TSTP Solution File: KLE072+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE072+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 17:24:05 EDT 2022
% Result : Theorem 0.23s 0.43s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : KLE072+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Sep 1 08:12:34 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.37 Usage: tptp [options] [-file:]file
% 0.14/0.37 -h, -? prints this message.
% 0.14/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.37 -m, -model generate model.
% 0.14/0.37 -p, -proof generate proof.
% 0.14/0.37 -c, -core generate unsat core of named formulas.
% 0.14/0.37 -st, -statistics display statistics.
% 0.14/0.37 -t:timeout set timeout (in second).
% 0.14/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.37 -<param>:<value> configuration parameter and value.
% 0.14/0.37 -o:<output-file> file to place output in.
% 0.23/0.43 % SZS status Theorem
% 0.23/0.43 % SZS output start Proof
% 0.23/0.43 tff(addition_type, type, (
% 0.23/0.43 addition: ( $i * $i ) > $i)).
% 0.23/0.43 tff(domain_type, type, (
% 0.23/0.43 domain: $i > $i)).
% 0.23/0.43 tff(multiplication_type, type, (
% 0.23/0.43 multiplication: ( $i * $i ) > $i)).
% 0.23/0.43 tff(tptp_fun_X2_0_type, type, (
% 0.23/0.43 tptp_fun_X2_0: $i)).
% 0.23/0.43 tff(tptp_fun_X1_1_type, type, (
% 0.23/0.43 tptp_fun_X1_1: $i)).
% 0.23/0.43 tff(tptp_fun_X0_2_type, type, (
% 0.23/0.43 tptp_fun_X0_2: $i)).
% 0.23/0.43 tff(1,plain,
% 0.23/0.43 (^[X0: $i, X1: $i] : refl((domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(2,plain,
% 0.23/0.43 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.43 tff(3,plain,
% 0.23/0.43 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1))) <=> ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(4,axiom,(![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax','domain5')).
% 0.23/0.43 tff(5,plain,
% 0.23/0.43 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.23/0.43 tff(6,plain,(
% 0.23/0.43 ![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.23/0.43 inference(skolemize,[status(sab)],[5])).
% 0.23/0.43 tff(7,plain,
% 0.23/0.43 (![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.23/0.43 tff(8,plain,
% 0.23/0.43 ((~![X0: $i, X1: $i] : (domain(addition(X0, X1)) = addition(domain(X0), domain(X1)))) | (domain(addition(multiplication(X0!2, domain(X2!0)), multiplication(X1!1, domain(X2!0)))) = addition(domain(multiplication(X0!2, domain(X2!0))), domain(multiplication(X1!1, domain(X2!0)))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(9,plain,
% 0.23/0.43 (domain(addition(multiplication(X0!2, domain(X2!0)), multiplication(X1!1, domain(X2!0)))) = addition(domain(multiplication(X0!2, domain(X2!0))), domain(multiplication(X1!1, domain(X2!0))))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.23/0.43 tff(10,plain,
% 0.23/0.43 (^[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))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(11,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[10])).
% 0.23/0.43 tff(12,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(13,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')).
% 0.23/0.43 tff(14,plain,
% 0.23/0.43 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.23/0.43 tff(15,plain,(
% 0.23/0.43 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.23/0.43 inference(skolemize,[status(sab)],[14])).
% 0.23/0.43 tff(16,plain,
% 0.23/0.43 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.23/0.43 tff(17,plain,
% 0.23/0.43 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!2, X1!1), domain(X2!0)) = addition(multiplication(X0!2, domain(X2!0)), multiplication(X1!1, domain(X2!0))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(18,plain,
% 0.23/0.43 (multiplication(addition(X0!2, X1!1), domain(X2!0)) = addition(multiplication(X0!2, domain(X2!0)), multiplication(X1!1, domain(X2!0)))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.23/0.43 tff(19,plain,
% 0.23/0.43 (domain(multiplication(addition(X0!2, X1!1), domain(X2!0))) = domain(addition(multiplication(X0!2, domain(X2!0)), multiplication(X1!1, domain(X2!0))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[18])).
% 0.23/0.43 tff(20,plain,
% 0.23/0.43 (domain(multiplication(addition(X0!2, X1!1), domain(X2!0))) = addition(domain(multiplication(X0!2, domain(X2!0))), domain(multiplication(X1!1, domain(X2!0))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[19, 9])).
% 0.23/0.43 tff(21,plain,
% 0.23/0.43 ((~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))) <=> (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2))))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(22,axiom,(~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.23/0.43 tff(23,plain,
% 0.23/0.43 (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.23/0.43 tff(24,plain,
% 0.23/0.43 (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.23/0.43 tff(25,plain,
% 0.23/0.43 (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.23/0.43 tff(26,plain,
% 0.23/0.43 (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.23/0.43 tff(27,plain,
% 0.23/0.43 (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.23/0.43 tff(28,plain,
% 0.23/0.43 (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.23/0.43 tff(29,plain,
% 0.23/0.43 (~![X0: $i, X1: $i, X2: $i] : (domain(multiplication(addition(X0, X1), domain(X2))) = addition(domain(multiplication(X0, domain(X2))), domain(multiplication(X1, domain(X2)))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.23/0.43 tff(30,plain,(
% 0.23/0.43 ~(domain(multiplication(addition(X0!2, X1!1), domain(X2!0))) = addition(domain(multiplication(X0!2, domain(X2!0))), domain(multiplication(X1!1, domain(X2!0)))))),
% 0.23/0.43 inference(skolemize,[status(sab)],[29])).
% 0.23/0.43 tff(31,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[30, 20])).
% 0.23/0.43 % SZS output end Proof
%------------------------------------------------------------------------------