%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM851+1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.14s 0.42s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM851+1 : TPTP v9.0.0. Released v4.1.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 02:01:10 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.42 % SZS status Theorem
% 0.14/0.42 % SZS output start Proof
% 0.14/0.42 tff(vplus_type, type, (
% 0.14/0.42 vplus: ( $i * $i ) > $i)).
% 0.14/0.42 tff(vmul_type, type, (
% 0.14/0.42 vmul: ( $i * $i ) > $i)).
% 0.14/0.42 tff(vd469_type, type, (
% 0.14/0.42 vd469: $i)).
% 0.14/0.42 tff(vd473_type, type, (
% 0.14/0.42 vd473: $i)).
% 0.14/0.42 tff(vd471_type, type, (
% 0.14/0.42 vd471: $i)).
% 0.14/0.42 tff(1,plain,
% 0.14/0.42 (^[Vd418: $i, Vd419: $i] : refl((vmul(Vd418, Vd419) = vmul(Vd419, Vd418)) <=> (vmul(Vd418, Vd419) = vmul(Vd419, Vd418)))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(2,plain,
% 0.14/0.42 (![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418)) <=> ![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.42 tff(3,plain,
% 0.14/0.42 (![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418)) <=> ![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(4,axiom,(![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(270, 0), 0)'')).
% 0.14/0.42 tff(5,plain,
% 0.14/0.42 (![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.42 tff(6,plain,(
% 0.14/0.42 ![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))),
% 0.14/0.42 inference(skolemize,[status(sab)],[5])).
% 0.14/0.42 tff(7,plain,
% 0.14/0.42 (![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.42 tff(8,plain,
% 0.14/0.42 ((~![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))) | (vmul(vd469, vd473) = vmul(vd473, vd469))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(9,plain,
% 0.14/0.42 (vmul(vd469, vd473) = vmul(vd473, vd469)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.42 tff(10,plain,
% 0.14/0.42 ((~![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))) | (vmul(vd469, vd471) = vmul(vd471, vd469))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(11,plain,
% 0.14/0.42 (vmul(vd469, vd471) = vmul(vd471, vd469)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.14/0.42 tff(12,plain,
% 0.14/0.42 (vplus(vmul(vd469, vd471), vmul(vd469, vd473)) = vplus(vmul(vd471, vd469), vmul(vd473, vd469))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[11, 9])).
% 0.14/0.42 tff(13,plain,
% 0.14/0.42 (^[Vd432: $i, Vd433: $i, Vd434: $i] : refl((vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434))) <=> (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(14,plain,
% 0.14/0.42 (![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434))) <=> ![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.14/0.42 tff(15,plain,
% 0.14/0.42 (![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434))) <=> ![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(16,axiom,(![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(281, 0), 0)'')).
% 0.14/0.42 tff(17,plain,
% 0.14/0.42 (![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.14/0.42 tff(18,plain,(
% 0.14/0.42 ![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))),
% 0.14/0.42 inference(skolemize,[status(sab)],[17])).
% 0.14/0.42 tff(19,plain,
% 0.14/0.42 (![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.14/0.42 tff(20,plain,
% 0.14/0.42 ((~![Vd432: $i, Vd433: $i, Vd434: $i] : (vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)))) | (vmul(vd469, vplus(vd471, vd473)) = vplus(vmul(vd469, vd471), vmul(vd469, vd473)))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(21,plain,
% 0.14/0.42 (vmul(vd469, vplus(vd471, vd473)) = vplus(vmul(vd469, vd471), vmul(vd469, vd473))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.14/0.42 tff(22,plain,
% 0.14/0.42 ((~![Vd418: $i, Vd419: $i] : (vmul(Vd418, Vd419) = vmul(Vd419, Vd418))) | (vmul(vd469, vplus(vd471, vd473)) = vmul(vplus(vd471, vd473), vd469))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(23,plain,
% 0.14/0.42 (vmul(vd469, vplus(vd471, vd473)) = vmul(vplus(vd471, vd473), vd469)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[22, 7])).
% 0.14/0.42 tff(24,plain,
% 0.14/0.42 (vmul(vplus(vd471, vd473), vd469) = vmul(vd469, vplus(vd471, vd473))),
% 0.14/0.42 inference(symmetry,[status(thm)],[23])).
% 0.14/0.42 tff(25,plain,
% 0.14/0.42 (vmul(vplus(vd471, vd473), vd469) = vplus(vmul(vd471, vd469), vmul(vd473, vd469))),
% 0.14/0.42 inference(transitivity,[status(thm)],[24, 21, 12])).
% 0.14/0.42 tff(26,plain,
% 0.14/0.42 ((~(vmul(vplus(vd471, vd473), vd469) = vplus(vmul(vd471, vd469), vmul(vd473, vd469)))) <=> (~(vmul(vplus(vd471, vd473), vd469) = vplus(vmul(vd471, vd469), vmul(vd473, vd469))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(27,axiom,(~(vmul(vplus(vd471, vd473), vd469) = vplus(vmul(vd471, vd469), vmul(vd473, vd469)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(conseq_conjunct2(conseq(302)), 475, 1)'')).
% 0.14/0.42 tff(28,plain,
% 0.14/0.42 (~(vmul(vplus(vd471, vd473), vd469) = vplus(vmul(vd471, vd469), vmul(vd473, vd469)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.14/0.42 tff(29,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.14/0.42 % SZS output end Proof
% 0.14/0.42 % E exiting
%------------------------------------------------------------------------------