%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO331+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 05:06:15 AM UTC 2025
% Result : Theorem 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO331+1 : TPTP v9.0.0. Released v4.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 : Thu Jun 19 14:52:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 tff(rless_type, type, (
% 0.20/0.50 rless: ( $i * $i ) > $o)).
% 0.20/0.50 tff(vf_type, type, (
% 0.20/0.50 vf: ( $i * $i ) > $i)).
% 0.20/0.50 tff(vd1353_type, type, (
% 0.20/0.50 vd1353: $i)).
% 0.20/0.50 tff(vd1352_type, type, (
% 0.20/0.50 vd1352: $i)).
% 0.20/0.50 tff(vd1354_type, type, (
% 0.20/0.50 vd1354: $i)).
% 0.20/0.50 tff(vangle_type, type, (
% 0.20/0.50 vangle: ( $i * $i * $i ) > $i)).
% 0.20/0.50 tff(rpoint_type, type, (
% 0.20/0.50 rpoint: $i > $o)).
% 0.20/0.50 tff(1,plain,
% 0.20/0.50 (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : refl(((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(2,plain,
% 0.20/0.50 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.50 tff(3,plain,
% 0.20/0.50 (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(trans(monotonicity(rewrite(((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)) <=> (~((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))), ((~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))) <=> (~(~((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))))), rewrite((~(~((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))) <=> ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))), ((~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))) <=> ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))), (((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))))), rewrite(((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))), (((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(4,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.51 tff(5,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(6,plain,
% 0.20/0.51 (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)))), (((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)))), (((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))))), trans(der(?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) <=> ?[Vd1368: $i] : rpoint(Vd1363)), elim_unused(?[Vd1368: $i] : rpoint(Vd1363) <=> rpoint(Vd1363)), (?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) <=> rpoint(Vd1363))), ((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))) & rpoint(Vd1363)))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))) & rpoint(Vd1363)) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363))), ((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363)))), trans(der(?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) <=> ?[Vd1367: $i] : rpoint(Vd1362)), elim_unused(?[Vd1367: $i] : rpoint(Vd1362) <=> rpoint(Vd1362)), (?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) <=> rpoint(Vd1362))), (((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363)) & rpoint(Vd1362)))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363)) & rpoint(Vd1362)) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362))), (((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362)))), trans(der(?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)) <=> ?[Vd1366: $i] : rpoint(Vd1361)), elim_unused(?[Vd1366: $i] : rpoint(Vd1361) <=> rpoint(Vd1361)), (?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)) <=> rpoint(Vd1361))), ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362)) & rpoint(Vd1361)))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362)) & rpoint(Vd1361)) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))), ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))), rewrite(((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))), (((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)) => ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)) => ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))), (((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(7,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.51 tff(8,axiom,(![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(proof(385), 0), 2)'')).
% 0.20/0.51 tff(9,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.51 tff(10,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.51 tff(11,plain,(
% 0.20/0.51 ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[10])).
% 0.20/0.51 tff(12,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.51 tff(13,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.51 tff(14,plain,
% 0.20/0.51 (rpoint(vd1352) <=> rpoint(vd1352)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(15,plain,
% 0.20/0.51 (?[Vd1357: $i] : rpoint(vd1352) <=> rpoint(vd1352)),
% 0.20/0.51 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.51 tff(16,plain,
% 0.20/0.51 (?[Vd1357: $i] : ((vd1352 = Vd1357) & rpoint(Vd1357)) <=> ?[Vd1357: $i] : rpoint(vd1352)),
% 0.20/0.51 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.51 tff(17,plain,
% 0.20/0.51 (?[Vd1357: $i] : ((vd1352 = Vd1357) & rpoint(Vd1357)) <=> rpoint(vd1352)),
% 0.20/0.51 inference(transitivity,[status(thm)],[16, 15])).
% 0.20/0.51 tff(18,axiom,(?[Vd1357: $i] : ((vd1352 = Vd1357) & rpoint(Vd1357))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''qe(s1(plural(383)))'')).
% 0.20/0.51 tff(19,plain,
% 0.20/0.51 (rpoint(vd1352)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.51 tff(20,plain,
% 0.20/0.51 (rpoint(vd1352)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.20/0.51 tff(21,plain,
% 0.20/0.51 (rpoint(vd1353) <=> rpoint(vd1353)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(22,plain,
% 0.20/0.51 (?[Vd1358: $i] : rpoint(vd1353) <=> rpoint(vd1353)),
% 0.20/0.51 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.51 tff(23,plain,
% 0.20/0.51 (?[Vd1358: $i] : ((vd1353 = Vd1358) & rpoint(Vd1358)) <=> ?[Vd1358: $i] : rpoint(vd1353)),
% 0.20/0.51 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.51 tff(24,plain,
% 0.20/0.51 (?[Vd1358: $i] : ((vd1353 = Vd1358) & rpoint(Vd1358)) <=> rpoint(vd1353)),
% 0.20/0.51 inference(transitivity,[status(thm)],[23, 22])).
% 0.20/0.51 tff(25,axiom,(?[Vd1358: $i] : ((vd1353 = Vd1358) & rpoint(Vd1358))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''qe(s2(plural(383)))'')).
% 0.20/0.51 tff(26,plain,
% 0.20/0.51 (rpoint(vd1353)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.51 tff(27,plain,
% 0.20/0.51 (rpoint(vd1353)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.51 tff(28,plain,
% 0.20/0.51 (rpoint(vd1354) <=> rpoint(vd1354)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(29,plain,
% 0.20/0.51 (?[Vd1359: $i] : rpoint(vd1354) <=> rpoint(vd1354)),
% 0.20/0.51 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.51 tff(30,plain,
% 0.20/0.51 (?[Vd1359: $i] : ((vd1354 = Vd1359) & rpoint(Vd1359)) <=> ?[Vd1359: $i] : rpoint(vd1354)),
% 0.20/0.51 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.51 tff(31,plain,
% 0.20/0.51 (?[Vd1359: $i] : ((vd1354 = Vd1359) & rpoint(Vd1359)) <=> rpoint(vd1354)),
% 0.20/0.51 inference(transitivity,[status(thm)],[30, 29])).
% 0.20/0.51 tff(32,axiom,(?[Vd1359: $i] : ((vd1354 = Vd1359) & rpoint(Vd1359))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''qe(s3(plural(383)))'')).
% 0.20/0.51 tff(33,plain,
% 0.20/0.51 (rpoint(vd1354)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.51 tff(34,plain,
% 0.20/0.51 (rpoint(vd1354)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.20/0.51 tff(35,plain,
% 0.20/0.51 ((~(vd1352 = vd1353)) <=> (~(vd1352 = vd1353))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(36,axiom,(~(vd1352 = vd1353)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''pred(383, 7)'')).
% 0.20/0.51 tff(37,plain,
% 0.20/0.51 (~(vd1352 = vd1353)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.51 tff(38,plain,
% 0.20/0.51 ((~(vd1352 = vd1354)) <=> (~(vd1352 = vd1354))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(39,axiom,(~(vd1352 = vd1354)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''pred(383, 8)'')).
% 0.20/0.51 tff(40,plain,
% 0.20/0.51 (~(vd1352 = vd1354)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.51 tff(41,plain,
% 0.20/0.51 ((~(vd1353 = vd1354)) <=> (~(vd1353 = vd1354))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(42,axiom,(~(vd1353 = vd1354)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''pred(383, 9)'')).
% 0.20/0.51 tff(43,plain,
% 0.20/0.51 (~(vd1353 = vd1354)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.51 tff(44,plain,
% 0.20/0.51 ((vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353)) <=> (vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(45,axiom,(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(383, 1356, 0)'')).
% 0.20/0.51 tff(46,plain,
% 0.20/0.51 (vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.51 tff(47,plain,
% 0.20/0.51 ((~(vf(vd1352, vd1353) = vf(vd1352, vd1354))) <=> (~(vf(vd1352, vd1353) = vf(vd1352, vd1354)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(48,axiom,(~(vf(vd1352, vd1353) = vf(vd1352, vd1354))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(384, 1360, 0)'')).
% 0.20/0.51 tff(49,plain,
% 0.20/0.51 (~(vf(vd1352, vd1353) = vf(vd1352, vd1354))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.51 tff(50,plain,
% 0.20/0.51 (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | (~rless(vf(vd1352, vd1354), vf(vd1352, vd1353))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | (~rless(vf(vd1352, vd1354), vf(vd1352, vd1353))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(51,plain,
% 0.20/0.51 (((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1352 = vd1354) | (vd1353 = vd1354) | (vd1352 = vd1353) | (~rless(vf(vd1352, vd1354), vf(vd1352, vd1353))) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353)))) <=> ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | (~rless(vf(vd1352, vd1354), vf(vd1352, vd1353))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(52,plain,
% 0.20/0.51 (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1352 = vd1354) | (vd1353 = vd1354) | (vd1352 = vd1353) | (~rless(vf(vd1352, vd1354), vf(vd1352, vd1353))) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | (~rless(vf(vd1352, vd1354), vf(vd1352, vd1353)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.51 tff(53,plain,
% 0.20/0.51 (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1352 = vd1354) | (vd1353 = vd1354) | (vd1352 = vd1353) | (~rless(vf(vd1352, vd1354), vf(vd1352, vd1353))) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | (~rless(vf(vd1352, vd1354), vf(vd1352, vd1353))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[52, 50])).
% 0.20/0.51 tff(54,plain,
% 0.20/0.51 ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1352 = vd1354) | (vd1353 = vd1354) | (vd1352 = vd1353) | (~rless(vf(vd1352, vd1354), vf(vd1352, vd1353))) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(55,plain,
% 0.20/0.51 ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | (~rless(vf(vd1352, vd1354), vf(vd1352, vd1353)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.51 tff(56,plain,
% 0.20/0.51 (~rless(vf(vd1352, vd1354), vf(vd1352, vd1353))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[55, 49, 46, 43, 40, 37, 34, 27, 20, 13])).
% 0.20/0.51 tff(57,plain,
% 0.20/0.51 (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : refl(((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(58,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.51 tff(59,plain,
% 0.20/0.51 (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(trans(monotonicity(rewrite(((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)) <=> (~((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))), ((~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))) <=> (~(~((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))))), rewrite((~(~((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))) <=> ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))), ((~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))) <=> ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))), (((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))))), rewrite(((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))), (((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(60,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.51 tff(61,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(62,plain,
% 0.20/0.51 (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)))), (((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)))), (((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))))), trans(der(?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) <=> ?[Vd1368: $i] : rpoint(Vd1363)), elim_unused(?[Vd1368: $i] : rpoint(Vd1363) <=> rpoint(Vd1363)), (?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) <=> rpoint(Vd1363))), ((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))) & rpoint(Vd1363)))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))) & rpoint(Vd1363)) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363))), ((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363)))), trans(der(?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) <=> ?[Vd1367: $i] : rpoint(Vd1362)), elim_unused(?[Vd1367: $i] : rpoint(Vd1362) <=> rpoint(Vd1362)), (?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) <=> rpoint(Vd1362))), (((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363)) & rpoint(Vd1362)))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363)) & rpoint(Vd1362)) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362))), (((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362)))), trans(der(?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)) <=> ?[Vd1366: $i] : rpoint(Vd1361)), elim_unused(?[Vd1366: $i] : rpoint(Vd1361) <=> rpoint(Vd1361)), (?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)) <=> rpoint(Vd1361))), ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362)) & rpoint(Vd1361)))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362)) & rpoint(Vd1361)) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))), ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))), rewrite(((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)))), (((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)) => ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)) => ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))), (((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))))) <=> ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(63,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.51 tff(64,axiom,(![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(proof(385), 0), 1)'')).
% 0.20/0.51 tff(65,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.51 tff(66,plain,
% 0.20/0.51 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.20/0.52 tff(67,plain,(
% 0.20/0.52 ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[66])).
% 0.20/0.52 tff(68,plain,
% 0.20/0.52 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.52 tff(69,plain,
% 0.20/0.52 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.20/0.52 tff(70,plain,
% 0.20/0.52 (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | (~rless(vf(vd1352, vd1353), vf(vd1352, vd1354))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | (~rless(vf(vd1352, vd1353), vf(vd1352, vd1354))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(71,plain,
% 0.20/0.52 (((~rless(vf(vd1352, vd1353), vf(vd1352, vd1354))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1352 = vd1354) | (vd1353 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353)))) <=> ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | (~rless(vf(vd1352, vd1353), vf(vd1352, vd1354))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(72,plain,
% 0.20/0.52 (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | ((~rless(vf(vd1352, vd1353), vf(vd1352, vd1354))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1352 = vd1354) | (vd1353 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | (~rless(vf(vd1352, vd1353), vf(vd1352, vd1354)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.52 tff(73,plain,
% 0.20/0.52 (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | ((~rless(vf(vd1352, vd1353), vf(vd1352, vd1354))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1352 = vd1354) | (vd1353 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | (~rless(vf(vd1352, vd1353), vf(vd1352, vd1354))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.52 tff(74,plain,
% 0.20/0.52 ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | ((~rless(vf(vd1352, vd1353), vf(vd1352, vd1354))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1352 = vd1354) | (vd1353 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(75,plain,
% 0.20/0.52 ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((~rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363))) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | (~rless(vf(vd1352, vd1353), vf(vd1352, vd1354)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.52 tff(76,plain,
% 0.20/0.52 (~rless(vf(vd1352, vd1353), vf(vd1352, vd1354))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[75, 49, 46, 43, 40, 37, 34, 27, 20, 69])).
% 0.20/0.52 tff(77,plain,
% 0.20/0.52 (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : refl((rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(78,plain,
% 0.20/0.52 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.52 tff(79,plain,
% 0.20/0.52 (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(trans(monotonicity(rewrite(((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)) <=> (~((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))), ((~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))) <=> (~(~((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))))), rewrite((~(~((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))) <=> ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))), ((~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))) <=> ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)))))), ((rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))))), rewrite((rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | ((Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))), ((rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(80,plain,
% 0.20/0.52 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.52 tff(81,plain,
% 0.20/0.52 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(82,plain,
% 0.20/0.52 (^[Vd1361: $i, Vd1362: $i, Vd1363: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)))), (((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)))), (((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))))), trans(der(?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) <=> ?[Vd1368: $i] : rpoint(Vd1363)), elim_unused(?[Vd1368: $i] : rpoint(Vd1363) <=> rpoint(Vd1363)), (?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368)) <=> rpoint(Vd1363))), ((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))) & rpoint(Vd1363)))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362))) & rpoint(Vd1363)) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363))), ((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363)))), trans(der(?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) <=> ?[Vd1367: $i] : rpoint(Vd1362)), elim_unused(?[Vd1367: $i] : rpoint(Vd1362) <=> rpoint(Vd1362)), (?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367)) <=> rpoint(Vd1362))), (((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363)) & rpoint(Vd1362)))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363)) & rpoint(Vd1362)) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362))), (((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362)))), trans(der(?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)) <=> ?[Vd1366: $i] : rpoint(Vd1361)), elim_unused(?[Vd1366: $i] : rpoint(Vd1361) <=> rpoint(Vd1361)), (?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366)) <=> rpoint(Vd1361))), ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362)) & rpoint(Vd1361)))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362)) & rpoint(Vd1361)) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))), ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) <=> ((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)))), trans(monotonicity(rewrite((rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)))), (((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)))) <=> ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)))))), rewrite(((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)))), (((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))))), (((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> (((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)) => (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)))))), rewrite((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361)) => (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))), (((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(83,plain,
% 0.20/0.52 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362))))) <=> ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.52 tff(84,axiom,(![Vd1361: $i, Vd1362: $i, Vd1363: $i] : ((((((((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363))) & (~(Vd1361 = Vd1363))) & (~(Vd1361 = Vd1362))) & ?[Vd1368: $i] : ((Vd1363 = Vd1368) & rpoint(Vd1368))) & ?[Vd1367: $i] : ((Vd1362 = Vd1367) & rpoint(Vd1367))) & ?[Vd1366: $i] : ((Vd1361 = Vd1366) & rpoint(Vd1366))) => ((~(vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363))) => (rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(proof(385), 0), 0)'')).
% 0.20/0.52 tff(85,plain,
% 0.20/0.52 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.52 tff(86,plain,
% 0.20/0.52 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.20/0.52 tff(87,plain,(
% 0.20/0.52 ![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (~((vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362)) & (~(Vd1362 = Vd1363)) & (~(Vd1361 = Vd1363)) & (~(Vd1361 = Vd1362)) & rpoint(Vd1363) & rpoint(Vd1362) & rpoint(Vd1361))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[86])).
% 0.20/0.52 tff(88,plain,
% 0.20/0.52 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.20/0.52 tff(89,plain,
% 0.20/0.52 (![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[88, 78])).
% 0.20/0.52 tff(90,plain,
% 0.20/0.52 (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | rless(vf(vd1352, vd1353), vf(vd1352, vd1354)) | rless(vf(vd1352, vd1354), vf(vd1352, vd1353)))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | rless(vf(vd1352, vd1353), vf(vd1352, vd1354)) | rless(vf(vd1352, vd1354), vf(vd1352, vd1353)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(91,plain,
% 0.20/0.52 ((rless(vf(vd1352, vd1354), vf(vd1352, vd1353)) | rless(vf(vd1352, vd1353), vf(vd1352, vd1354)) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1352 = vd1354) | (vd1353 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353)))) <=> ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | rless(vf(vd1352, vd1353), vf(vd1352, vd1354)) | rless(vf(vd1352, vd1354), vf(vd1352, vd1353)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(92,plain,
% 0.20/0.52 (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | (rless(vf(vd1352, vd1354), vf(vd1352, vd1353)) | rless(vf(vd1352, vd1353), vf(vd1352, vd1354)) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1352 = vd1354) | (vd1353 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | ((vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | rless(vf(vd1352, vd1353), vf(vd1352, vd1354)) | rless(vf(vd1352, vd1354), vf(vd1352, vd1353))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.52 tff(93,plain,
% 0.20/0.52 (((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | (rless(vf(vd1352, vd1354), vf(vd1352, vd1353)) | rless(vf(vd1352, vd1353), vf(vd1352, vd1354)) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1352 = vd1354) | (vd1353 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))))) <=> ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | rless(vf(vd1352, vd1353), vf(vd1352, vd1354)) | rless(vf(vd1352, vd1354), vf(vd1352, vd1353)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[92, 90])).
% 0.20/0.52 tff(94,plain,
% 0.20/0.52 ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | (rless(vf(vd1352, vd1354), vf(vd1352, vd1353)) | rless(vf(vd1352, vd1353), vf(vd1352, vd1354)) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1352 = vd1354) | (vd1353 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(95,plain,
% 0.20/0.54 ((~![Vd1361: $i, Vd1362: $i, Vd1363: $i] : (rless(vf(Vd1361, Vd1363), vf(Vd1361, Vd1362)) | rless(vf(Vd1361, Vd1362), vf(Vd1361, Vd1363)) | (vf(Vd1361, Vd1362) = vf(Vd1361, Vd1363)) | (Vd1361 = Vd1363) | (Vd1362 = Vd1363) | (Vd1361 = Vd1362) | (~rpoint(Vd1363)) | (~rpoint(Vd1361)) | (~rpoint(Vd1362)) | (~(vangle(Vd1361, Vd1362, Vd1363) = vangle(Vd1361, Vd1363, Vd1362))))) | (vf(vd1352, vd1353) = vf(vd1352, vd1354)) | (vd1353 = vd1354) | (vd1352 = vd1354) | (vd1352 = vd1353) | (~rpoint(vd1354)) | (~rpoint(vd1352)) | (~rpoint(vd1353)) | (~(vangle(vd1352, vd1353, vd1354) = vangle(vd1352, vd1354, vd1353))) | rless(vf(vd1352, vd1353), vf(vd1352, vd1354)) | rless(vf(vd1352, vd1354), vf(vd1352, vd1353))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.54 tff(96,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[95, 49, 46, 43, 40, 37, 34, 27, 20, 89, 76, 56])).
% 0.20/0.54 % SZS output end Proof
% 0.20/0.54 % E exiting
%------------------------------------------------------------------------------