TSTP Solution File: KLE064+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE064+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 0.07s 0.28s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.06 % Problem : KLE064+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.07 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.25 % Computer : n007.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Thu Sep 1 07:56:32 EDT 2022
% 0.07/0.25 % CPUTime :
% 0.07/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.26 Usage: tptp [options] [-file:]file
% 0.07/0.26 -h, -? prints this message.
% 0.07/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.07/0.26 -m, -model generate model.
% 0.07/0.26 -p, -proof generate proof.
% 0.07/0.26 -c, -core generate unsat core of named formulas.
% 0.07/0.26 -st, -statistics display statistics.
% 0.07/0.26 -t:timeout set timeout (in second).
% 0.07/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.07/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.26 -<param>:<value> configuration parameter and value.
% 0.07/0.26 -o:<output-file> file to place output in.
% 0.07/0.28 % SZS status Theorem
% 0.07/0.28 % SZS output start Proof
% 0.07/0.28 tff(multiplication_type, type, (
% 0.07/0.28 multiplication: ( $i * $i ) > $i)).
% 0.07/0.28 tff(tptp_fun_X0_1_type, type, (
% 0.07/0.28 tptp_fun_X0_1: $i)).
% 0.07/0.28 tff(domain_type, type, (
% 0.07/0.28 domain: $i > $i)).
% 0.07/0.28 tff(tptp_fun_X1_0_type, type, (
% 0.07/0.28 tptp_fun_X1_0: $i)).
% 0.07/0.28 tff(addition_type, type, (
% 0.07/0.28 addition: ( $i * $i ) > $i)).
% 0.07/0.28 tff(1,plain,
% 0.07/0.28 ((~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))) <=> (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0))))),
% 0.07/0.28 inference(rewrite,[status(thm)],[])).
% 0.07/0.28 tff(2,plain,
% 0.07/0.28 ((~![X0: $i, X1: $i] : ((addition(domain(X0), domain(X1)) = domain(X1)) => (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))) <=> (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0))))),
% 0.07/0.28 inference(rewrite,[status(thm)],[])).
% 0.07/0.28 tff(3,axiom,(~![X0: $i, X1: $i] : ((addition(domain(X0), domain(X1)) = domain(X1)) => (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.07/0.28 tff(4,plain,
% 0.07/0.28 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))),
% 0.07/0.28 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.07/0.28 tff(5,plain,
% 0.07/0.28 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))),
% 0.07/0.28 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.07/0.28 tff(6,plain,
% 0.07/0.28 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))),
% 0.07/0.28 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.07/0.28 tff(7,plain,
% 0.07/0.28 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))),
% 0.07/0.28 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.07/0.28 tff(8,plain,
% 0.07/0.28 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))),
% 0.07/0.28 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.07/0.28 tff(9,plain,
% 0.07/0.28 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))),
% 0.07/0.28 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.07/0.28 tff(10,plain,
% 0.07/0.28 (~![X0: $i, X1: $i] : ((~(addition(domain(X0), domain(X1)) = domain(X1))) | (addition(X0, multiplication(domain(X1), X0)) = multiplication(domain(X1), X0)))),
% 0.07/0.28 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.07/0.28 tff(11,plain,(
% 0.07/0.28 ~((~(addition(domain(X0!1), domain(X1!0)) = domain(X1!0))) | (addition(X0!1, multiplication(domain(X1!0), X0!1)) = multiplication(domain(X1!0), X0!1)))),
% 0.07/0.28 inference(skolemize,[status(sab)],[10])).
% 0.07/0.28 tff(12,plain,
% 0.07/0.28 (addition(domain(X0!1), domain(X1!0)) = domain(X1!0)),
% 0.07/0.28 inference(or_elim,[status(thm)],[11])).
% 0.07/0.28 tff(13,plain,
% 0.07/0.28 (domain(X1!0) = addition(domain(X0!1), domain(X1!0))),
% 0.07/0.28 inference(symmetry,[status(thm)],[12])).
% 0.07/0.28 tff(14,plain,
% 0.07/0.28 (multiplication(domain(X1!0), X0!1) = multiplication(addition(domain(X0!1), domain(X1!0)), X0!1)),
% 0.07/0.28 inference(monotonicity,[status(thm)],[13])).
% 0.07/0.28 tff(15,plain,
% 0.07/0.28 (multiplication(addition(domain(X0!1), domain(X1!0)), X0!1) = multiplication(domain(X1!0), X0!1)),
% 0.07/0.28 inference(symmetry,[status(thm)],[14])).
% 0.07/0.28 tff(16,plain,
% 0.07/0.28 (^[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))))),
% 0.07/0.28 inference(bind,[status(th)],[])).
% 0.07/0.28 tff(17,plain,
% 0.07/0.28 (![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)))),
% 0.07/0.28 inference(quant_intro,[status(thm)],[16])).
% 0.07/0.28 tff(18,plain,
% 0.07/0.28 (![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)))),
% 0.07/0.28 inference(rewrite,[status(thm)],[])).
% 0.07/0.28 tff(19,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')).
% 0.07/0.28 tff(20,plain,
% 0.07/0.28 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.07/0.28 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.07/0.28 tff(21,plain,(
% 0.07/0.28 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.07/0.28 inference(skolemize,[status(sab)],[20])).
% 0.07/0.28 tff(22,plain,
% 0.07/0.28 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.07/0.28 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.07/0.28 tff(23,plain,
% 0.07/0.28 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(domain(X0!1), domain(X1!0)), X0!1) = addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)))),
% 0.07/0.28 inference(quant_inst,[status(thm)],[])).
% 0.07/0.28 tff(24,plain,
% 0.07/0.28 (multiplication(addition(domain(X0!1), domain(X1!0)), X0!1) = addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))),
% 0.07/0.28 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.07/0.28 tff(25,plain,
% 0.07/0.28 (addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)) = multiplication(addition(domain(X0!1), domain(X1!0)), X0!1)),
% 0.07/0.28 inference(symmetry,[status(thm)],[24])).
% 0.07/0.28 tff(26,plain,
% 0.07/0.28 (addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)) = multiplication(domain(X1!0), X0!1)),
% 0.07/0.28 inference(transitivity,[status(thm)],[25, 15])).
% 0.07/0.28 tff(27,plain,
% 0.07/0.28 (^[X0: $i] : refl((addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)))),
% 0.07/0.28 inference(bind,[status(th)],[])).
% 0.07/0.28 tff(28,plain,
% 0.07/0.28 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.07/0.28 inference(quant_intro,[status(thm)],[27])).
% 0.07/0.28 tff(29,plain,
% 0.07/0.28 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0)) <=> ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.07/0.28 inference(rewrite,[status(thm)],[])).
% 0.07/0.28 tff(30,axiom,(![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain1')).
% 0.07/0.28 tff(31,plain,
% 0.07/0.28 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.07/0.28 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.07/0.28 tff(32,plain,(
% 0.07/0.28 ![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.07/0.28 inference(skolemize,[status(sab)],[31])).
% 0.07/0.28 tff(33,plain,
% 0.07/0.28 (![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))),
% 0.07/0.28 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.07/0.28 tff(34,plain,
% 0.07/0.28 ((~![X0: $i] : (addition(X0, multiplication(domain(X0), X0)) = multiplication(domain(X0), X0))) | (addition(X0!1, multiplication(domain(X0!1), X0!1)) = multiplication(domain(X0!1), X0!1))),
% 0.07/0.28 inference(quant_inst,[status(thm)],[])).
% 0.07/0.28 tff(35,plain,
% 0.07/0.28 (addition(X0!1, multiplication(domain(X0!1), X0!1)) = multiplication(domain(X0!1), X0!1)),
% 0.07/0.28 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.07/0.28 tff(36,plain,
% 0.07/0.28 (addition(addition(X0!1, multiplication(domain(X0!1), X0!1)), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))) = addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))),
% 0.07/0.29 inference(monotonicity,[status(thm)],[35, 26])).
% 0.07/0.29 tff(37,plain,
% 0.07/0.29 (^[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)))),
% 0.07/0.29 inference(bind,[status(th)],[])).
% 0.07/0.29 tff(38,plain,
% 0.07/0.29 (![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))),
% 0.07/0.29 inference(quant_intro,[status(thm)],[37])).
% 0.07/0.29 tff(39,plain,
% 0.07/0.29 (![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))),
% 0.07/0.29 inference(rewrite,[status(thm)],[])).
% 0.07/0.29 tff(40,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')).
% 0.07/0.29 tff(41,plain,
% 0.07/0.29 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.07/0.29 tff(42,plain,(
% 0.07/0.29 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.07/0.29 inference(skolemize,[status(sab)],[41])).
% 0.07/0.29 tff(43,plain,
% 0.07/0.29 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.07/0.29 tff(44,plain,
% 0.07/0.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!1, addition(multiplication(domain(X0!1), X0!1), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)))) = addition(addition(X0!1, multiplication(domain(X0!1), X0!1)), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))))),
% 0.07/0.29 inference(quant_inst,[status(thm)],[])).
% 0.07/0.29 tff(45,plain,
% 0.07/0.29 (addition(X0!1, addition(multiplication(domain(X0!1), X0!1), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)))) = addition(addition(X0!1, multiplication(domain(X0!1), X0!1)), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)))),
% 0.07/0.29 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.07/0.29 tff(46,plain,
% 0.07/0.29 (addition(multiplication(domain(X0!1), X0!1), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))) = addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))),
% 0.07/0.29 inference(monotonicity,[status(thm)],[26])).
% 0.07/0.29 tff(47,plain,
% 0.07/0.29 (addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)) = addition(multiplication(domain(X0!1), X0!1), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)))),
% 0.07/0.29 inference(symmetry,[status(thm)],[46])).
% 0.07/0.29 tff(48,plain,
% 0.07/0.29 (multiplication(domain(X1!0), X0!1) = addition(multiplication(domain(X0!1), X0!1), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1)))),
% 0.07/0.29 inference(transitivity,[status(thm)],[14, 24, 47])).
% 0.07/0.29 tff(49,plain,
% 0.07/0.29 (addition(X0!1, multiplication(domain(X1!0), X0!1)) = addition(X0!1, addition(multiplication(domain(X0!1), X0!1), addition(multiplication(domain(X0!1), X0!1), multiplication(domain(X1!0), X0!1))))),
% 0.07/0.29 inference(monotonicity,[status(thm)],[48])).
% 0.07/0.29 tff(50,plain,
% 0.07/0.29 (addition(X0!1, multiplication(domain(X1!0), X0!1)) = multiplication(domain(X1!0), X0!1)),
% 0.07/0.29 inference(transitivity,[status(thm)],[49, 45, 36, 25, 15])).
% 0.07/0.29 tff(51,plain,
% 0.07/0.29 (~(addition(X0!1, multiplication(domain(X1!0), X0!1)) = multiplication(domain(X1!0), X0!1))),
% 0.07/0.29 inference(or_elim,[status(thm)],[11])).
% 0.07/0.29 tff(52,plain,
% 0.07/0.29 ($false),
% 0.07/0.29 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.07/0.29 % SZS output end Proof
%------------------------------------------------------------------------------