%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM840+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:22:11 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
% 0.07/0.12 % Problem : NUM840+2 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n002.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 02:03:16 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(greater_type, type, (
% 0.11/0.37 greater: ( $i * $i ) > $o)).
% 0.11/0.37 tff(vplus_type, type, (
% 0.11/0.37 vplus: ( $i * $i ) > $i)).
% 0.11/0.37 tff(vd330_type, type, (
% 0.11/0.37 vd330: $i)).
% 0.11/0.37 tff(vd328_type, type, (
% 0.11/0.37 vd328: $i)).
% 0.11/0.37 tff(vd329_type, type, (
% 0.11/0.37 vd329: $i)).
% 0.11/0.37 tff(less_type, type, (
% 0.11/0.37 less: ( $i * $i ) > $o)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[Vd203: $i, Vd204: $i] : refl(((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204))) <=> ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(4,axiom,(![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(goal(130), 0), 2)'')).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.37 tff(6,plain,(
% 0.11/0.37 ![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[5])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (less(vplus(vd328, vd330), vplus(vd329, vd330)) <=> less(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(9,axiom,(less(vplus(vd328, vd330), vplus(vd329, vd330))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(antec(conjunct2(conjunct2(204))), 335, 0)'')).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (less(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | ((~greater(vplus(vd328, vd330), vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330))))) <=> ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | (~greater(vplus(vd328, vd330), vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | ((~greater(vplus(vd328, vd330), vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 ((~![Vd203: $i, Vd204: $i] : ((~greater(Vd203, Vd204)) | (~less(Vd203, Vd204)))) | (~greater(vplus(vd328, vd330), vplus(vd329, vd330))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (~greater(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[13, 10, 7])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (^[Vd301: $i, Vd302: $i, Vd303: $i] : refl(((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (^[Vd301: $i, Vd302: $i, Vd303: $i] : rewrite((greater(Vd301, Vd302) => greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (![Vd301: $i, Vd302: $i, Vd303: $i] : (greater(Vd301, Vd302) => greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303))) <=> ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.11/0.38 tff(20,axiom,(![Vd301: $i, Vd302: $i, Vd303: $i] : (greater(Vd301, Vd302) => greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(goal(193), 0), 2)'')).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.11/0.38 tff(23,plain,(
% 0.11/0.38 ![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[22])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | ((~greater(vd328, vd329)) | greater(vplus(vd328, vd330), vplus(vd329, vd330)))) <=> ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | (~greater(vd328, vd329)) | greater(vplus(vd328, vd330), vplus(vd329, vd330)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | ((~greater(vd328, vd329)) | greater(vplus(vd328, vd330), vplus(vd329, vd330)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 ((~![Vd301: $i, Vd302: $i, Vd303: $i] : ((~greater(Vd301, Vd302)) | greater(vplus(Vd301, Vd303), vplus(Vd302, Vd303)))) | (~greater(vd328, vd329)) | greater(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 ((~greater(vd328, vd329)) | greater(vplus(vd328, vd330), vplus(vd329, vd330))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (~greater(vd328, vd329)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[28, 14])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (^[Vd203: $i, Vd204: $i] : refl((less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)) <=> (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (^[Vd203: $i, Vd204: $i] : rewrite((((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204)) <=> (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 (![Vd203: $i, Vd204: $i] : (((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204)) <=> ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.11/0.38 tff(35,axiom,(![Vd203: $i, Vd204: $i] : (((Vd203 = Vd204) | greater(Vd203, Vd204)) | less(Vd203, Vd204))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(goal(130), 0), 0)'')).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.11/0.38 tff(38,plain,(
% 0.11/0.38 ![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.11/0.38 inference(skolemize,[status(sab)],[37])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 ((~less(vd328, vd329)) <=> (~less(vd328, vd329))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(41,axiom,(~less(vd328, vd329)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conseq(conjunct2(conjunct2(204))), 336, 0)'')).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (~less(vd328, vd329)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | (less(vd328, vd329) | (vd328 = vd329) | greater(vd328, vd329))) <=> ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | less(vd328, vd329) | (vd328 = vd329) | greater(vd328, vd329))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 ((less(vd328, vd329) | greater(vd328, vd329) | (vd328 = vd329)) <=> (less(vd328, vd329) | (vd328 = vd329) | greater(vd328, vd329))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | (less(vd328, vd329) | greater(vd328, vd329) | (vd328 = vd329))) <=> ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | (less(vd328, vd329) | (vd328 = vd329) | greater(vd328, vd329)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[44])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | (less(vd328, vd329) | greater(vd328, vd329) | (vd328 = vd329))) <=> ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | less(vd328, vd329) | (vd328 = vd329) | greater(vd328, vd329))),
% 0.11/0.38 inference(transitivity,[status(thm)],[45, 43])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | (less(vd328, vd329) | greater(vd328, vd329) | (vd328 = vd329))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 ((~![Vd203: $i, Vd204: $i] : (less(Vd203, Vd204) | greater(Vd203, Vd204) | (Vd203 = Vd204))) | less(vd328, vd329) | (vd328 = vd329) | greater(vd328, vd329)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 ((vd328 = vd329) | greater(vd328, vd329)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[48, 42, 39])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (vd328 = vd329),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[49, 29])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (vplus(vd328, vd330) = vplus(vd329, vd330)),
% 0.11/0.38 inference(monotonicity,[status(thm)],[50])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (greater(vplus(vd329, vd330), vplus(vd328, vd330)) <=> greater(vplus(vd329, vd330), vplus(vd329, vd330))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[51])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (greater(vplus(vd329, vd330), vplus(vd329, vd330)) <=> greater(vplus(vd329, vd330), vplus(vd328, vd330))),
% 0.11/0.38 inference(symmetry,[status(thm)],[52])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 ((~greater(vplus(vd329, vd330), vplus(vd329, vd330))) <=> (~greater(vplus(vd329, vd330), vplus(vd328, vd330)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[53])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 (greater(vplus(vd328, vd330), vplus(vd329, vd330)) <=> greater(vplus(vd329, vd330), vplus(vd329, vd330))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[51])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 ((~greater(vplus(vd328, vd330), vplus(vd329, vd330))) <=> (~greater(vplus(vd329, vd330), vplus(vd329, vd330)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[55])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (~greater(vplus(vd329, vd330), vplus(vd329, vd330))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[14, 56])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 (~greater(vplus(vd329, vd330), vplus(vd328, vd330))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 (^[Vd226: $i, Vd227: $i] : refl(((~less(Vd226, Vd227)) | greater(Vd227, Vd226)) <=> ((~less(Vd226, Vd227)) | greater(Vd227, Vd226)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226)) <=> ![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[59])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226)) <=> ![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (^[Vd226: $i, Vd227: $i] : rewrite((less(Vd226, Vd227) => greater(Vd227, Vd226)) <=> ((~less(Vd226, Vd227)) | greater(Vd227, Vd226)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (![Vd226: $i, Vd227: $i] : (less(Vd226, Vd227) => greater(Vd227, Vd226)) <=> ![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[62])).
% 0.11/0.38 tff(64,axiom,(![Vd226: $i, Vd227: $i] : (less(Vd226, Vd227) => greater(Vd227, Vd226))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(147, 0), 0)'')).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.11/0.38 tff(67,plain,(
% 0.11/0.38 ![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.11/0.38 inference(skolemize,[status(sab)],[66])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (((~![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))) | ((~less(vplus(vd328, vd330), vplus(vd329, vd330))) | greater(vplus(vd329, vd330), vplus(vd328, vd330)))) <=> ((~![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330))) | greater(vplus(vd329, vd330), vplus(vd328, vd330)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 ((~![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))) | ((~less(vplus(vd328, vd330), vplus(vd329, vd330))) | greater(vplus(vd329, vd330), vplus(vd328, vd330)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 ((~![Vd226: $i, Vd227: $i] : ((~less(Vd226, Vd227)) | greater(Vd227, Vd226))) | (~less(vplus(vd328, vd330), vplus(vd329, vd330))) | greater(vplus(vd329, vd330), vplus(vd328, vd330))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 (greater(vplus(vd329, vd330), vplus(vd328, vd330))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[71, 10, 68])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[72, 58])).
% 0.11/0.38 % SZS output end Proof
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------