, addition(X0!0, multiplication(domain(X0!0), X0!0))) = addition(addition(X0!0, X0!0), multiplication(domain(X0!0), X0!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (addition(addition(X0!0, X0!0), multiplication(domain(X0!0), X0!0)) = addition(X0!0, addition(X0!0, multiplication(domain(X0!0), X0!0)))),
% 0.19/0.39 inference(symmetry,[status(thm)],[64])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (multiplication(zero, X0!0) = multiplication(domain(X0!0), X0!0)),
% 0.19/0.39 inference(symmetry,[status(thm)],[45])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (zero = multiplication(zero, X0!0)),
% 0.19/0.39 inference(symmetry,[status(thm)],[32])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (zero = multiplication(domain(X0!0), X0!0)),
% 0.19/0.39 inference(transitivity,[status(thm)],[67, 66])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (addition(addition(X0!0, X0!0), zero) = addition(addition(X0!0, X0!0), multiplication(domain(X0!0), X0!0))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (addition(addition(X0!0, X0!0), zero) = zero),
% 0.19/0.39 inference(transitivity,[status(thm)],[69, 65, 55, 54, 45, 32])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (X0!0 = zero),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[70, 23])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (~(X0!0 = zero)),
% 0.19/0.39 inference(or_elim,[status(thm)],[43])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.39 % SZS output end Proof
%------------------------------------------------------------------------------