%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM837+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 05:22:10 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM837+2 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % 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 02:01:39 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(vplus_type, type, (
% 0.19/0.38 vplus: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_Vd201_0_type, type, (
% 0.19/0.38 tptp_fun_Vd201_0: ( $i * $i ) > $i)).
% 0.19/0.38 tff(vd269_type, type, (
% 0.19/0.38 vd269: $i)).
% 0.19/0.38 tff(vd268_type, type, (
% 0.19/0.38 vd268: $i)).
% 0.19/0.38 tff(less_type, type, (
% 0.19/0.38 less: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[Vd198: $i, Vd199: $i] : refl((~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))))) <=> (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![Vd198: $i, Vd199: $i] : (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))))) <=> ![Vd198: $i, Vd199: $i] : (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (^[Vd198: $i, Vd199: $i] : rewrite((~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))))) <=> (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![Vd198: $i, Vd199: $i] : (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))))) <=> ![Vd198: $i, Vd199: $i] : (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![Vd198: $i, Vd199: $i] : (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))))) <=> ![Vd198: $i, Vd199: $i] : (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201)))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (^[Vd198: $i, Vd199: $i] : trans(monotonicity(rewrite((less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201)))) <=> (less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))), ((((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198)))) & (less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))) <=> (((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198)))) & (less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))))), rewrite((((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198)))) & (less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))) <=> (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201)))))))), ((((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198)))) & (less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))) <=> (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201)))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![Vd198: $i, Vd199: $i] : (((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198)))) & (less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201))))) <=> ![Vd198: $i, Vd199: $i] : (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![Vd198: $i, Vd199: $i] : (less(Vd199, Vd198) <=> ?[Vd201: $i] : (Vd198 = vplus(Vd199, Vd201))) <=> ![Vd198: $i, Vd199: $i] : (less(Vd199, Vd198) <=> ?[Vd201: $i] : (Vd198 = vplus(Vd199, Vd201)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(9,axiom,(![Vd198: $i, Vd199: $i] : (less(Vd199, Vd198) <=> ?[Vd201: $i] : (Vd198 = vplus(Vd199, Vd201)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''def(cond(conseq(axiom(3)), 12), 1)'')).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (![Vd198: $i, Vd199: $i] : (less(Vd199, Vd198) <=> ?[Vd201: $i] : (Vd198 = vplus(Vd199, Vd201)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.38 tff(11,plain,(
% 0.19/0.38 ![Vd198: $i, Vd199: $i] : (((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198)))) & (less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201)))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[10])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (![Vd198: $i, Vd199: $i] : (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (![Vd198: $i, Vd199: $i] : (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201)))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 ((~![Vd198: $i, Vd199: $i] : (~((~((~less(Vd199, Vd198)) | (Vd198 = vplus(Vd199, tptp_fun_Vd201_0(Vd199, Vd198))))) | (~(less(Vd199, Vd198) | ![Vd201: $i] : (~(Vd198 = vplus(Vd199, Vd201)))))))) | (~((~((~less(vd268, vd269)) | (vd269 = vplus(vd268, tptp_fun_Vd201_0(vd268, vd269))))) | (~(less(vd268, vd269) | ![Vd201: $i] : (~(vd269 = vplus(vd268, Vd201)))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (~((~((~less(vd268, vd269)) | (vd269 = vplus(vd268, tptp_fun_Vd201_0(vd268, vd269))))) | (~(less(vd268, vd269) | ![Vd201: $i] : (~(vd269 = vplus(vd268, Vd201))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (((~((~less(vd268, vd269)) | (vd269 = vplus(vd268, tptp_fun_Vd201_0(vd268, vd269))))) | (~(less(vd268, vd269) | ![Vd201: $i] : (~(vd269 = vplus(vd268, Vd201)))))) | ((~less(vd268, vd269)) | (vd269 = vplus(vd268, tptp_fun_Vd201_0(vd268, vd269))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 ((~less(vd268, vd269)) | (vd269 = vplus(vd268, tptp_fun_Vd201_0(vd268, vd269)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (less(vd268, vd269) <=> less(vd268, vd269)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(19,axiom,(less(vd268, vd269)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(conjunct1(170), 270, 0)'')).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (less(vd268, vd269)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 ((~((~less(vd268, vd269)) | (vd269 = vplus(vd268, tptp_fun_Vd201_0(vd268, vd269))))) | (~less(vd268, vd269)) | (vd269 = vplus(vd268, tptp_fun_Vd201_0(vd268, vd269)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 ((~((~less(vd268, vd269)) | (vd269 = vplus(vd268, tptp_fun_Vd201_0(vd268, vd269))))) | (vd269 = vplus(vd268, tptp_fun_Vd201_0(vd268, vd269)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (vd269 = vplus(vd268, tptp_fun_Vd201_0(vd268, vd269))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[22, 17])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (^[Vd273: $i] : refl((~(vd269 = vplus(vd268, Vd273))) <=> (~(vd269 = vplus(vd268, Vd273))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (![Vd273: $i] : (~(vd269 = vplus(vd268, Vd273))) <=> ![Vd273: $i] : (~(vd269 = vplus(vd268, Vd273)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 ((~?[Vd273: $i] : (vd269 = vplus(vd268, Vd273))) <=> (~?[Vd273: $i] : (vd269 = vplus(vd268, Vd273)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(27,axiom,(~?[Vd273: $i] : (vd269 = vplus(vd268, Vd273))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''qe(171)'')).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (~?[Vd273: $i] : (vd269 = vplus(vd268, Vd273))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (~?[Vd273: $i] : (vd269 = vplus(vd268, Vd273))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[28, 26])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (~?[Vd273: $i] : (vd269 = vplus(vd268, Vd273))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (~?[Vd273: $i] : (vd269 = vplus(vd268, Vd273))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (^[Vd273: $i] : refl($oeq((~(vd269 = vplus(vd268, Vd273))), (~(vd269 = vplus(vd268, Vd273)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(33,plain,(
% 0.19/0.38 ![Vd273: $i] : (~(vd269 = vplus(vd268, Vd273)))),
% 0.19/0.38 inference(nnf-neg,[status(sab)],[31, 32])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (![Vd273: $i] : (~(vd269 = vplus(vd268, Vd273)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 ((~![Vd273: $i] : (~(vd269 = vplus(vd268, Vd273)))) | (~(vd269 = vplus(vd268, tptp_fun_Vd201_0(vd268, vd269))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[35, 34, 23])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------