%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO172+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:05:44 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO172+2 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:39:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(apart_point_and_line_type, type, (
% 0.11/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.37 tptp_fun_Y_1: $i)).
% 0.11/0.37 tff(intersection_point_type, type, (
% 0.11/0.37 intersection_point: ( $i * $i ) > $i)).
% 0.11/0.37 tff(tptp_fun_X_2_type, type, (
% 0.11/0.37 tptp_fun_X_2: $i)).
% 0.11/0.37 tff(distinct_points_type, type, (
% 0.11/0.37 distinct_points: ( $i * $i ) > $o)).
% 0.11/0.37 tff(convergent_lines_type, type, (
% 0.11/0.37 convergent_lines: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_Z_0_type, type, (
% 0.11/0.37 tptp_fun_Z_0: $i)).
% 0.11/0.37 tff(distinct_lines_type, type, (
% 0.11/0.37 distinct_lines: ( $i * $i ) > $o)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(4,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![X: $i] : (~distinct_points(X, X))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.37 tff(6,plain,(
% 0.11/0.37 ![X: $i] : (~distinct_points(X, X))),
% 0.11/0.37 inference(skolemize,[status(sab)],[5])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![X: $i] : (~distinct_points(X, X))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(Z, intersection_point(X, Y))) | (~(convergent_lines(X, Y) & (~apart_point_and_line(Z, X)) & (~apart_point_and_line(Z, Y)))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_points(Z, intersection_point(X, Y))) | (~(convergent_lines(X, Y) & (~apart_point_and_line(Z, X)) & (~apart_point_and_line(Z, Y))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 ((~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & (~apart_point_and_line(Z, X))) & (~apart_point_and_line(Z, Y))) => (~distinct_points(Z, intersection_point(X, Y))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_points(Z, intersection_point(X, Y))) | (~(convergent_lines(X, Y) & (~apart_point_and_line(Z, X)) & (~apart_point_and_line(Z, Y))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(12,axiom,(~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & (~apart_point_and_line(Z, X))) & (~apart_point_and_line(Z, Y))) => (~distinct_points(Z, intersection_point(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (~![X: $i, Y: $i, Z: $i] : ((~distinct_points(Z, intersection_point(X, Y))) | (~(convergent_lines(X, Y) & (~apart_point_and_line(Z, X)) & (~apart_point_and_line(Z, Y)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (~![X: $i, Y: $i, Z: $i] : ((~distinct_points(Z, intersection_point(X, Y))) | (~(convergent_lines(X, Y) & (~apart_point_and_line(Z, X)) & (~apart_point_and_line(Z, Y)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (~![X: $i, Y: $i, Z: $i] : ((~distinct_points(Z, intersection_point(X, Y))) | (~(convergent_lines(X, Y) & (~apart_point_and_line(Z, X)) & (~apart_point_and_line(Z, Y)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (~![X: $i, Y: $i, Z: $i] : ((~distinct_points(Z, intersection_point(X, Y))) | (~(convergent_lines(X, Y) & (~apart_point_and_line(Z, X)) & (~apart_point_and_line(Z, Y)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.11/0.37 tff(17,plain,(
% 0.11/0.37 ~((~distinct_points(Z!0, intersection_point(X!2, Y!1))) | (~(convergent_lines(X!2, Y!1) & (~apart_point_and_line(Z!0, X!2)) & (~apart_point_and_line(Z!0, Y!1)))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[16])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (convergent_lines(X!2, Y!1) & (~apart_point_and_line(Z!0, X!2)) & (~apart_point_and_line(Z!0, Y!1))),
% 0.11/0.37 inference(or_elim,[status(thm)],[17])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (convergent_lines(X!2, Y!1)),
% 0.11/0.37 inference(and_elim,[status(thm)],[18])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[20])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) <=> (apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))))), rewrite(((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))))), rewrite((convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.11/0.37 tff(25,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.11/0.38 tff(28,plain,(
% 0.11/0.38 ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[27])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 ((~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))) <=> (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[32])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[33, 31])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[34])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[35, 30])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[38, 29, 19, 9])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 ((apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 ((apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[47])).
% 0.11/0.38 tff(49,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.11/0.38 tff(52,plain,(
% 0.11/0.38 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.38 inference(skolemize,[status(sab)],[51])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (distinct_lines(X!2, Y!1)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[56, 53, 19])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 (~apart_point_and_line(Z!0, Y!1)),
% 0.11/0.38 inference(and_elim,[status(thm)],[18])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 (~apart_point_and_line(Z!0, X!2)),
% 0.11/0.38 inference(and_elim,[status(thm)],[18])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (distinct_points(Z!0, intersection_point(X!2, Y!1))),
% 0.11/0.38 inference(or_elim,[status(thm)],[17])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[61])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[63])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[66])).
% 0.11/0.38 tff(68,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','cu1')).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.11/0.38 tff(71,plain,(
% 0.11/0.38 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[70])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.11/0.38 tff(74,plain,
% 0.11/0.38 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | ((~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 ((apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(Z!0, Y!1) | apart_point_and_line(Z!0, X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | (~distinct_lines(X!2, Y!1))) <=> ((~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(Z!0, Y!1) | apart_point_and_line(Z!0, X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | (~distinct_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | ((~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[75])).
% 0.11/0.39 tff(77,plain,
% 0.11/0.39 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(Z!0, Y!1) | apart_point_and_line(Z!0, X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | (~distinct_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.11/0.39 inference(transitivity,[status(thm)],[76, 74])).
% 0.11/0.39 tff(78,plain,
% 0.11/0.39 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(Z!0, Y!1) | apart_point_and_line(Z!0, X!2) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | (~distinct_lines(X!2, Y!1)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(79,plain,
% 0.11/0.39 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(Z!0, X!2) | apart_point_and_line(Z!0, Y!1) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.11/0.39 tff(80,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[79, 73, 60, 59, 58, 57, 43, 41])).
% 0.11/0.39 % SZS output end Proof
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------