%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO343+1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:06:16 AM UTC 2025
% Result : Theorem 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : GEO343+1 : TPTP v9.0.0. Released v4.1.0.
% 0.01/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.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 : Thu Jun 19 14:52:26 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 tff(rline_type, type, (
% 0.19/0.52 rline: $i > $o)).
% 0.19/0.52 tff(ron_type, type, (
% 0.19/0.52 ron: ( $i * $i ) > $o)).
% 0.19/0.52 tff(rpoint_type, type, (
% 0.19/0.52 rpoint: $i > $o)).
% 0.19/0.52 tff(vd1399_type, type, (
% 0.19/0.52 vd1399: $i)).
% 0.19/0.52 tff(vd1400_type, type, (
% 0.19/0.52 vd1400: $i)).
% 0.19/0.52 tff(vd1401_type, type, (
% 0.19/0.52 vd1401: $i)).
% 0.19/0.52 tff(vd1407_type, type, (
% 0.19/0.52 vd1407: $i)).
% 0.19/0.52 tff(vd1406_type, type, (
% 0.19/0.52 vd1406: $i)).
% 0.19/0.52 tff(vd1416_type, type, (
% 0.19/0.52 vd1416: $i)).
% 0.19/0.52 tff(tptp_fun_Vdthex_0_type, type, (
% 0.19/0.52 tptp_fun_Vdthex_0: $i)).
% 0.19/0.52 tff(1,plain,
% 0.19/0.52 (^[Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : refl(((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319))) <=> ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(2,plain,
% 0.19/0.52 (![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319))) <=> ![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.52 tff(3,plain,
% 0.19/0.52 (^[Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : trans(monotonicity(trans(monotonicity(rewrite((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314)) <=> (~((Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319))))), ((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) <=> (~(~((Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319))))))), rewrite((~(~((Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319))))) <=> ((Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))), ((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) <=> ((Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319))))), (((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) | (Vd319 = Vd320)) <=> (((Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319))) | (Vd319 = Vd320)))), rewrite((((Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319))) | (Vd319 = Vd320)) <=> ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))), (((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) | (Vd319 = Vd320)) <=> ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(4,plain,
% 0.19/0.53 (![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) | (Vd319 = Vd320)) <=> ![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.53 tff(5,plain,
% 0.19/0.53 (![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) | (Vd319 = Vd320)) <=> ![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) | (Vd319 = Vd320))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(6,plain,
% 0.19/0.53 (^[Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320))), ((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) <=> ((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)))), rewrite(((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319))), ((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319)))), trans(der(?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324)) <=> ?[Vd324: $i] : rline(Vd320)), elim_unused(?[Vd324: $i] : rline(Vd320) <=> rline(Vd320)), (?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324)) <=> rline(Vd320))), (((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) <=> ((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319)) & rline(Vd320)))), rewrite(((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319)) & rline(Vd320)) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320))), (((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320)))), trans(der(?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323)) <=> ?[Vd323: $i] : rline(Vd319)), elim_unused(?[Vd323: $i] : rline(Vd319) <=> rline(Vd319)), (?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323)) <=> rline(Vd319))), ((((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) & ?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323))) <=> ((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320)) & rline(Vd319)))), rewrite(((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320)) & rline(Vd319)) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319))), ((((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) & ?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323))) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319)))), (((((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) & ?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323))) & (~(Vd314 = Vd315))) <=> ((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319)) & (~(Vd314 = Vd315))))), rewrite(((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319)) & (~(Vd314 = Vd315))) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)))), (((((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) & ?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323))) & (~(Vd314 = Vd315))) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315))))), trans(der(?[Vd318: $i] : ((Vd315 = Vd318) & rpoint(Vd318)) <=> ?[Vd318: $i] : rpoint(Vd315)), elim_unused(?[Vd318: $i] : rpoint(Vd315) <=> rpoint(Vd315)), (?[Vd318: $i] : ((Vd315 = Vd318) & rpoint(Vd318)) <=> rpoint(Vd315))), ((((((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) & ?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323))) & (~(Vd314 = Vd315))) & ?[Vd318: $i] : ((Vd315 = Vd318) & rpoint(Vd318))) <=> ((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315))) & rpoint(Vd315)))), rewrite(((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315))) & rpoint(Vd315)) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315))), ((((((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) & ?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323))) & (~(Vd314 = Vd315))) & ?[Vd318: $i] : ((Vd315 = Vd318) & rpoint(Vd318))) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315)))), trans(der(?[Vd317: $i] : ((Vd314 = Vd317) & rpoint(Vd317)) <=> ?[Vd317: $i] : rpoint(Vd314)), elim_unused(?[Vd317: $i] : rpoint(Vd314) <=> rpoint(Vd314)), (?[Vd317: $i] : ((Vd314 = Vd317) & rpoint(Vd317)) <=> rpoint(Vd314))), (((((((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) & ?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323))) & (~(Vd314 = Vd315))) & ?[Vd318: $i] : ((Vd315 = Vd318) & rpoint(Vd318))) & ?[Vd317: $i] : ((Vd314 = Vd317) & rpoint(Vd317))) <=> ((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315)) & rpoint(Vd314)))), rewrite(((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315)) & rpoint(Vd314)) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))), (((((((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) & ?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323))) & (~(Vd314 = Vd315))) & ?[Vd318: $i] : ((Vd315 = Vd318) & rpoint(Vd318))) & ?[Vd317: $i] : ((Vd314 = Vd317) & rpoint(Vd317))) <=> (ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314)))), ((((((((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) & ?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323))) & (~(Vd314 = Vd315))) & ?[Vd318: $i] : ((Vd315 = Vd318) & rpoint(Vd318))) & ?[Vd317: $i] : ((Vd314 = Vd317) & rpoint(Vd317))) => (Vd319 = Vd320)) <=> ((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314)) => (Vd319 = Vd320)))), rewrite(((ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314)) => (Vd319 = Vd320)) <=> ((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) | (Vd319 = Vd320))), ((((((((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) & ?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323))) & (~(Vd314 = Vd315))) & ?[Vd318: $i] : ((Vd315 = Vd318) & rpoint(Vd318))) & ?[Vd317: $i] : ((Vd314 = Vd317) & rpoint(Vd317))) => (Vd319 = Vd320)) <=> ((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) | (Vd319 = Vd320))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(7,plain,
% 0.19/0.53 (![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : (((((((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) & ?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323))) & (~(Vd314 = Vd315))) & ?[Vd318: $i] : ((Vd315 = Vd318) & rpoint(Vd318))) & ?[Vd317: $i] : ((Vd314 = Vd317) & rpoint(Vd317))) => (Vd319 = Vd320)) <=> ![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) | (Vd319 = Vd320))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.53 tff(8,axiom,(![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : (((((((((ron(Vd315, Vd320) & ron(Vd315, Vd319)) & ron(Vd314, Vd320)) & ron(Vd314, Vd319)) & ?[Vd324: $i] : ((Vd320 = Vd324) & rline(Vd324))) & ?[Vd323: $i] : ((Vd319 = Vd323) & rline(Vd323))) & (~(Vd314 = Vd315))) & ?[Vd318: $i] : ((Vd315 = Vd318) & rpoint(Vd318))) & ?[Vd317: $i] : ((Vd314 = Vd317) & rpoint(Vd317))) => (Vd319 = Vd320))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))'')).
% 0.19/0.53 tff(9,plain,
% 0.19/0.53 (![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) | (Vd319 = Vd320))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.53 tff(10,plain,
% 0.19/0.53 (![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) | (Vd319 = Vd320))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.53 tff(11,plain,(
% 0.19/0.53 ![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((~(ron(Vd315, Vd320) & ron(Vd315, Vd319) & ron(Vd314, Vd320) & ron(Vd314, Vd319) & rline(Vd320) & rline(Vd319) & (~(Vd314 = Vd315)) & rpoint(Vd315) & rpoint(Vd314))) | (Vd319 = Vd320))),
% 0.19/0.53 inference(skolemize,[status(sab)],[10])).
% 0.19/0.53 tff(12,plain,
% 0.19/0.53 (![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.53 tff(13,plain,
% 0.19/0.53 (![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.53 tff(14,plain,
% 0.19/0.53 (rpoint(vd1399) <=> rpoint(vd1399)),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(15,plain,
% 0.19/0.53 (?[Vd1403: $i] : rpoint(vd1399) <=> rpoint(vd1399)),
% 0.19/0.53 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.53 tff(16,plain,
% 0.19/0.53 (?[Vd1403: $i] : ((vd1399 = Vd1403) & rpoint(Vd1403)) <=> ?[Vd1403: $i] : rpoint(vd1399)),
% 0.19/0.53 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.53 tff(17,plain,
% 0.19/0.53 (?[Vd1403: $i] : ((vd1399 = Vd1403) & rpoint(Vd1403)) <=> rpoint(vd1399)),
% 0.19/0.53 inference(transitivity,[status(thm)],[16, 15])).
% 0.19/0.53 tff(18,axiom,((((((((((vd1406 = vd1407) & ron(vd1400, vd1406)) & ron(vd1399, vd1406)) & rline(vd1407)) & (~(vd1400 = vd1401))) & (~(vd1399 = vd1401))) & (~(vd1399 = vd1400))) & ?[Vd1405: $i] : ((vd1401 = Vd1405) & rpoint(Vd1405))) & ?[Vd1404: $i] : ((vd1400 = Vd1404) & rpoint(Vd1404))) & ?[Vd1403: $i] : ((vd1399 = Vd1403) & rpoint(Vd1403))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''and(pred(conjunct2(405), 5), and(pred(s2(plural(conjunct2(405))), 0), and(pred(s1(plural(conjunct2(405))), 0), and(pred(conjunct2(405), 1), and(pred(conjunct1(405), 9), and(pred(conjunct1(405), 8), and(pred(conjunct1(405), 7), and(qe(s3(plural(405))), and(qe(s2(plural(405))), qe(s1(plural(405))))))))))))'')).
% 0.19/0.53 tff(19,plain,
% 0.19/0.53 (?[Vd1403: $i] : ((vd1399 = Vd1403) & rpoint(Vd1403))),
% 0.19/0.53 inference(and_elim,[status(thm)],[18])).
% 0.19/0.53 tff(20,plain,
% 0.19/0.53 (rpoint(vd1399)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.19/0.53 tff(21,plain,
% 0.19/0.53 (rpoint(vd1399)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.19/0.53 tff(22,plain,
% 0.19/0.53 (rpoint(vd1401) <=> rpoint(vd1401)),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(23,plain,
% 0.19/0.53 (?[Vd1405: $i] : rpoint(vd1401) <=> rpoint(vd1401)),
% 0.19/0.53 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.53 tff(24,plain,
% 0.19/0.53 (?[Vd1405: $i] : ((vd1401 = Vd1405) & rpoint(Vd1405)) <=> ?[Vd1405: $i] : rpoint(vd1401)),
% 0.19/0.53 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.53 tff(25,plain,
% 0.19/0.53 (?[Vd1405: $i] : ((vd1401 = Vd1405) & rpoint(Vd1405)) <=> rpoint(vd1401)),
% 0.19/0.53 inference(transitivity,[status(thm)],[24, 23])).
% 0.19/0.53 tff(26,plain,
% 0.19/0.53 (((((((((vd1406 = vd1407) & ron(vd1400, vd1406)) & ron(vd1399, vd1406)) & rline(vd1407)) & (~(vd1400 = vd1401))) & (~(vd1399 = vd1401))) & (~(vd1399 = vd1400))) & ?[Vd1405: $i] : ((vd1401 = Vd1405) & rpoint(Vd1405))) & ?[Vd1404: $i] : ((vd1400 = Vd1404) & rpoint(Vd1404))),
% 0.19/0.53 inference(and_elim,[status(thm)],[18])).
% 0.19/0.53 tff(27,plain,
% 0.19/0.53 ((((((((vd1406 = vd1407) & ron(vd1400, vd1406)) & ron(vd1399, vd1406)) & rline(vd1407)) & (~(vd1400 = vd1401))) & (~(vd1399 = vd1401))) & (~(vd1399 = vd1400))) & ?[Vd1405: $i] : ((vd1401 = Vd1405) & rpoint(Vd1405))),
% 0.19/0.53 inference(and_elim,[status(thm)],[26])).
% 0.19/0.53 tff(28,plain,
% 0.19/0.53 (?[Vd1405: $i] : ((vd1401 = Vd1405) & rpoint(Vd1405))),
% 0.19/0.53 inference(and_elim,[status(thm)],[27])).
% 0.19/0.53 tff(29,plain,
% 0.19/0.53 (rpoint(vd1401)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.19/0.53 tff(30,plain,
% 0.19/0.53 (rpoint(vd1401)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.19/0.53 tff(31,plain,
% 0.19/0.53 ((~(vd1399 = vd1401)) <=> (~(vd1399 = vd1401))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(32,plain,
% 0.19/0.53 (((((((vd1406 = vd1407) & ron(vd1400, vd1406)) & ron(vd1399, vd1406)) & rline(vd1407)) & (~(vd1400 = vd1401))) & (~(vd1399 = vd1401))) & (~(vd1399 = vd1400))),
% 0.19/0.53 inference(and_elim,[status(thm)],[27])).
% 0.19/0.53 tff(33,plain,
% 0.19/0.53 ((((((vd1406 = vd1407) & ron(vd1400, vd1406)) & ron(vd1399, vd1406)) & rline(vd1407)) & (~(vd1400 = vd1401))) & (~(vd1399 = vd1401))),
% 0.19/0.53 inference(and_elim,[status(thm)],[32])).
% 0.19/0.53 tff(34,plain,
% 0.19/0.53 (~(vd1399 = vd1401)),
% 0.19/0.53 inference(and_elim,[status(thm)],[33])).
% 0.19/0.53 tff(35,plain,
% 0.19/0.53 (~(vd1399 = vd1401)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.19/0.53 tff(36,plain,
% 0.19/0.53 (rline(vd1416) <=> rline(vd1416)),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(37,axiom,((ron(vd1399, vd1416) & ron(vd1401, vd1416)) & rline(vd1416)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''and(pred(s2(plural(the(408))), 0), and(pred(s1(plural(the(408))), 0), pred(the(408), 0)))'')).
% 0.19/0.53 tff(38,plain,
% 0.19/0.53 (rline(vd1416)),
% 0.19/0.53 inference(and_elim,[status(thm)],[37])).
% 0.19/0.53 tff(39,plain,
% 0.19/0.53 (rline(vd1416)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[38, 36])).
% 0.19/0.53 tff(40,plain,
% 0.19/0.53 (ron(vd1401, vd1416) <=> ron(vd1401, vd1416)),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(41,plain,
% 0.19/0.53 (ron(vd1399, vd1416) & ron(vd1401, vd1416)),
% 0.19/0.53 inference(and_elim,[status(thm)],[37])).
% 0.19/0.53 tff(42,plain,
% 0.19/0.53 (ron(vd1401, vd1416)),
% 0.19/0.53 inference(and_elim,[status(thm)],[41])).
% 0.19/0.53 tff(43,plain,
% 0.19/0.53 (ron(vd1401, vd1416)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[42, 40])).
% 0.19/0.53 tff(44,plain,
% 0.19/0.53 (ron(vd1399, vd1416) <=> ron(vd1399, vd1416)),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(45,plain,
% 0.19/0.53 (ron(vd1399, vd1416)),
% 0.19/0.53 inference(and_elim,[status(thm)],[41])).
% 0.19/0.53 tff(46,plain,
% 0.19/0.53 (ron(vd1399, vd1416)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.53 tff(47,plain,
% 0.19/0.53 ((~![Vdthex: $i] : ((~(ron(vd1399, Vdthex) & ron(vd1401, Vdthex) & rline(Vdthex))) | (Vdthex = vd1416))) <=> (~![Vdthex: $i] : ((~(ron(vd1399, Vdthex) & ron(vd1401, Vdthex) & rline(Vdthex))) | (Vdthex = vd1416)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(48,plain,
% 0.19/0.53 ((~![Vdthex: $i] : (((ron(vd1399, Vdthex) & ron(vd1401, Vdthex)) & rline(Vdthex)) => (Vdthex = vd1416))) <=> (~![Vdthex: $i] : ((~(ron(vd1399, Vdthex) & ron(vd1401, Vdthex) & rline(Vdthex))) | (Vdthex = vd1416)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(49,axiom,(~![Vdthex: $i] : (((ron(vd1399, Vdthex) & ron(vd1401, Vdthex)) & rline(Vdthex)) => (Vdthex = vd1416))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''qu(theu(the(408), 1), imp(the(408)))'')).
% 0.19/0.53 tff(50,plain,
% 0.19/0.53 (~![Vdthex: $i] : ((~(ron(vd1399, Vdthex) & ron(vd1401, Vdthex) & rline(Vdthex))) | (Vdthex = vd1416))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.53 tff(51,plain,
% 0.19/0.53 (~![Vdthex: $i] : ((~(ron(vd1399, Vdthex) & ron(vd1401, Vdthex) & rline(Vdthex))) | (Vdthex = vd1416))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.19/0.53 tff(52,plain,
% 0.19/0.53 (~![Vdthex: $i] : ((~(ron(vd1399, Vdthex) & ron(vd1401, Vdthex) & rline(Vdthex))) | (Vdthex = vd1416))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.53 tff(53,plain,
% 0.19/0.53 (~![Vdthex: $i] : ((~(ron(vd1399, Vdthex) & ron(vd1401, Vdthex) & rline(Vdthex))) | (Vdthex = vd1416))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[52, 47])).
% 0.19/0.53 tff(54,plain,(
% 0.19/0.53 ~((~(ron(vd1399, Vdthex!0) & ron(vd1401, Vdthex!0) & rline(Vdthex!0))) | (Vdthex!0 = vd1416))),
% 0.19/0.53 inference(skolemize,[status(sab)],[53])).
% 0.19/0.53 tff(55,plain,
% 0.19/0.53 (~(Vdthex!0 = vd1416)),
% 0.19/0.53 inference(or_elim,[status(thm)],[54])).
% 0.19/0.53 tff(56,plain,
% 0.19/0.53 (ron(vd1399, Vdthex!0) & ron(vd1401, Vdthex!0) & rline(Vdthex!0)),
% 0.19/0.53 inference(or_elim,[status(thm)],[54])).
% 0.19/0.53 tff(57,plain,
% 0.19/0.53 (rline(Vdthex!0)),
% 0.19/0.53 inference(and_elim,[status(thm)],[56])).
% 0.19/0.53 tff(58,plain,
% 0.19/0.53 (ron(vd1401, Vdthex!0)),
% 0.19/0.53 inference(and_elim,[status(thm)],[56])).
% 0.19/0.53 tff(59,plain,
% 0.19/0.53 (ron(vd1399, Vdthex!0)),
% 0.19/0.53 inference(and_elim,[status(thm)],[56])).
% 0.19/0.53 tff(60,plain,
% 0.19/0.53 (((~![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))) | ((vd1399 = vd1401) | (Vdthex!0 = vd1416) | (~rpoint(vd1401)) | (~rpoint(vd1399)) | (~ron(vd1399, Vdthex!0)) | (~rline(Vdthex!0)) | (~ron(vd1401, Vdthex!0)) | (~ron(vd1399, vd1416)) | (~rline(vd1416)) | (~ron(vd1401, vd1416)))) <=> ((~![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))) | (vd1399 = vd1401) | (Vdthex!0 = vd1416) | (~rpoint(vd1401)) | (~rpoint(vd1399)) | (~ron(vd1399, Vdthex!0)) | (~rline(Vdthex!0)) | (~ron(vd1401, Vdthex!0)) | (~ron(vd1399, vd1416)) | (~rline(vd1416)) | (~ron(vd1401, vd1416)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(61,plain,
% 0.19/0.53 (((Vdthex!0 = vd1416) | (vd1399 = vd1401) | (~ron(vd1401, Vdthex!0)) | (~ron(vd1401, vd1416)) | (~ron(vd1399, Vdthex!0)) | (~rpoint(vd1401)) | (~rpoint(vd1399)) | (~rline(vd1416)) | (~ron(vd1399, vd1416)) | (~rline(Vdthex!0))) <=> ((vd1399 = vd1401) | (Vdthex!0 = vd1416) | (~rpoint(vd1401)) | (~rpoint(vd1399)) | (~ron(vd1399, Vdthex!0)) | (~rline(Vdthex!0)) | (~ron(vd1401, Vdthex!0)) | (~ron(vd1399, vd1416)) | (~rline(vd1416)) | (~ron(vd1401, vd1416)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(62,plain,
% 0.19/0.54 (((~![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))) | ((Vdthex!0 = vd1416) | (vd1399 = vd1401) | (~ron(vd1401, Vdthex!0)) | (~ron(vd1401, vd1416)) | (~ron(vd1399, Vdthex!0)) | (~rpoint(vd1401)) | (~rpoint(vd1399)) | (~rline(vd1416)) | (~ron(vd1399, vd1416)) | (~rline(Vdthex!0)))) <=> ((~![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))) | ((vd1399 = vd1401) | (Vdthex!0 = vd1416) | (~rpoint(vd1401)) | (~rpoint(vd1399)) | (~ron(vd1399, Vdthex!0)) | (~rline(Vdthex!0)) | (~ron(vd1401, Vdthex!0)) | (~ron(vd1399, vd1416)) | (~rline(vd1416)) | (~ron(vd1401, vd1416))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.54 tff(63,plain,
% 0.19/0.54 (((~![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))) | ((Vdthex!0 = vd1416) | (vd1399 = vd1401) | (~ron(vd1401, Vdthex!0)) | (~ron(vd1401, vd1416)) | (~ron(vd1399, Vdthex!0)) | (~rpoint(vd1401)) | (~rpoint(vd1399)) | (~rline(vd1416)) | (~ron(vd1399, vd1416)) | (~rline(Vdthex!0)))) <=> ((~![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))) | (vd1399 = vd1401) | (Vdthex!0 = vd1416) | (~rpoint(vd1401)) | (~rpoint(vd1399)) | (~ron(vd1399, Vdthex!0)) | (~rline(Vdthex!0)) | (~ron(vd1401, Vdthex!0)) | (~ron(vd1399, vd1416)) | (~rline(vd1416)) | (~ron(vd1401, vd1416)))),
% 0.19/0.54 inference(transitivity,[status(thm)],[62, 60])).
% 0.19/0.54 tff(64,plain,
% 0.19/0.54 ((~![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))) | ((Vdthex!0 = vd1416) | (vd1399 = vd1401) | (~ron(vd1401, Vdthex!0)) | (~ron(vd1401, vd1416)) | (~ron(vd1399, Vdthex!0)) | (~rpoint(vd1401)) | (~rpoint(vd1399)) | (~rline(vd1416)) | (~ron(vd1399, vd1416)) | (~rline(Vdthex!0)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(65,plain,
% 0.19/0.54 ((~![Vd314: $i, Vd315: $i, Vd319: $i, Vd320: $i] : ((Vd319 = Vd320) | (Vd314 = Vd315) | (~ron(Vd315, Vd319)) | (~ron(Vd315, Vd320)) | (~ron(Vd314, Vd319)) | (~rpoint(Vd315)) | (~rpoint(Vd314)) | (~rline(Vd320)) | (~ron(Vd314, Vd320)) | (~rline(Vd319)))) | (vd1399 = vd1401) | (Vdthex!0 = vd1416) | (~rpoint(vd1401)) | (~rpoint(vd1399)) | (~ron(vd1399, Vdthex!0)) | (~rline(Vdthex!0)) | (~ron(vd1401, Vdthex!0)) | (~ron(vd1399, vd1416)) | (~rline(vd1416)) | (~ron(vd1401, vd1416))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.54 tff(66,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[65, 59, 58, 57, 55, 46, 43, 39, 35, 30, 21, 13])).
% 0.19/0.54 % SZS output end Proof
% 0.19/0.55 % E exiting
%------------------------------------------------------------------------------