%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO226+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:06:02 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO226+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 14:42:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(apart_point_and_line_type, type, (
% 0.12/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_M_0_type, type, (
% 0.12/0.37 tptp_fun_M_0: $i)).
% 0.12/0.37 tff(intersection_point_type, type, (
% 0.12/0.37 intersection_point: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_L_1_type, type, (
% 0.12/0.37 tptp_fun_L_1: $i)).
% 0.12/0.37 tff(point_type, type, (
% 0.12/0.37 point: $i > $o)).
% 0.12/0.37 tff(convergent_lines_type, type, (
% 0.12/0.37 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.37 tff(line_type, type, (
% 0.12/0.37 line: $i > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (((line(L!1) & line(M!0) & convergent_lines(L!1, M!0)) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0)))))) <=> (line(L!1) & line(M!0) & convergent_lines(L!1, M!0) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))) <=> (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 ((~![L: $i, M: $i] : (((line(L) & line(M)) & convergent_lines(L, M)) => ?[X: $i] : (point(X) => ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))) <=> (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(~![L: $i, M: $i] : (((line(L) & line(M)) & convergent_lines(L, M)) => ?[X: $i] : (point(X) => ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (line(L!1) & line(M!0) & convergent_lines(L!1, M!0) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (convergent_lines(L!1, M!0)),
% 0.12/0.37 inference(and_elim,[status(thm)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.37 tff(16,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.37 tff(19,plain,(
% 0.12/0.37 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[18])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), L!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), L!1)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), L!1)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), L!1))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (~apart_point_and_line(intersection_point(L!1, M!0), L!1)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.37 tff(30,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.12/0.38 tff(33,plain,(
% 0.12/0.38 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[32])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), M!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), M!0)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), M!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), M!0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (~apart_point_and_line(intersection_point(L!1, M!0), M!0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[37, 34, 10])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 ((~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[39, 38, 24])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (((~point(intersection_point(L!1, M!0))) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)))) | (apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~point(intersection_point(L!1, M!0))) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (^[X: $i] : refl((~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0))))) <=> (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0))))) <=> ![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (^[X: $i] : rewrite((~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0))))) <=> (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0))))) <=> ![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[45])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0)))))),
% 0.12/0.38 inference(and_elim,[status(thm)],[9])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 ((~![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))) | (~((~point(intersection_point(L!1, M!0))) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[50, 49, 42])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------