%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM844+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:22:12 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM844+2 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 02:01:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(vplus_type, type, (
% 0.11/0.37 vplus: ( $i * $i ) > $i)).
% 0.11/0.37 tff(vd413_type, type, (
% 0.11/0.37 vd413: $i)).
% 0.11/0.37 tff(vsucc_type, type, (
% 0.11/0.37 vsucc: $i > $i)).
% 0.11/0.37 tff(vd411_type, type, (
% 0.11/0.37 vd411: $i)).
% 0.11/0.37 tff(vmul_type, type, (
% 0.11/0.37 vmul: ( $i * $i ) > $i)).
% 0.11/0.37 tff(v1_type, type, (
% 0.11/0.37 v1: $i)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 ((vsucc(vmul(vd411, v1)) = vplus(vmul(vd411, v1), v1)) <=> (vsucc(vmul(vd411, v1)) = vplus(vmul(vd411, v1), v1))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(2,axiom,(vsucc(vmul(vd411, v1)) = vplus(vmul(vd411, v1), v1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(264, 412, 2)'')).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (vsucc(vmul(vd411, v1)) = vplus(vmul(vd411, v1), v1)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 ((vsucc(vd411) = vsucc(vmul(vd411, v1))) <=> (vsucc(vd411) = vsucc(vmul(vd411, v1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(5,axiom,(vsucc(vd411) = vsucc(vmul(vd411, v1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(264, 412, 1)'')).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (vsucc(vd411) = vsucc(vmul(vd411, v1))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (vsucc(vd411) = vplus(vmul(vd411, v1), v1)),
% 0.11/0.37 inference(transitivity,[status(thm)],[6, 3])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (vplus(vsucc(vd411), vd413) = vplus(vplus(vmul(vd411, v1), v1), vd413)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[7])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413)) = vplus(vmul(vd411, vd413), vplus(vplus(vmul(vd411, v1), v1), vd413))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[8])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (vplus(vmul(vd411, vd413), vplus(vplus(vmul(vd411, v1), v1), vd413)) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413))),
% 0.11/0.37 inference(symmetry,[status(thm)],[9])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (vplus(vd413, vsucc(vd411)) = vplus(vd413, vplus(vmul(vd411, v1), v1))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[7])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (vplus(vd413, vplus(vmul(vd411, v1), v1)) = vplus(vd413, vsucc(vd411))),
% 0.11/0.37 inference(symmetry,[status(thm)],[11])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (^[Vd78: $i, Vd79: $i] : refl((vplus(Vd79, Vd78) = vplus(Vd78, Vd79)) <=> (vplus(Vd79, Vd78) = vplus(Vd78, Vd79)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79)) <=> ![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79)) <=> ![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(16,axiom,(![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''ass(cond(61, 0), 0)'')).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.37 tff(18,plain,(
% 0.11/0.37 ![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.11/0.37 inference(skolemize,[status(sab)],[17])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((~![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))) | (vplus(vplus(vmul(vd411, v1), v1), vd413) = vplus(vd413, vplus(vmul(vd411, v1), v1)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (vplus(vplus(vmul(vd411, v1), v1), vd413) = vplus(vd413, vplus(vmul(vd411, v1), v1))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (vplus(vplus(vmul(vd411, v1), v1), vd413) = vplus(vd413, vsucc(vd411))),
% 0.11/0.37 inference(transitivity,[status(thm)],[21, 12])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (vplus(vmul(vd411, vd413), vplus(vplus(vmul(vd411, v1), v1), vd413)) = vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[22])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))) = vplus(vmul(vd411, vd413), vplus(vplus(vmul(vd411, v1), v1), vd413))),
% 0.11/0.37 inference(symmetry,[status(thm)],[23])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413))),
% 0.11/0.37 inference(transitivity,[status(thm)],[24, 10])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 ((~(vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413)))) <=> (~(vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(27,axiom,(~(vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''holds(266, 415, 3)'')).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (~(vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------