TSTP Solution File: KLE002+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 17:23:44 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 07:38:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(multiplication_type, type, (
% 0.19/0.38 multiplication: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_X2_0_type, type, (
% 0.19/0.38 tptp_fun_X2_0: $i)).
% 0.19/0.38 tff(tptp_fun_X1_1_type, type, (
% 0.19/0.38 tptp_fun_X1_1: $i)).
% 0.19/0.38 tff(addition_type, type, (
% 0.19/0.38 addition: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_X0_2_type, type, (
% 0.19/0.38 tptp_fun_X0_2: $i)).
% 0.19/0.38 tff(leq_type, type, (
% 0.19/0.38 leq: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(4,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','order')).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.38 tff(6,plain,(
% 0.19/0.38 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.38 inference(skolemize,[status(sab)],[5])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!2, X1!1) <=> (addition(X0!2, X1!1) = X1!1))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (leq(X0!2, X1!1) <=> (addition(X0!2, X1!1) = X1!1)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 ((~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(multiplication(X0, X2), multiplication(X1, X2)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(multiplication(X0, X2), multiplication(X1, X2))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 ((~![X0: $i, X1: $i, X2: $i] : (leq(X0, X1) => leq(multiplication(X0, X2), multiplication(X1, X2)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(multiplication(X0, X2), multiplication(X1, X2))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(12,axiom,(~![X0: $i, X1: $i, X2: $i] : (leq(X0, X1) => leq(multiplication(X0, X2), multiplication(X1, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(multiplication(X0, X2), multiplication(X1, X2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(multiplication(X0, X2), multiplication(X1, X2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(multiplication(X0, X2), multiplication(X1, X2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(multiplication(X0, X2), multiplication(X1, X2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(multiplication(X0, X2), multiplication(X1, X2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(multiplication(X0, X2), multiplication(X1, X2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (~![X0: $i, X1: $i, X2: $i] : ((~leq(X0, X1)) | leq(multiplication(X0, X2), multiplication(X1, X2)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.19/0.38 tff(20,plain,(
% 0.19/0.38 ~((~leq(X0!2, X1!1)) | leq(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[19])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (leq(X0!2, X1!1)),
% 0.19/0.38 inference(or_elim,[status(thm)],[20])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 ((~(leq(X0!2, X1!1) <=> (addition(X0!2, X1!1) = X1!1))) | (~leq(X0!2, X1!1)) | (addition(X0!2, X1!1) = X1!1)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 ((~(leq(X0!2, X1!1) <=> (addition(X0!2, X1!1) = X1!1))) | (addition(X0!2, X1!1) = X1!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (addition(X0!2, X1!1) = X1!1),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[23, 9])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (X1!1 = addition(X0!2, X1!1)),
% 0.19/0.39 inference(symmetry,[status(thm)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (multiplication(X1!1, X2!0) = multiplication(addition(X0!2, X1!1), X2!0)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[25])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (multiplication(addition(X0!2, X1!1), X2!0) = multiplication(X1!1, X2!0)),
% 0.19/0.39 inference(symmetry,[status(thm)],[26])).
% 0.19/0.39 tff(28,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(29,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)],[28])).
% 0.19/0.39 tff(30,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(31,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(32,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)],[31, 30])).
% 0.19/0.39 tff(33,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)],[32])).
% 0.19/0.39 tff(34,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)],[33, 29])).
% 0.19/0.39 tff(35,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(X0!2, X1!1), X2!0) = addition(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (multiplication(addition(X0!2, X1!1), X2!0) = addition(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (addition(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) = multiplication(addition(X0!2, X1!1), X2!0)),
% 0.19/0.39 inference(symmetry,[status(thm)],[36])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (addition(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)),
% 0.19/0.39 inference(transitivity,[status(thm)],[37, 27])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) <=> (addition(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (leq(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) <=> (addition(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 7])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (~leq(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0))),
% 0.19/0.39 inference(or_elim,[status(thm)],[20])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 ((~(leq(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) <=> (addition(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)))) | leq(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) | (~(addition(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 ((~(leq(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) <=> (addition(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)))) | (~(addition(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (~(addition(multiplication(X0!2, X2!0), multiplication(X1!1, X2!0)) = multiplication(X1!1, X2!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[44, 38])).
% 0.19/0.39 % SZS output end Proof
%------------------------------------------------------------------------------