%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO199+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:05:54 AM UTC 2025
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO199+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 14:41:09 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(distinct_lines_type, type, (
% 0.21/0.41 distinct_lines: ( $i * $i ) > $o)).
% 0.21/0.41 tff(parallel_through_point_type, type, (
% 0.21/0.41 parallel_through_point: ( $i * $i ) > $i)).
% 0.21/0.41 tff(intersection_point_type, type, (
% 0.21/0.41 intersection_point: ( $i * $i ) > $i)).
% 0.21/0.41 tff(tptp_fun_X_2_type, type, (
% 0.21/0.41 tptp_fun_X_2: $i)).
% 0.21/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.41 tptp_fun_Y_1: $i)).
% 0.21/0.41 tff(tptp_fun_Z_0_type, type, (
% 0.21/0.41 tptp_fun_Z_0: $i)).
% 0.21/0.41 tff(convergent_lines_type, type, (
% 0.21/0.41 convergent_lines: ( $i * $i ) > $o)).
% 0.21/0.41 tff(apart_point_and_line_type, type, (
% 0.21/0.41 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.41 tff(incident_point_and_line_type, type, (
% 0.21/0.41 incident_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(4,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.41 tff(6,plain,(
% 0.21/0.41 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.21/0.41 inference(skolemize,[status(sab)],[5])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (~convergent_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.41 tff(15,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.41 tff(18,plain,(
% 0.21/0.41 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.41 inference(skolemize,[status(sab)],[17])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0)) | convergent_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0)) | convergent_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0)) | convergent_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0)) | convergent_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (~distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(27,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.41 tff(29,plain,(
% 0.21/0.41 ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.41 inference(skolemize,[status(sab)],[28])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(Z!0, Z!0))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (~convergent_lines(Z!0, Z!0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Y, X), Z))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Y, X), Z)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : ((((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) & incident_point_and_line(intersection_point(X, Y), Z)) => incident_point_and_line(intersection_point(Y, X), Z))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Y, X), Z)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(35,axiom,(~![X: $i, Y: $i, Z: $i] : ((((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) & incident_point_and_line(intersection_point(X, Y), Z)) => incident_point_and_line(intersection_point(Y, X), Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Y, X), Z))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Y, X), Z))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Y, X), Z))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & incident_point_and_line(intersection_point(X, Y), Z))) | incident_point_and_line(intersection_point(Y, X), Z))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.21/0.42 tff(40,plain,(
% 0.21/0.42 ~((~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0) & incident_point_and_line(intersection_point(X!2, Y!1), Z!0))) | incident_point_and_line(intersection_point(Y!1, X!2), Z!0))),
% 0.21/0.42 inference(skolemize,[status(sab)],[39])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0) & incident_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.21/0.42 inference(or_elim,[status(thm)],[40])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (convergent_lines(Z!0, Y!1)),
% 0.21/0.42 inference(and_elim,[status(thm)],[41])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[46])).
% 0.21/0.42 tff(48,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.21/0.42 tff(51,plain,(
% 0.21/0.42 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[50])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Z!0, Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[55, 52, 42])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[57])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) <=> (apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> ((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)))), rewrite(((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))))), rewrite((distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.42 tff(62,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cup1')).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.21/0.42 tff(65,plain,(
% 0.21/0.42 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[64])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Z!0)) | convergent_lines(Z!0, Z!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Z!0)) | convergent_lines(Z!0, Z!0))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 ((convergent_lines(Z!0, Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Z!0))) <=> (apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Z!0)) | convergent_lines(Z!0, Z!0))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Z!0, Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Z!0)) | convergent_lines(Z!0, Z!0)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[68])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Z!0, Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Z!0)) | convergent_lines(Z!0, Z!0))),
% 0.21/0.42 inference(transitivity,[status(thm)],[69, 67])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Z!0, Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Z!0)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | (~distinct_lines(Z!0, Z!0)) | convergent_lines(Z!0, Z!0)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (~distinct_lines(Z!0, Z!0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[72, 66, 56, 32])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[77])).
% 0.21/0.42 tff(79,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart5')).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.21/0.42 tff(82,plain,(
% 0.21/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[81])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 ((distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2))))) <=> (distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[85])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2)))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[86, 84])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2)))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(Y!1, X!2)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[89, 83, 73, 23])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : refl((~apart_point_and_line(X, parallel_through_point(Y, X))) <=> (~apart_point_and_line(X, parallel_through_point(Y, X))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(94,axiom,(![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp2')).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.42 tff(96,plain,(
% 0.21/0.42 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[95])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Z!0, intersection_point(Y!1, X!2))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (~apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Z!0, intersection_point(Y!1, X!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : refl((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[100])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (^[X: $i, Y: $i] : trans(rewrite((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), rewrite((~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))), ((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[103])).
% 0.21/0.43 tff(105,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.21/0.43 tff(108,plain,(
% 0.21/0.43 ![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[107])).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 (![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : (~(apart_point_and_line(X, Y) <=> incident_point_and_line(X, Y)))) | (~(apart_point_and_line(intersection_point(Y!1, X!2), Z!0) <=> incident_point_and_line(intersection_point(Y!1, X!2), Z!0)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 (~(apart_point_and_line(intersection_point(Y!1, X!2), Z!0) <=> incident_point_and_line(intersection_point(Y!1, X!2), Z!0))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.21/0.43 tff(112,plain,
% 0.21/0.43 (~incident_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 0.21/0.43 inference(or_elim,[status(thm)],[40])).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 ((apart_point_and_line(intersection_point(Y!1, X!2), Z!0) <=> incident_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | incident_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 ((apart_point_and_line(intersection_point(Y!1, X!2), Z!0) <=> incident_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.21/0.43 tff(115,plain,
% 0.21/0.43 (apart_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[114, 111])).
% 0.21/0.43 tff(116,plain,
% 0.21/0.43 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(117,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.43 tff(118,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(119,plain,
% 0.21/0.43 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(120,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[119])).
% 0.21/0.43 tff(121,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.21/0.43 tff(122,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.43 tff(123,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.21/0.43 tff(124,plain,(
% 0.21/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[123])).
% 0.21/0.43 tff(125,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.21/0.43 tff(126,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(127,plain,
% 0.21/0.43 ((distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0))) <=> ((~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(128,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[128, 126])).
% 0.21/0.43 tff(130,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(131,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(Y!1, X!2), parallel_through_point(Z!0, intersection_point(Y!1, X!2))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(Y!1, X!2)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[131, 125, 115, 99, 90])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------