TSTP Solution File: NUM847+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.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 : Fri Sep 2 15:23:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -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(vplus_type, type, (
% 0.20/0.39 vplus: ( $i * $i ) > $i)).
% 0.20/0.39 tff(vd436_type, type, (
% 0.20/0.39 vd436: $i)).
% 0.20/0.39 tff(vmul_type, type, (
% 0.20/0.39 vmul: ( $i * $i ) > $i)).
% 0.20/0.39 tff(vd439_type, type, (
% 0.20/0.39 vd439: $i)).
% 0.20/0.39 tff(vd437_type, type, (
% 0.20/0.39 vd437: $i)).
% 0.20/0.39 tff(vsucc_type, type, (
% 0.20/0.39 vsucc: $i > $i)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[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))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 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)'')).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.39 tff(6,plain,(
% 0.20/0.39 ![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[5])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![Vd46: $i, Vd47: $i, Vd48: $i] : (vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 ((~![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)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 ((vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439))) <=> (vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 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)'')).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 ((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))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 ((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))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(16,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)'')).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vplus(vd437, vd439)), vd436)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))),
% 0.20/0.39 inference(transitivity,[status(thm)],[18, 13, 9])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 ((~(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))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 ((~(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))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 ((~(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))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(23,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)'')).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (~(vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (~(vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (~(vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[26, 19])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------