%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM850+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 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM850+2 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 02:02:09 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(vplus_type, type, (
% 0.13/0.39 vplus: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_Vd196_1_type, type, (
% 0.13/0.39 tptp_fun_Vd196_1: ( $i * $i ) > $i)).
% 0.13/0.39 tff(vd471_type, type, (
% 0.13/0.39 vd471: $i)).
% 0.13/0.39 tff(vd470_type, type, (
% 0.13/0.39 vd470: $i)).
% 0.13/0.39 tff(greater_type, type, (
% 0.13/0.39 greater: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[Vd193: $i, Vd194: $i] : refl((~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> ![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (^[Vd193: $i, Vd194: $i] : rewrite((~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> ![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))) <=> ![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (^[Vd193: $i, Vd194: $i] : trans(monotonicity(rewrite((greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))) <=> (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))), ((((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))) <=> (((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))))), rewrite((((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))) <=> (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))), ((((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))) <=> (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![Vd193: $i, Vd194: $i] : (((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196))))) <=> ![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196))) <=> ![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(9,axiom,(![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''def(cond(conseq(axiom(3)), 11), 1)'')).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (![Vd193: $i, Vd194: $i] : (greater(Vd194, Vd193) <=> ?[Vd196: $i] : (Vd194 = vplus(Vd193, Vd196)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.13/0.39 tff(11,plain,(
% 0.13/0.39 ![Vd193: $i, Vd194: $i] : (((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193)))) & (greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 ((~![Vd193: $i, Vd194: $i] : (~((~((~greater(Vd194, Vd193)) | (Vd194 = vplus(Vd193, tptp_fun_Vd196_1(Vd194, Vd193))))) | (~(greater(Vd194, Vd193) | ![Vd196: $i] : (~(Vd194 = vplus(Vd193, Vd196)))))))) | (~((~((~greater(vd470, vd471)) | (vd470 = vplus(vd471, tptp_fun_Vd196_1(vd470, vd471))))) | (~(greater(vd470, vd471) | ![Vd196: $i] : (~(vd470 = vplus(vd471, Vd196)))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (~((~((~greater(vd470, vd471)) | (vd470 = vplus(vd471, tptp_fun_Vd196_1(vd470, vd471))))) | (~(greater(vd470, vd471) | ![Vd196: $i] : (~(vd470 = vplus(vd471, Vd196))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (((~((~greater(vd470, vd471)) | (vd470 = vplus(vd471, tptp_fun_Vd196_1(vd470, vd471))))) | (~(greater(vd470, vd471) | ![Vd196: $i] : (~(vd470 = vplus(vd471, Vd196)))))) | ((~greater(vd470, vd471)) | (vd470 = vplus(vd471, tptp_fun_Vd196_1(vd470, vd471))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 ((~greater(vd470, vd471)) | (vd470 = vplus(vd471, tptp_fun_Vd196_1(vd470, vd471)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (greater(vd470, vd471) <=> greater(vd470, vd471)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(19,axiom,(greater(vd470, vd471)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(antec(302), 472, 0)'')).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (greater(vd470, vd471)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((~((~greater(vd470, vd471)) | (vd470 = vplus(vd471, tptp_fun_Vd196_1(vd470, vd471))))) | (~greater(vd470, vd471)) | (vd470 = vplus(vd471, tptp_fun_Vd196_1(vd470, vd471)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ((~((~greater(vd470, vd471)) | (vd470 = vplus(vd471, tptp_fun_Vd196_1(vd470, vd471))))) | (vd470 = vplus(vd471, tptp_fun_Vd196_1(vd470, vd471)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (vd470 = vplus(vd471, tptp_fun_Vd196_1(vd470, vd471))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[22, 17])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (^[Vd473: $i] : refl((~(vd470 = vplus(vd471, Vd473))) <=> (~(vd470 = vplus(vd471, Vd473))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![Vd473: $i] : (~(vd470 = vplus(vd471, Vd473))) <=> ![Vd473: $i] : (~(vd470 = vplus(vd471, Vd473)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~?[Vd473: $i] : (vd470 = vplus(vd471, Vd473))) <=> (~?[Vd473: $i] : (vd470 = vplus(vd471, Vd473)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(27,axiom,(~?[Vd473: $i] : (vd470 = vplus(vd471, Vd473))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''qe(conseq_conjunct1(conseq(302)))'')).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (~?[Vd473: $i] : (vd470 = vplus(vd471, Vd473))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (~?[Vd473: $i] : (vd470 = vplus(vd471, Vd473))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 26])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (~?[Vd473: $i] : (vd470 = vplus(vd471, Vd473))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (~?[Vd473: $i] : (vd470 = vplus(vd471, Vd473))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (^[Vd473: $i] : refl($oeq((~(vd470 = vplus(vd471, Vd473))), (~(vd470 = vplus(vd471, Vd473)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(33,plain,(
% 0.13/0.39 ![Vd473: $i] : (~(vd470 = vplus(vd471, Vd473)))),
% 0.13/0.39 inference(nnf-neg,[status(sab)],[31, 32])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![Vd473: $i] : (~(vd470 = vplus(vd471, Vd473)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 ((~![Vd473: $i] : (~(vd470 = vplus(vd471, Vd473)))) | (~(vd470 = vplus(vd471, tptp_fun_Vd196_1(vd470, vd471))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[35, 34, 23])).
% 0.13/0.39 % SZS output end Proof
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------