TSTP Solution File: NUM847+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM847+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Sun Sep 18 13:12:15 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM847+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 15:23:31 EDT 2022
% 0.13/0.35 % 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.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(vplus_type, type, (
% 0.20/0.42 vplus: ( $i * $i ) > $i)).
% 0.20/0.42 tff(vd436_type, type, (
% 0.20/0.42 vd436: $i)).
% 0.20/0.42 tff(vmul_type, type, (
% 0.20/0.42 vmul: ( $i * $i ) > $i)).
% 0.20/0.42 tff(vd439_type, type, (
% 0.20/0.42 vd439: $i)).
% 0.20/0.42 tff(vd437_type, type, (
% 0.20/0.42 vd437: $i)).
% 0.20/0.42 tff(vsucc_type, type, (
% 0.20/0.42 vsucc: $i > $i)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 (^[Vd46: $i, Vd47: $i, Vd48: $i] : refl((vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48))) <=> (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48))) <=> ![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48))) <=> ![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(4,axiom,(![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(33, 0), 0)'')).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.42 tff(6,plain,(
% 0.20/0.42 ![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[5])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 ((~![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))) | (vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 ((vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439))) <=> (vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(11,axiom,(vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(285, 440, 0)'')).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (vplus(vmul(vd436, vd437), vmul(vd436, vd439)) = vmul(vd436, vplus(vd437, vd439))),
% 0.20/0.42 inference(symmetry,[status(thm)],[12])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vplus(vd437, vd439)), vd436)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[13])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436)),
% 0.20/0.42 inference(symmetry,[status(thm)],[14])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 ((vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436)) <=> (vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vplus(vd437, vd439)), vd436))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 ((vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436)) <=> (vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(18,axiom,(vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(286, 441, 2)'')).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vplus(vd437, vd439)), vd436)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))),
% 0.20/0.42 inference(transitivity,[status(thm)],[20, 15, 9])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 ((~(vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))) <=> (~(vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ((~(vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))) <=> (~(vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 ((~(vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))) <=> (~(vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(25,axiom,(~(vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(286, 441, 3)'')).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (~(vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (~(vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (~(vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[28, 21])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------