TSTP Solution File: KLE066+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE066+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 17:24:04 EDT 2022
% Result : Theorem 0.13s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE066+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.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 08:33:49 EDT 2022
% 0.13/0.35 % 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.
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start Proof
% 0.13/0.42 tff(multiplication_type, type, (
% 0.13/0.42 multiplication: ( $i * $i ) > $i)).
% 0.13/0.42 tff(tptp_fun_X1_0_type, type, (
% 0.13/0.42 tptp_fun_X1_0: $i)).
% 0.13/0.42 tff(tptp_fun_X0_1_type, type, (
% 0.13/0.42 tptp_fun_X0_1: $i)).
% 0.13/0.42 tff(addition_type, type, (
% 0.13/0.42 addition: ( $i * $i ) > $i)).
% 0.13/0.42 tff(zero_type, type, (
% 0.13/0.42 zero: $i)).
% 0.13/0.42 tff(domain_type, type, (
% 0.13/0.42 domain: $i > $i)).
% 0.13/0.42 tff(1,plain,
% 0.13/0.42 ((zero = multiplication(X0!1, X1!0)) <=> (multiplication(X0!1, X1!0) = zero)),
% 0.13/0.42 inference(commutativity,[status(thm)],[])).
% 0.13/0.42 tff(2,plain,
% 0.13/0.42 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(3,plain,
% 0.13/0.42 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.13/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.42 tff(4,plain,
% 0.13/0.42 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(5,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 0.13/0.42 tff(6,plain,
% 0.13/0.42 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.42 tff(7,plain,(
% 0.13/0.42 ![A: $i] : (multiplication(zero, A) = zero)),
% 0.13/0.42 inference(skolemize,[status(sab)],[6])).
% 0.13/0.42 tff(8,plain,
% 0.13/0.42 (![A: $i] : (multiplication(zero, A) = zero)),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.42 tff(9,plain,
% 0.13/0.42 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, multiplication(X0!1, X1!0)) = zero)),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(10,plain,
% 0.13/0.42 (multiplication(zero, multiplication(X0!1, X1!0)) = zero),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.13/0.42 tff(11,plain,
% 0.13/0.42 ((domain(zero) = zero) <=> (domain(zero) = zero)),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(12,axiom,(domain(zero) = zero), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain4')).
% 0.13/0.42 tff(13,plain,
% 0.13/0.42 (domain(zero) = zero),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.13/0.42 tff(14,plain,
% 0.13/0.42 ((~![X0: $i, X1: $i] : ((~(multiplication(X0, domain(X1)) = zero)) | (multiplication(X0, X1) = zero))) <=> (~![X0: $i, X1: $i] : ((~(multiplication(X0, domain(X1)) = zero)) | (multiplication(X0, X1) = zero)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(15,plain,
% 0.13/0.42 ((~![X0: $i, X1: $i] : ((multiplication(X0, domain(X1)) = zero) => (multiplication(X0, X1) = zero))) <=> (~![X0: $i, X1: $i] : ((~(multiplication(X0, domain(X1)) = zero)) | (multiplication(X0, X1) = zero)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(16,axiom,(~![X0: $i, X1: $i] : ((multiplication(X0, domain(X1)) = zero) => (multiplication(X0, X1) = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.13/0.42 tff(17,plain,
% 0.13/0.42 (~![X0: $i, X1: $i] : ((~(multiplication(X0, domain(X1)) = zero)) | (multiplication(X0, X1) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.42 tff(18,plain,
% 0.13/0.42 (~![X0: $i, X1: $i] : ((~(multiplication(X0, domain(X1)) = zero)) | (multiplication(X0, X1) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.13/0.42 tff(19,plain,
% 0.13/0.42 (~![X0: $i, X1: $i] : ((~(multiplication(X0, domain(X1)) = zero)) | (multiplication(X0, X1) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.42 tff(20,plain,
% 0.13/0.42 (~![X0: $i, X1: $i] : ((~(multiplication(X0, domain(X1)) = zero)) | (multiplication(X0, X1) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.13/0.42 tff(21,plain,
% 0.13/0.42 (~![X0: $i, X1: $i] : ((~(multiplication(X0, domain(X1)) = zero)) | (multiplication(X0, X1) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.13/0.42 tff(22,plain,
% 0.13/0.42 (~![X0: $i, X1: $i] : ((~(multiplication(X0, domain(X1)) = zero)) | (multiplication(X0, X1) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.13/0.42 tff(23,plain,
% 0.13/0.42 (~![X0: $i, X1: $i] : ((~(multiplication(X0, domain(X1)) = zero)) | (multiplication(X0, X1) = zero))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.13/0.42 tff(24,plain,(
% 0.13/0.42 ~((~(multiplication(X0!1, domain(X1!0)) = zero)) | (multiplication(X0!1, X1!0) = zero))),
% 0.13/0.42 inference(skolemize,[status(sab)],[23])).
% 0.13/0.42 tff(25,plain,
% 0.13/0.42 (multiplication(X0!1, domain(X1!0)) = zero),
% 0.13/0.42 inference(or_elim,[status(thm)],[24])).
% 0.13/0.42 tff(26,plain,
% 0.13/0.42 (domain(multiplication(X0!1, domain(X1!0))) = domain(zero)),
% 0.13/0.42 inference(monotonicity,[status(thm)],[25])).
% 0.13/0.42 tff(27,plain,
% 0.13/0.42 (^[X0: $i, X1: $i] : refl((domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(28,plain,
% 0.13/0.42 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.42 tff(29,plain,
% 0.13/0.42 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(30,axiom,(![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain2')).
% 0.13/0.42 tff(31,plain,
% 0.13/0.42 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.42 tff(32,plain,(
% 0.13/0.42 ![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[31])).
% 0.13/0.42 tff(33,plain,
% 0.13/0.42 (![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.13/0.42 tff(34,plain,
% 0.13/0.42 ((~![X0: $i, X1: $i] : (domain(multiplication(X0, X1)) = domain(multiplication(X0, domain(X1))))) | (domain(multiplication(X0!1, X1!0)) = domain(multiplication(X0!1, domain(X1!0))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(35,plain,
% 0.13/0.42 (domain(multiplication(X0!1, X1!0)) = domain(multiplication(X0!1, domain(X1!0)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.13/0.42 tff(36,plain,
% 0.13/0.42 (domain(multiplication(X0!1, X1!0)) = zero),
% 0.13/0.42 inference(transitivity,[status(thm)],[35, 26, 13])).
% 0.13/0.42 tff(37,plain,
% 0.13/0.42 (multiplication(domain(multiplication(X0!1, X1!0)), multiplication(X0!1, X1!0)) = multiplication(zero, multiplication(X0!1, X1!0))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[36])).
% 0.13/0.42 tff(38,plain,
% 0.13/0.42 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(39,plain,
% 0.13/0.42 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[38])).
% 0.13/0.42 tff(40,plain,
% 0.13/0.42 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(41,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain1')).
% 0.13/0.42 tff(42,plain,
% 0.13/0.42 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.42 tff(43,plain,(
% 0.13/0.42 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.13/0.42 inference(skolemize,[status(sab)],[42])).
% 0.13/0.42 tff(44,plain,
% 0.13/0.42 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.13/0.42 tff(45,plain,
% 0.13/0.42 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(multiplication(X0!1, X1!0), multiplication(domain(multiplication(X0!1, X1!0)), multiplication(X0!1, X1!0))) = multiplication(domain(multiplication(X0!1, X1!0)), multiplication(X0!1, X1!0)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (addition(multiplication(X0!1, X1!0), multiplication(domain(multiplication(X0!1, X1!0)), multiplication(X0!1, X1!0))) = multiplication(domain(multiplication(X0!1, X1!0)), multiplication(X0!1, X1!0))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (multiplication(zero, multiplication(X0!1, X1!0)) = multiplication(domain(multiplication(X0!1, X1!0)), multiplication(X0!1, X1!0))),
% 0.20/0.43 inference(symmetry,[status(thm)],[37])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (zero = multiplication(zero, multiplication(X0!1, X1!0))),
% 0.20/0.43 inference(symmetry,[status(thm)],[10])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (zero = multiplication(domain(multiplication(X0!1, X1!0)), multiplication(X0!1, X1!0))),
% 0.20/0.43 inference(transitivity,[status(thm)],[48, 47])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (addition(multiplication(X0!1, X1!0), zero) = addition(multiplication(X0!1, X1!0), multiplication(domain(multiplication(X0!1, X1!0)), multiplication(X0!1, X1!0)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (addition(multiplication(X0!1, X1!0), zero) = zero),
% 0.20/0.43 inference(transitivity,[status(thm)],[50, 46, 37, 10])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 ((addition(multiplication(X0!1, X1!0), zero) = multiplication(X0!1, X1!0)) <=> (zero = multiplication(X0!1, X1!0))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 ((addition(multiplication(X0!1, X1!0), zero) = multiplication(X0!1, X1!0)) <=> (multiplication(X0!1, X1!0) = zero)),
% 0.20/0.43 inference(transitivity,[status(thm)],[52, 1])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 ((multiplication(X0!1, X1!0) = zero) <=> (addition(multiplication(X0!1, X1!0), zero) = multiplication(X0!1, X1!0))),
% 0.20/0.43 inference(symmetry,[status(thm)],[53])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 ((~(multiplication(X0!1, X1!0) = zero)) <=> (~(addition(multiplication(X0!1, X1!0), zero) = multiplication(X0!1, X1!0)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[54])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (~(multiplication(X0!1, X1!0) = zero)),
% 0.20/0.43 inference(or_elim,[status(thm)],[24])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (~(addition(multiplication(X0!1, X1!0), zero) = multiplication(X0!1, X1!0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.20/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(61,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (![A: $i] : (addition(A, zero) = A)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.43 tff(63,plain,(
% 0.20/0.43 ![A: $i] : (addition(A, zero) = A)),
% 0.20/0.43 inference(skolemize,[status(sab)],[62])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (![A: $i] : (addition(A, zero) = A)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(X0!1, X1!0), zero) = multiplication(X0!1, X1!0))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (addition(multiplication(X0!1, X1!0), zero) = multiplication(X0!1, X1!0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[66, 57])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------