TSTP Solution File: KLE003+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE003+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE003+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 07:45:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(one_type, type, (
% 0.20/0.39 one: $i)).
% 0.20/0.39 tff(addition_type, type, (
% 0.20/0.39 addition: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_X0_0_type, type, (
% 0.20/0.39 tptp_fun_X0_0: $i)).
% 0.20/0.39 tff(1,assumption,(~(addition(X0!0, X0!0) = X0!0)), introduced(assumption)).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.20/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(5,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (![A: $i] : (addition(A, A) = A)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.39 tff(7,plain,(
% 0.20/0.39 ![A: $i] : (addition(A, A) = A)),
% 0.20/0.39 inference(skolemize,[status(sab)],[6])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (![A: $i] : (addition(A, A) = A)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!0, X0!0) = X0!0)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.39 tff(11,plain,(addition(X0!0, X0!0) = X0!0), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (((![X0: $i] : (addition(X0, X0) = X0) | (addition(one, one) = one)) & ((~(addition(X0!0, X0!0) = X0!0)) | (~(addition(one, one) = one)))) <=> (((addition(one, one) = one) | ![X0: $i] : (addition(X0, X0) = X0)) & ((~(addition(X0!0, X0!0) = X0!0)) | (~(addition(one, one) = one))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 ((~![X0: $i] : (addition(X0, X0) = X0)) <=> (~![X0: $i] : (addition(X0, X0) = X0))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one)) <=> ((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[13])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one)) <=> ((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 ((~(![X0: $i] : (addition(X0, X0) = X0) <=> (addition(one, one) = one))) <=> ((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 ((![X0: $i] : (addition(X0, X0) = X0) <=> (addition(one, one) = one)) <=> (![X0: $i] : (addition(X0, X0) = X0) <=> (addition(one, one) = one))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 ((~(![X0: $i] : (addition(X0, X0) = X0) <=> (addition(one, one) = one))) <=> (~(![X0: $i] : (addition(X0, X0) = X0) <=> (addition(one, one) = one)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 ((~(![X0: $i] : (addition(X0, X0) = X0) <=> (addition(one, one) = one))) <=> ((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one))),
% 0.20/0.39 inference(transitivity,[status(thm)],[18, 16])).
% 0.20/0.39 tff(20,axiom,(~(![X0: $i] : (addition(X0, X0) = X0) <=> (addition(one, one) = one))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 ((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 ((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 ((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[23, 14])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 ((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 ((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 14])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 ((~![X0: $i] : (addition(X0, X0) = X0)) <=> (addition(one, one) = one)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[26, 14])).
% 0.20/0.39 tff(28,plain,(
% 0.20/0.39 (![X0: $i] : (addition(X0, X0) = X0) | (addition(one, one) = one)) & ((~(addition(X0!0, X0!0) = X0!0)) | (~(addition(one, one) = one)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[27])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (((addition(one, one) = one) | ![X0: $i] : (addition(X0, X0) = X0)) & ((~(addition(X0!0, X0!0) = X0!0)) | (~(addition(one, one) = one)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[28, 12])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((~(addition(X0!0, X0!0) = X0!0)) | (~(addition(one, one) = one))),
% 0.20/0.39 inference(and_elim,[status(thm)],[29])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (~(addition(one, one) = one)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[30, 11])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[32, 8, 31])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------