%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO194+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:05:52 AM UTC 2025
% Result : Theorem 0.85s 1.02s
% Output : Proof 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO194+3 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 14:40:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.85/1.02 % SZS status Theorem
% 0.85/1.02 % SZS output start Proof
% 0.85/1.02 tff(convergent_lines_type, type, (
% 0.85/1.02 convergent_lines: ( $i * $i ) > $o)).
% 0.85/1.02 tff(tptp_fun_X_2_type, type, (
% 0.85/1.02 tptp_fun_X_2: $i)).
% 0.85/1.02 tff(distinct_lines_type, type, (
% 0.85/1.02 distinct_lines: ( $i * $i ) > $o)).
% 0.85/1.02 tff(tptp_fun_Y_1_type, type, (
% 0.85/1.02 tptp_fun_Y_1: $i)).
% 0.85/1.02 tff(distinct_points_type, type, (
% 0.85/1.02 distinct_points: ( $i * $i ) > $o)).
% 0.85/1.02 tff(intersection_point_type, type, (
% 0.85/1.02 intersection_point: ( $i * $i ) > $i)).
% 0.85/1.02 tff(tptp_fun_Z_0_type, type, (
% 0.85/1.02 tptp_fun_Z_0: $i)).
% 0.85/1.02 tff(apart_point_and_line_type, type, (
% 0.85/1.02 apart_point_and_line: ( $i * $i ) > $o)).
% 0.85/1.02 tff(1,assumption,(~convergent_lines(X!2, X!2)), introduced(assumption)).
% 0.85/1.02 tff(2,plain,
% 0.85/1.02 ((~(apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0))))) <=> (~(apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0)))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(3,plain,
% 0.85/1.02 ((~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z)))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(4,plain,
% 0.85/1.02 ((~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) => (apart_point_and_line(intersection_point(X, Y), Z) => apart_point_and_line(intersection_point(X, Z), Y)))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z)))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(5,axiom,(~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) => (apart_point_and_line(intersection_point(X, Y), Z) => apart_point_and_line(intersection_point(X, Z), Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.85/1.02 tff(6,plain,
% 0.85/1.02 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.85/1.02 tff(7,plain,
% 0.85/1.02 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.85/1.02 tff(8,plain,
% 0.85/1.02 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.85/1.02 tff(9,plain,
% 0.85/1.02 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(X, Z), Y) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.85/1.02 tff(10,plain,(
% 0.85/1.02 ~(apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0))))),
% 0.85/1.02 inference(skolemize,[status(sab)],[9])).
% 0.85/1.02 tff(11,plain,
% 0.85/1.02 (~(apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0))))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.85/1.02 tff(12,plain,
% 0.85/1.02 (convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0)),
% 0.85/1.02 inference(or_elim,[status(thm)],[11])).
% 0.85/1.02 tff(13,plain,
% 0.85/1.02 (convergent_lines(X!2, Z!0)),
% 0.85/1.02 inference(and_elim,[status(thm)],[12])).
% 0.85/1.02 tff(14,plain,
% 0.85/1.02 (^[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))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(15,plain,
% 0.85/1.02 (![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)))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[14])).
% 0.85/1.02 tff(16,plain,
% 0.85/1.02 (![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)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(17,plain,
% 0.85/1.02 (^[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))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(18,plain,
% 0.85/1.02 (![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)))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[17])).
% 0.85/1.02 tff(19,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')).
% 0.85/1.02 tff(20,plain,
% 0.85/1.02 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.85/1.02 tff(21,plain,
% 0.85/1.02 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.85/1.02 tff(22,plain,(
% 0.85/1.02 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.85/1.02 inference(skolemize,[status(sab)],[21])).
% 0.85/1.02 tff(23,plain,
% 0.85/1.02 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.85/1.02 tff(24,plain,
% 0.85/1.02 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(25,plain,
% 0.85/1.02 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(26,plain,
% 0.85/1.02 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.85/1.02 tff(27,plain,
% 0.85/1.02 (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.85/1.02 tff(28,plain,
% 0.85/1.02 (apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.85/1.02 inference(or_elim,[status(thm)],[11])).
% 0.85/1.02 tff(29,plain,
% 0.85/1.02 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(30,plain,
% 0.85/1.02 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[29])).
% 0.85/1.02 tff(31,plain,
% 0.85/1.02 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(32,plain,
% 0.85/1.02 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | apart_point_and_line(Z, Y)) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))))), rewrite((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(33,plain,
% 0.85/1.02 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[32])).
% 0.85/1.02 tff(34,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 0.85/1.02 tff(35,plain,
% 0.85/1.02 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.85/1.02 tff(36,plain,
% 0.85/1.02 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.85/1.02 tff(37,plain,(
% 0.85/1.02 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.85/1.02 inference(skolemize,[status(sab)],[36])).
% 0.85/1.02 tff(38,plain,
% 0.85/1.02 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.85/1.02 tff(39,plain,
% 0.85/1.02 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(40,plain,
% 0.85/1.02 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))) <=> ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(41,plain,
% 0.85/1.02 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[40])).
% 0.85/1.02 tff(42,plain,
% 0.85/1.02 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[41, 39])).
% 0.85/1.02 tff(43,plain,
% 0.85/1.02 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(44,plain,
% 0.85/1.03 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.85/1.03 tff(45,plain,
% 0.85/1.03 (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[44, 38, 28, 27])).
% 0.85/1.03 tff(46,plain,
% 0.85/1.03 (^[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))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(47,plain,
% 0.85/1.03 (![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)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[46])).
% 0.85/1.03 tff(48,plain,
% 0.85/1.03 (![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)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(49,plain,
% 0.85/1.03 (^[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))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(50,plain,
% 0.85/1.03 (![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)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[49])).
% 0.85/1.03 tff(51,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')).
% 0.85/1.03 tff(52,plain,
% 0.85/1.03 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.85/1.03 tff(53,plain,
% 0.85/1.03 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.85/1.03 tff(54,plain,(
% 0.85/1.03 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.85/1.03 inference(skolemize,[status(sab)],[53])).
% 0.85/1.03 tff(55,plain,
% 0.85/1.03 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.85/1.03 tff(56,plain,
% 0.85/1.03 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(57,plain,
% 0.85/1.03 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(58,plain,
% 0.85/1.03 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.85/1.03 tff(59,plain,
% 0.85/1.03 (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[58, 55, 13])).
% 0.85/1.03 tff(60,plain,
% 0.85/1.03 (convergent_lines(X!2, Y!1)),
% 0.85/1.03 inference(and_elim,[status(thm)],[12])).
% 0.85/1.03 tff(61,plain,
% 0.85/1.03 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(62,plain,
% 0.85/1.03 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(63,plain,
% 0.85/1.03 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.85/1.03 tff(64,plain,
% 0.85/1.03 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[63, 55, 60])).
% 0.85/1.03 tff(65,plain,
% 0.85/1.03 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(66,plain,
% 0.85/1.03 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(67,plain,
% 0.85/1.03 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.85/1.03 tff(68,plain,
% 0.85/1.03 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[67, 23, 60])).
% 0.85/1.03 tff(69,plain,
% 0.85/1.03 (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.85/1.03 inference(or_elim,[status(thm)],[11])).
% 0.85/1.03 tff(70,plain,
% 0.85/1.03 (^[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_lines(U, V)) | (~distinct_points(X, Y))) <=> (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_lines(U, V)) | (~distinct_points(X, Y))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(71,plain,
% 0.85/1.03 (![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_lines(U, V)) | (~distinct_points(X, Y))) <=> ![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[70])).
% 0.85/1.03 tff(72,plain,
% 0.85/1.03 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))))), rewrite((~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((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_lines(U, V)) | (~distinct_points(X, Y)))))), 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_lines(U, V)) | (~distinct_points(X, Y)))) <=> (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_lines(U, V)) | (~distinct_points(X, Y)))), ((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_lines(U, V)) | (~distinct_points(X, Y)))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(73,plain,
% 0.85/1.03 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[72])).
% 0.85/1.03 tff(74,plain,
% 0.85/1.03 (![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))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(75,plain,
% 0.85/1.03 (^[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))))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(76,plain,
% 0.85/1.03 (![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))))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[75])).
% 0.85/1.03 tff(77,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/GEO006+0.ax','cu1')).
% 0.85/1.03 tff(78,plain,
% 0.85/1.03 (![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))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.85/1.03 tff(79,plain,
% 0.85/1.03 (![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))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.85/1.03 tff(80,plain,(
% 0.85/1.03 ![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))))),
% 0.85/1.03 inference(skolemize,[status(sab)],[79])).
% 0.85/1.03 tff(81,plain,
% 0.85/1.03 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.85/1.03 tff(82,plain,
% 0.85/1.03 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.85/1.03 tff(83,plain,
% 0.85/1.03 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2)))) <=> ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(84,plain,
% 0.85/1.03 ((apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) <=> (apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(85,plain,
% 0.85/1.03 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[84])).
% 0.85/1.03 tff(86,plain,
% 0.85/1.03 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[85, 83])).
% 0.85/1.03 tff(87,plain,
% 0.85/1.03 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(88,plain,
% 0.85/1.03 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.85/1.03 tff(89,plain,
% 0.85/1.03 ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(Y!1, X!2))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[88, 82, 69, 68, 64, 59])).
% 0.85/1.03 tff(90,plain,
% 0.85/1.03 (~distinct_lines(Y!1, X!2)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[89, 45])).
% 0.85/1.03 tff(91,plain,
% 0.85/1.03 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(92,plain,
% 0.85/1.03 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[91])).
% 0.85/1.03 tff(93,plain,
% 0.85/1.03 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(94,plain,
% 0.85/1.03 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(95,plain,
% 0.85/1.03 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[94])).
% 0.85/1.03 tff(96,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.85/1.03 tff(97,plain,
% 0.85/1.03 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.85/1.03 tff(98,plain,
% 0.85/1.03 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.85/1.03 tff(99,plain,(
% 0.85/1.03 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.85/1.03 inference(skolemize,[status(sab)],[98])).
% 0.85/1.03 tff(100,plain,
% 0.85/1.03 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.85/1.03 tff(101,plain,
% 0.85/1.03 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(102,plain,
% 0.85/1.03 ((distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(103,plain,
% 0.85/1.03 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[102])).
% 0.85/1.03 tff(104,plain,
% 0.85/1.03 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.85/1.03 inference(transitivity,[status(thm)],[103, 101])).
% 0.85/1.03 tff(105,plain,
% 0.85/1.03 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(106,plain,
% 0.85/1.03 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.85/1.03 tff(107,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[106, 100, 60, 90, 1])).
% 0.85/1.03 tff(108,plain,(convergent_lines(X!2, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.85/1.03 tff(109,plain,
% 0.85/1.03 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(110,plain,
% 0.85/1.03 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[109])).
% 0.85/1.03 tff(111,plain,
% 0.85/1.03 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(112,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.85/1.03 tff(113,plain,
% 0.85/1.03 (![X: $i] : (~convergent_lines(X, X))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.85/1.03 tff(114,plain,(
% 0.85/1.03 ![X: $i] : (~convergent_lines(X, X))),
% 0.85/1.03 inference(skolemize,[status(sab)],[113])).
% 0.85/1.03 tff(115,plain,
% 0.85/1.03 (![X: $i] : (~convergent_lines(X, X))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.85/1.03 tff(116,plain,
% 0.85/1.03 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!2, X!2))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(117,plain,
% 0.85/1.03 ($false),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[116, 115, 108])).
% 0.85/1.03 % SZS output end Proof
% 0.85/1.03 % E exiting
%------------------------------------------------------------------------------