%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM848+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:22:13 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM848+2 : TPTP v9.0.0. Released v4.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:01:54 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(vplus_type, type, (
% 0.19/0.37 vplus: ( $i * $i ) > $i)).
% 0.19/0.37 tff(vmul_type, type, (
% 0.19/0.37 vmul: ( $i * $i ) > $i)).
% 0.19/0.37 tff(vsucc_type, type, (
% 0.19/0.37 vsucc: $i > $i)).
% 0.19/0.37 tff(vd439_type, type, (
% 0.19/0.37 vd439: $i)).
% 0.19/0.37 tff(vd436_type, type, (
% 0.19/0.37 vd436: $i)).
% 0.19/0.37 tff(vd437_type, type, (
% 0.19/0.37 vd437: $i)).
% 0.19/0.37 tff(v1_type, type, (
% 0.19/0.37 v1: $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[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)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![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))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (^[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)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (![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))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![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))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(6,axiom,(![Vd396: $i, Vd397: $i] : ((vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396)) & (vmul(Vd396, v1) = Vd396))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))'')).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![Vd396: $i, Vd397: $i] : ((vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396)) & (vmul(Vd396, v1) = Vd396))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.37 tff(8,plain,(
% 0.19/0.37 ![Vd396: $i, Vd397: $i] : ((vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396)) & (vmul(Vd396, v1) = Vd396))),
% 0.19/0.37 inference(skolemize,[status(sab)],[7])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (![Vd396: $i, Vd397: $i] : (~((~(vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396))) | (~(vmul(Vd396, v1) = Vd396))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (![Vd396: $i, Vd397: $i] : (~((~(vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396))) | (~(vmul(Vd396, v1) = Vd396))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 ((~![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))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (~((~(vmul(vd436, vsucc(vd439)) = vplus(vmul(vd436, vd439), vd436))) | (~(vmul(vd436, v1) = vd436)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (((~(vmul(vd436, vsucc(vd439)) = vplus(vmul(vd436, vd439), vd436))) | (~(vmul(vd436, v1) = vd436))) | (vmul(vd436, vsucc(vd439)) = vplus(vmul(vd436, vd439), vd436))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (vmul(vd436, vsucc(vd439)) = vplus(vmul(vd436, vd439), vd436)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))) = vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439)))),
% 0.19/0.38 inference(symmetry,[status(thm)],[15])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 ((~(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)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(18,axiom,(~(vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(286, 441, 4)'')).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (~(vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[19, 16])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------