%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO195+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:52 AM UTC 2025
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO195+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:40:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(distinct_lines_type, type, (
% 0.19/0.42 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.42 tff(parallel_through_point_type, type, (
% 0.19/0.42 parallel_through_point: ( $i * $i ) > $i)).
% 0.19/0.42 tff(intersection_point_type, type, (
% 0.19/0.42 intersection_point: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.42 tptp_fun_Y_1: $i)).
% 0.19/0.42 tff(tptp_fun_X_2_type, type, (
% 0.19/0.42 tptp_fun_X_2: $i)).
% 0.19/0.42 tff(tptp_fun_Z_0_type, type, (
% 0.19/0.42 tptp_fun_Z_0: $i)).
% 0.19/0.42 tff(convergent_lines_type, type, (
% 0.19/0.42 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.42 tff(apart_point_and_line_type, type, (
% 0.19/0.42 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(4,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.42 tff(6,plain,(
% 0.19/0.42 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.42 inference(skolemize,[status(sab)],[5])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (~convergent_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.42 tff(15,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.42 tff(18,plain,(
% 0.19/0.42 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.42 inference(skolemize,[status(sab)],[17])).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.42 tff(20,plain,
% 0.19/0.42 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)) | convergent_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)) | convergent_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)) | convergent_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)) | convergent_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (~distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(27,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.42 tff(29,plain,(
% 0.19/0.42 ![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.42 inference(skolemize,[status(sab)],[28])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 (![X: $i] : (~convergent_lines(X, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(Z!0, Z!0))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (~convergent_lines(Z!0, Z!0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 ((~(apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~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(Y!1, X!2), Z!0) | (~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)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~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(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 ((~![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(Y, X), Z)))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(36,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(Y, X), Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.19/0.42 tff(41,plain,(
% 0.19/0.42 ~(apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~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))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[40])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (~(apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 0.19/0.42 inference(or_elim,[status(thm)],[42])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.42 tff(49,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/sandbox2/benchmark/Axioms/GEO006+2.ax','cup1')).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.42 tff(52,plain,(
% 0.19/0.42 ![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)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[51])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (((~![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(Y!1, X!2), 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(Y!1, X!2), Z!0) | (~distinct_lines(Z!0, Z!0)) | convergent_lines(Z!0, Z!0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 ((convergent_lines(Z!0, Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~distinct_lines(Z!0, Z!0))) <=> (apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~distinct_lines(Z!0, Z!0)) | convergent_lines(Z!0, Z!0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (((~![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(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), 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(Y!1, X!2), Z!0) | (~distinct_lines(Z!0, Z!0)) | convergent_lines(Z!0, Z!0)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (((~![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(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), 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(Y!1, X!2), Z!0) | (~distinct_lines(Z!0, Z!0)) | convergent_lines(Z!0, Z!0))),
% 0.19/0.42 inference(transitivity,[status(thm)],[56, 54])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 ((~![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(Y!1, X!2), Z!0) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~distinct_lines(Z!0, Z!0)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 ((~![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(Y!1, X!2), Z!0) | (~distinct_lines(Z!0, Z!0)) | convergent_lines(Z!0, Z!0)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (~distinct_lines(Z!0, Z!0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[59, 53, 43, 32])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.43 tff(66,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart5')).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.43 tff(69,plain,(
% 0.19/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[68])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 (((~![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(X!2, Y!1)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))) <=> ((~![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(X!2, Y!1)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 ((distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))) <=> (distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (((~![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(X!2, Y!1)), Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))) <=> ((~![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(X!2, Y!1)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[72])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (((~![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(X!2, Y!1)), Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))) <=> ((~![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(X!2, Y!1)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 ((~![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(X!2, Y!1)), Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 ((~![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(X!2, Y!1)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[76, 70, 60, 23])).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(81,axiom,(![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cp2')).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.43 tff(83,plain,(
% 0.19/0.43 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[82])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 (apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.19/0.43 inference(or_elim,[status(thm)],[42])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.43 tff(93,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/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.19/0.43 tff(96,plain,(
% 0.19/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[95])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (((~![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(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))) <=> ((~![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(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 ((distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | (~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, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 (((~![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(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), 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(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[99])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 (((~![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(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), 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(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[100, 98])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 ((~![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(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[103, 97, 87, 86, 77])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------