TSTP Solution File: NUM848+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM848+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM848+2 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 15:21:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(vplus_type, type, (
% 0.19/0.39 vplus: ( $i * $i ) > $i)).
% 0.19/0.39 tff(vmul_type, type, (
% 0.19/0.39 vmul: ( $i * $i ) > $i)).
% 0.19/0.39 tff(vsucc_type, type, (
% 0.19/0.39 vsucc: $i > $i)).
% 0.19/0.39 tff(vd439_type, type, (
% 0.19/0.39 vd439: $i)).
% 0.19/0.39 tff(vd436_type, type, (
% 0.19/0.39 vd436: $i)).
% 0.19/0.39 tff(vd437_type, type, (
% 0.19/0.39 vd437: $i)).
% 0.19/0.39 tff(v1_type, type, (
% 0.19/0.39 v1: $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[Vd396: $i, Vd397: $i] : refl((~((~(vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396))) | (~(vmul(Vd396, v1) = Vd396)))) <=> (~((~(vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396))) | (~(vmul(Vd396, v1) = Vd396)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![Vd396: $i, Vd397: $i] : (~((~(vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396))) | (~(vmul(Vd396, v1) = Vd396)))) <=> ![Vd396: $i, Vd397: $i] : (~((~(vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396))) | (~(vmul(Vd396, v1) = Vd396))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[Vd396: $i, Vd397: $i] : rewrite(((vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396)) & (vmul(Vd396, v1) = Vd396)) <=> (~((~(vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396))) | (~(vmul(Vd396, v1) = Vd396)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![Vd396: $i, Vd397: $i] : ((vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396)) & (vmul(Vd396, v1) = Vd396)) <=> ![Vd396: $i, Vd397: $i] : (~((~(vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396))) | (~(vmul(Vd396, v1) = Vd396))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![Vd396: $i, Vd397: $i] : ((vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396)) & (vmul(Vd396, v1) = Vd396)) <=> ![Vd396: $i, Vd397: $i] : ((vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396)) & (vmul(Vd396, v1) = Vd396))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(6,axiom,(![Vd396: $i, Vd397: $i] : ((vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396)) & (vmul(Vd396, v1) = Vd396))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))'')).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![Vd396: $i, Vd397: $i] : ((vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396)) & (vmul(Vd396, v1) = Vd396))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.39 tff(8,plain,(
% 0.19/0.39 ![Vd396: $i, Vd397: $i] : ((vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396)) & (vmul(Vd396, v1) = Vd396))),
% 0.19/0.39 inference(skolemize,[status(sab)],[7])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![Vd396: $i, Vd397: $i] : (~((~(vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396))) | (~(vmul(Vd396, v1) = Vd396))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![Vd396: $i, Vd397: $i] : (~((~(vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396))) | (~(vmul(Vd396, v1) = Vd396))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ((~![Vd396: $i, Vd397: $i] : (~((~(vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396))) | (~(vmul(Vd396, v1) = Vd396))))) | (~((~(vmul(vd436, vsucc(vd439)) = vplus(vmul(vd436, vd439), vd436))) | (~(vmul(vd436, v1) = vd436))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (~((~(vmul(vd436, vsucc(vd439)) = vplus(vmul(vd436, vd439), vd436))) | (~(vmul(vd436, v1) = vd436)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (((~(vmul(vd436, vsucc(vd439)) = vplus(vmul(vd436, vd439), vd436))) | (~(vmul(vd436, v1) = vd436))) | (vmul(vd436, vsucc(vd439)) = vplus(vmul(vd436, vd439), vd436))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (vmul(vd436, vsucc(vd439)) = vplus(vmul(vd436, vd439), vd436)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439)))),
% 0.19/0.39 inference(symmetry,[status(thm)],[15])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 ((vmul(vd436, vsucc(vplus(vd437, vd439))) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))) <=> (vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((vmul(vd436, vsucc(vplus(vd437, vd439))) = vplus(vmul(vd436, vplus(vd437, vd439)), vd436)) <=> (vmul(vd436, vsucc(vplus(vd437, vd439))) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 ((vmul(vd436, vsucc(vplus(vd437, vd439))) = vplus(vmul(vd436, vplus(vd437, vd439)), vd436)) <=> (vmul(vd436, vsucc(vplus(vd437, vd439))) = vplus(vmul(vd436, vplus(vd437, vd439)), vd436))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(20,axiom,(vmul(vd436, vsucc(vplus(vd437, vd439))) = vplus(vmul(vd436, vplus(vd437, vd439)), vd436)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(286, 441, 1)'')).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (vmul(vd436, vsucc(vplus(vd437, vd439))) = vplus(vmul(vd436, vplus(vd437, vd439)), vd436)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (vmul(vd436, vsucc(vplus(vd437, vd439))) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[23, 16])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ((~(vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))))) <=> (~(vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 ((~(vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))))) <=> (~(vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(27,axiom,(~(vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(286, 441, 4)'')).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (~(vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (~(vmul(vd436, vplus(vd437, vsucc(vd439))) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[29, 24])).
% 0.19/0.39 % SZS output end Proof
%------------------------------------------------------------------------------