%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM854+2 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:22:14 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
% 0.00/0.12 % Problem : NUM854+2 : TPTP v9.0.0. Released v4.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 02:03:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(greater_type, type, (
% 0.19/0.37 greater: ( $i * $i ) > $o)).
% 0.19/0.37 tff(vmul_type, type, (
% 0.19/0.37 vmul: ( $i * $i ) > $i)).
% 0.19/0.37 tff(vd509_type, type, (
% 0.19/0.37 vd509: $i)).
% 0.19/0.37 tff(vd508_type, type, (
% 0.19/0.37 vd508: $i)).
% 0.19/0.37 tff(vd511_type, type, (
% 0.19/0.37 vd511: $i)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[Vd456: $i, Vd457: $i, Vd458: $i] : refl(((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (^[Vd456: $i, Vd457: $i, Vd458: $i] : rewrite((greater(Vd457, Vd458) => greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![Vd456: $i, Vd457: $i, Vd458: $i] : (greater(Vd457, Vd458) => greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456))) <=> ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.37 tff(6,axiom,(![Vd456: $i, Vd457: $i, Vd458: $i] : (greater(Vd457, Vd458) => greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(299, 0), 2)'')).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.37 tff(9,plain,(
% 0.19/0.37 ![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[8])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (greater(vd508, vd509) <=> greater(vd508, vd509)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(12,axiom,(greater(vd508, vd509)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conjunct1(314), 510, 0)'')).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (greater(vd508, vd509)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 ((~greater(vmul(vd508, vd511), vmul(vd509, vd511))) <=> (~greater(vmul(vd508, vd511), vmul(vd509, vd511)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(15,axiom,(~greater(vmul(vd508, vd511), vmul(vd509, vd511))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conjunct1(315), 514, 0)'')).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (~greater(vmul(vd508, vd511), vmul(vd509, vd511))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | ((~greater(vd508, vd509)) | greater(vmul(vd508, vd511), vmul(vd509, vd511)))) <=> ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | (~greater(vd508, vd509)) | greater(vmul(vd508, vd511), vmul(vd509, vd511)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | ((~greater(vd508, vd509)) | greater(vmul(vd508, vd511), vmul(vd509, vd511)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 ((~![Vd456: $i, Vd457: $i, Vd458: $i] : ((~greater(Vd457, Vd458)) | greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))) | (~greater(vd508, vd509)) | greater(vmul(vd508, vd511), vmul(vd509, vd511))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[19, 16, 13, 10])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------