TSTP Solution File: KLE089+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE089+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 Sep 17 17:24:08 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
% 0.07/0.12 % Problem : KLE089+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 08:16:50 EDT 2022
% 0.12/0.34 % 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(multiplication_type, type, (
% 0.19/0.39 multiplication: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_X1_0_type, type, (
% 0.19/0.39 tptp_fun_X1_0: $i)).
% 0.19/0.39 tff(domain_type, type, (
% 0.19/0.39 domain: $i > $i)).
% 0.19/0.39 tff(tptp_fun_X0_1_type, type, (
% 0.19/0.39 tptp_fun_X0_1: $i)).
% 0.19/0.39 tff(antidomain_type, type, (
% 0.19/0.39 antidomain: $i > $i)).
% 0.19/0.39 tff(addition_type, type, (
% 0.19/0.39 addition: ( $i * $i ) > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[X0: $i] : refl((multiplication(antidomain(X0), X0) = zero) <=> (multiplication(antidomain(X0), X0) = zero))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![X0: $i] : (multiplication(antidomain(X0), X0) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax','domain1')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![X0: $i] : (multiplication(antidomain(X0), X0) = zero)) | (multiplication(antidomain(X1!0), X1!0) = zero)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (multiplication(antidomain(X1!0), X1!0) = zero),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 ((~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))) <=> (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ((~![X0: $i, X1: $i] : ((addition(domain(X0), antidomain(X1)) = antidomain(X1)) => (multiplication(domain(X0), X1) = zero))) <=> (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(12,axiom,(~![X0: $i, X1: $i] : ((addition(domain(X0), antidomain(X1)) = antidomain(X1)) => (multiplication(domain(X0), X1) = zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.19/0.39 tff(20,plain,(
% 0.19/0.39 ~((~(addition(domain(X0!1), antidomain(X1!0)) = antidomain(X1!0))) | (multiplication(domain(X0!1), X1!0) = zero))),
% 0.19/0.39 inference(skolemize,[status(sab)],[19])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (addition(domain(X0!1), antidomain(X1!0)) = antidomain(X1!0)),
% 0.19/0.39 inference(or_elim,[status(thm)],[20])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (^[X0: $i] : refl((domain(X0) = antidomain(antidomain(X0))) <=> (domain(X0) = antidomain(antidomain(X0))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(25,axiom,(![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax','domain4')).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.39 tff(27,plain,(
% 0.19/0.39 ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(X0!1) = antidomain(antidomain(X0!1)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (domain(X0!1) = antidomain(antidomain(X0!1))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (antidomain(antidomain(X0!1)) = domain(X0!1)),
% 0.19/0.39 inference(symmetry,[status(thm)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (addition(antidomain(antidomain(X0!1)), antidomain(X1!0)) = addition(domain(X0!1), antidomain(X1!0))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (addition(antidomain(antidomain(X0!1)), antidomain(X1!0)) = antidomain(X1!0)),
% 0.19/0.39 inference(transitivity,[status(thm)],[32, 21])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (multiplication(addition(antidomain(antidomain(X0!1)), antidomain(X1!0)), X1!0) = multiplication(antidomain(X1!0), X1!0)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(38,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')).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.39 tff(40,plain,(
% 0.19/0.39 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[39])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(antidomain(antidomain(X0!1)), antidomain(X1!0)), X1!0) = addition(multiplication(antidomain(antidomain(X0!1)), X1!0), multiplication(antidomain(X1!0), X1!0)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (multiplication(addition(antidomain(antidomain(X0!1)), antidomain(X1!0)), X1!0) = addition(multiplication(antidomain(antidomain(X0!1)), X1!0), multiplication(antidomain(X1!0), X1!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (addition(multiplication(antidomain(antidomain(X0!1)), X1!0), multiplication(antidomain(X1!0), X1!0)) = multiplication(addition(antidomain(antidomain(X0!1)), antidomain(X1!0)), X1!0)),
% 0.19/0.40 inference(symmetry,[status(thm)],[43])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (zero = multiplication(antidomain(X1!0), X1!0)),
% 0.19/0.40 inference(symmetry,[status(thm)],[9])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (multiplication(antidomain(antidomain(X0!1)), X1!0) = multiplication(domain(X0!1), X1!0)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (multiplication(domain(X0!1), X1!0) = multiplication(antidomain(antidomain(X0!1)), X1!0)),
% 0.19/0.40 inference(symmetry,[status(thm)],[46])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (addition(multiplication(domain(X0!1), X1!0), zero) = addition(multiplication(antidomain(antidomain(X0!1)), X1!0), multiplication(antidomain(X1!0), X1!0))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[47, 45])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(52,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![A: $i] : (addition(A, zero) = A)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.40 tff(54,plain,(
% 0.19/0.40 ![A: $i] : (addition(A, zero) = A)),
% 0.19/0.40 inference(skolemize,[status(sab)],[53])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![A: $i] : (addition(A, zero) = A)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(domain(X0!1), X1!0), zero) = multiplication(domain(X0!1), X1!0))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (addition(multiplication(domain(X0!1), X1!0), zero) = multiplication(domain(X0!1), X1!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (multiplication(domain(X0!1), X1!0) = addition(multiplication(domain(X0!1), X1!0), zero)),
% 0.19/0.40 inference(symmetry,[status(thm)],[57])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (multiplication(domain(X0!1), X1!0) = zero),
% 0.19/0.40 inference(transitivity,[status(thm)],[58, 48, 44, 34, 9])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (~(multiplication(domain(X0!1), X1!0) = zero)),
% 0.19/0.40 inference(or_elim,[status(thm)],[20])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.40 % SZS output end Proof
%------------------------------------------------------------------------------