TSTP Solution File: KLE089+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : KLE089+1 : TPTP v7.3.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n026.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
% DateTime : Mon Jun  8 16:57:06 EDT 2020

% Result   : Theorem 0.22s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : KLE089+1 : TPTP v7.3.0. Released v4.0.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35  % Computer : n026.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  % DateTime : Fri Jun  5 06:03:29 EDT 2020
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36  Usage: tptp [options] [-file:]file
% 0.14/0.36    -h, -?       prints this message.
% 0.14/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.36    -m, -model   generate model.
% 0.14/0.36    -p, -proof   generate proof.
% 0.14/0.36    -c, -core    generate unsat core of named formulas.
% 0.14/0.36    -st, -statistics display statistics.
% 0.14/0.36    -t:timeout   set timeout (in second).
% 0.14/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36    -<param>:<value> configuration parameter and value.
% 0.14/0.36    -o:<output-file> file to place output in.
% 0.22/0.40  % SZS status Theorem
% 0.22/0.40  % SZS output start Proof
% 0.22/0.40  tff(zero_type, type, (
% 0.22/0.40     zero: $i)).
% 0.22/0.40  tff(multiplication_type, type, (
% 0.22/0.40     multiplication: ( $i * $i ) > $i)).
% 0.22/0.40  tff(tptp_fun_X1_0_type, type, (
% 0.22/0.40     tptp_fun_X1_0: $i)).
% 0.22/0.40  tff(domain_type, type, (
% 0.22/0.40     domain: $i > $i)).
% 0.22/0.40  tff(tptp_fun_X0_1_type, type, (
% 0.22/0.40     tptp_fun_X0_1: $i)).
% 0.22/0.40  tff(antidomain_type, type, (
% 0.22/0.40     antidomain: $i > $i)).
% 0.22/0.40  tff(addition_type, type, (
% 0.22/0.40     addition: ( $i * $i ) > $i)).
% 0.22/0.40  tff(1,plain,
% 0.22/0.40      (^[X0: $i] : refl((multiplication(antidomain(X0), X0) = zero) <=> (multiplication(antidomain(X0), X0) = zero))),
% 0.22/0.40      inference(bind,[status(th)],[])).
% 0.22/0.40  tff(2,plain,
% 0.22/0.40      (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.22/0.40      inference(quant_intro,[status(thm)],[1])).
% 0.22/0.40  tff(3,plain,
% 0.22/0.40      (![X0: $i] : (multiplication(antidomain(X0), X0) = zero) <=> ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.22/0.40      inference(rewrite,[status(thm)],[])).
% 0.22/0.40  tff(4,axiom,(![X0: $i] : (multiplication(antidomain(X0), X0) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax','domain1')).
% 0.22/0.40  tff(5,plain,
% 0.22/0.40      (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.22/0.40      inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.40  tff(6,plain,(
% 0.22/0.40      ![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.22/0.40      inference(skolemize,[status(sab)],[5])).
% 0.22/0.40  tff(7,plain,
% 0.22/0.40      (![X0: $i] : (multiplication(antidomain(X0), X0) = zero)),
% 0.22/0.40      inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.40  tff(8,plain,
% 0.22/0.40      ((~![X0: $i] : (multiplication(antidomain(X0), X0) = zero)) | (multiplication(antidomain(X1!0), X1!0) = zero)),
% 0.22/0.40      inference(quant_inst,[status(thm)],[])).
% 0.22/0.40  tff(9,plain,
% 0.22/0.40      (multiplication(antidomain(X1!0), X1!0) = zero),
% 0.22/0.40      inference(unit_resolution,[status(thm)],[8, 7])).
% 0.22/0.40  tff(10,plain,
% 0.22/0.40      ((~![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)))),
% 0.22/0.40      inference(rewrite,[status(thm)],[])).
% 0.22/0.40  tff(11,plain,
% 0.22/0.40      ((~![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)))),
% 0.22/0.40      inference(rewrite,[status(thm)],[])).
% 0.22/0.40  tff(12,axiom,(~![X0: $i, X1: $i] : ((addition(domain(X0), antidomain(X1)) = antidomain(X1)) => (multiplication(domain(X0), X1) = zero))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.22/0.40  tff(13,plain,
% 0.22/0.40      (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.22/0.40      inference(modus_ponens,[status(thm)],[12, 11])).
% 0.22/0.40  tff(14,plain,
% 0.22/0.40      (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.22/0.40      inference(modus_ponens,[status(thm)],[13, 10])).
% 0.22/0.40  tff(15,plain,
% 0.22/0.40      (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.22/0.40      inference(modus_ponens,[status(thm)],[14, 10])).
% 0.22/0.40  tff(16,plain,
% 0.22/0.40      (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.22/0.40      inference(modus_ponens,[status(thm)],[15, 10])).
% 0.22/0.40  tff(17,plain,
% 0.22/0.40      (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.22/0.40      inference(modus_ponens,[status(thm)],[16, 10])).
% 0.22/0.40  tff(18,plain,
% 0.22/0.40      (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.22/0.40      inference(modus_ponens,[status(thm)],[17, 10])).
% 0.22/0.40  tff(19,plain,
% 0.22/0.40      (~![X0: $i, X1: $i] : ((~(addition(domain(X0), antidomain(X1)) = antidomain(X1))) | (multiplication(domain(X0), X1) = zero))),
% 0.22/0.40      inference(modus_ponens,[status(thm)],[18, 10])).
% 0.22/0.40  tff(20,plain,(
% 0.22/0.40      ~((~(addition(domain(X0!1), antidomain(X1!0)) = antidomain(X1!0))) | (multiplication(domain(X0!1), X1!0) = zero))),
% 0.22/0.41      inference(skolemize,[status(sab)],[19])).
% 0.22/0.41  tff(21,plain,
% 0.22/0.41      (addition(domain(X0!1), antidomain(X1!0)) = antidomain(X1!0)),
% 0.22/0.41      inference(or_elim,[status(thm)],[20])).
% 0.22/0.41  tff(22,plain,
% 0.22/0.41      (^[X0: $i] : refl((domain(X0) = antidomain(antidomain(X0))) <=> (domain(X0) = antidomain(antidomain(X0))))),
% 0.22/0.41      inference(bind,[status(th)],[])).
% 0.22/0.41  tff(23,plain,
% 0.22/0.41      (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.22/0.41      inference(quant_intro,[status(thm)],[22])).
% 0.22/0.41  tff(24,plain,
% 0.22/0.41      (![X0: $i] : (domain(X0) = antidomain(antidomain(X0))) <=> ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.22/0.41      inference(rewrite,[status(thm)],[])).
% 0.22/0.41  tff(25,axiom,(![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax','domain4')).
% 0.22/0.41  tff(26,plain,
% 0.22/0.41      (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.22/0.41      inference(modus_ponens,[status(thm)],[25, 24])).
% 0.22/0.41  tff(27,plain,(
% 0.22/0.41      ![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.22/0.41      inference(skolemize,[status(sab)],[26])).
% 0.22/0.41  tff(28,plain,
% 0.22/0.41      (![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))),
% 0.22/0.41      inference(modus_ponens,[status(thm)],[27, 23])).
% 0.22/0.41  tff(29,plain,
% 0.22/0.41      ((~![X0: $i] : (domain(X0) = antidomain(antidomain(X0)))) | (domain(X0!1) = antidomain(antidomain(X0!1)))),
% 0.22/0.41      inference(quant_inst,[status(thm)],[])).
% 0.22/0.41  tff(30,plain,
% 0.22/0.41      (domain(X0!1) = antidomain(antidomain(X0!1))),
% 0.22/0.41      inference(unit_resolution,[status(thm)],[29, 28])).
% 0.22/0.41  tff(31,plain,
% 0.22/0.41      (antidomain(antidomain(X0!1)) = domain(X0!1)),
% 0.22/0.41      inference(symmetry,[status(thm)],[30])).
% 0.22/0.41  tff(32,plain,
% 0.22/0.41      (addition(antidomain(antidomain(X0!1)), antidomain(X1!0)) = addition(domain(X0!1), antidomain(X1!0))),
% 0.22/0.41      inference(monotonicity,[status(thm)],[31])).
% 0.22/0.41  tff(33,plain,
% 0.22/0.41      (addition(antidomain(antidomain(X0!1)), antidomain(X1!0)) = antidomain(X1!0)),
% 0.22/0.41      inference(transitivity,[status(thm)],[32, 21])).
% 0.22/0.41  tff(34,plain,
% 0.22/0.41      (multiplication(addition(antidomain(antidomain(X0!1)), antidomain(X1!0)), X1!0) = multiplication(antidomain(X1!0), X1!0)),
% 0.22/0.41      inference(monotonicity,[status(thm)],[33])).
% 0.22/0.41  tff(35,plain,
% 0.22/0.41      (^[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))))),
% 0.22/0.41      inference(bind,[status(th)],[])).
% 0.22/0.41  tff(36,plain,
% 0.22/0.41      (![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)))),
% 0.22/0.41      inference(quant_intro,[status(thm)],[35])).
% 0.22/0.41  tff(37,plain,
% 0.22/0.41      (![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)))),
% 0.22/0.41      inference(rewrite,[status(thm)],[])).
% 0.22/0.41  tff(38,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 0.22/0.41  tff(39,plain,
% 0.22/0.41      (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.22/0.41      inference(modus_ponens,[status(thm)],[38, 37])).
% 0.22/0.41  tff(40,plain,(
% 0.22/0.41      ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.22/0.41      inference(skolemize,[status(sab)],[39])).
% 0.22/0.41  tff(41,plain,
% 0.22/0.41      (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.22/0.41      inference(modus_ponens,[status(thm)],[40, 36])).
% 0.22/0.41  tff(42,plain,
% 0.22/0.41      ((~![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)))),
% 0.22/0.41      inference(quant_inst,[status(thm)],[])).
% 0.22/0.41  tff(43,plain,
% 0.22/0.41      (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))),
% 0.22/0.41      inference(unit_resolution,[status(thm)],[42, 41])).
% 0.22/0.41  tff(44,plain,
% 0.22/0.41      (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)),
% 0.22/0.41      inference(symmetry,[status(thm)],[43])).
% 0.22/0.41  tff(45,plain,
% 0.22/0.41      (zero = multiplication(antidomain(X1!0), X1!0)),
% 0.22/0.41      inference(symmetry,[status(thm)],[9])).
% 0.22/0.41  tff(46,plain,
% 0.22/0.41      (multiplication(antidomain(antidomain(X0!1)), X1!0) = multiplication(domain(X0!1), X1!0)),
% 0.22/0.41      inference(monotonicity,[status(thm)],[31])).
% 0.22/0.41  tff(47,plain,
% 0.22/0.41      (multiplication(domain(X0!1), X1!0) = multiplication(antidomain(antidomain(X0!1)), X1!0)),
% 0.22/0.41      inference(symmetry,[status(thm)],[46])).
% 0.22/0.41  tff(48,plain,
% 0.22/0.41      (addition(multiplication(domain(X0!1), X1!0), zero) = addition(multiplication(antidomain(antidomain(X0!1)), X1!0), multiplication(antidomain(X1!0), X1!0))),
% 0.22/0.41      inference(monotonicity,[status(thm)],[47, 45])).
% 0.22/0.41  tff(49,plain,
% 0.22/0.41      (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.22/0.41      inference(bind,[status(th)],[])).
% 0.22/0.41  tff(50,plain,
% 0.22/0.41      (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.22/0.41      inference(quant_intro,[status(thm)],[49])).
% 0.22/0.41  tff(51,plain,
% 0.22/0.41      (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.22/0.41      inference(rewrite,[status(thm)],[])).
% 0.22/0.41  tff(52,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 0.22/0.41  tff(53,plain,
% 0.22/0.41      (![A: $i] : (addition(A, zero) = A)),
% 0.22/0.41      inference(modus_ponens,[status(thm)],[52, 51])).
% 0.22/0.41  tff(54,plain,(
% 0.22/0.41      ![A: $i] : (addition(A, zero) = A)),
% 0.22/0.41      inference(skolemize,[status(sab)],[53])).
% 0.22/0.41  tff(55,plain,
% 0.22/0.41      (![A: $i] : (addition(A, zero) = A)),
% 0.22/0.41      inference(modus_ponens,[status(thm)],[54, 50])).
% 0.22/0.41  tff(56,plain,
% 0.22/0.41      ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(domain(X0!1), X1!0), zero) = multiplication(domain(X0!1), X1!0))),
% 0.22/0.41      inference(quant_inst,[status(thm)],[])).
% 0.22/0.41  tff(57,plain,
% 0.22/0.41      (addition(multiplication(domain(X0!1), X1!0), zero) = multiplication(domain(X0!1), X1!0)),
% 0.22/0.41      inference(unit_resolution,[status(thm)],[56, 55])).
% 0.22/0.41  tff(58,plain,
% 0.22/0.41      (multiplication(domain(X0!1), X1!0) = addition(multiplication(domain(X0!1), X1!0), zero)),
% 0.22/0.41      inference(symmetry,[status(thm)],[57])).
% 0.22/0.41  tff(59,plain,
% 0.22/0.41      (multiplication(domain(X0!1), X1!0) = zero),
% 0.22/0.41      inference(transitivity,[status(thm)],[58, 48, 44, 34, 9])).
% 0.22/0.41  tff(60,plain,
% 0.22/0.41      (~(multiplication(domain(X0!1), X1!0) = zero)),
% 0.22/0.41      inference(or_elim,[status(thm)],[20])).
% 0.22/0.41  tff(61,plain,
% 0.22/0.41      ($false),
% 0.22/0.41      inference(unit_resolution,[status(thm)],[60, 59])).
% 0.22/0.41  % SZS output end Proof
%------------------------------------------------------------------------------