%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO182+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 05:05:48 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO182+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % 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 14:39:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(distinct_lines_type, type, (
% 0.12/0.39 distinct_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(parallel_through_point_type, type, (
% 0.12/0.39 parallel_through_point: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_Z_0_type, type, (
% 0.12/0.39 tptp_fun_Z_0: $i)).
% 0.12/0.39 tff(line_connecting_type, type, (
% 0.12/0.39 line_connecting: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.39 tptp_fun_Y_1: $i)).
% 0.12/0.39 tff(tptp_fun_X_2_type, type, (
% 0.12/0.39 tptp_fun_X_2: $i)).
% 0.12/0.39 tff(convergent_lines_type, type, (
% 0.12/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(apart_point_and_line_type, type, (
% 0.12/0.39 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.39 tff(distinct_points_type, type, (
% 0.12/0.39 distinct_points: ( $i * $i ) > $o)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 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')).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.39 tff(6,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.12/0.39 inference(skolemize,[status(sab)],[5])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~convergent_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.39 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')).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.39 tff(18,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.12/0.39 inference(skolemize,[status(sab)],[17])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1))) | convergent_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1))) | convergent_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1))) | convergent_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1))) | convergent_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (~distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 ((~(apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> (~(apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => apart_point_and_line(Z, line_connecting(Y, X))))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(27,axiom,(~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => apart_point_and_line(Z, line_connecting(Y, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.12/0.40 tff(32,plain,(
% 0.12/0.40 ~(apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[31])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (~(apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (distinct_points(X!2, Y!1)),
% 0.12/0.40 inference(or_elim,[status(thm)],[33])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[35])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.40 tff(40,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.12/0.40 tff(43,plain,(
% 0.12/0.40 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[42])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[47, 44, 34])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.40 tff(54,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.12/0.40 tff(57,plain,(
% 0.12/0.40 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[56])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[61, 58, 34])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[63])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (^[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))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.12/0.40 tff(70,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/sandbox/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 (![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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.12/0.40 tff(73,plain,(
% 0.12/0.40 ![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))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[72])).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (((~![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)))) | ((~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 ((apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Y!1))) <=> ((~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 (((~![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(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | ((~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (((~![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(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[78, 76])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 ((~![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(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))) | (~distinct_points(X!2, Y!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((~![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)))) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[81, 75, 34, 62, 48])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.41 tff(88,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')).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.41 tff(91,plain,(
% 0.19/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[90])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 ((distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0)))) <=> (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[94])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[95, 93])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | distinct_lines(parallel_through_point(line_connecting(X!2, Y!1), Z!0), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (~distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[98, 92, 82, 23])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(103,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')).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.41 tff(105,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[104])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(Z!0, parallel_through_point(line_connecting(X!2, Y!1), Z!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (~apart_point_and_line(Z!0, parallel_through_point(line_connecting(X!2, Y!1), Z!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.19/0.41 inference(or_elim,[status(thm)],[33])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[113])).
% 0.19/0.41 tff(115,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')).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.19/0.41 tff(118,plain,(
% 0.19/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[117])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (((~![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(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(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(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 ((distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | apart_point_and_line(Z!0, parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))) <=> ((~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | apart_point_and_line(Z!0, parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | (~apart_point_and_line(Z!0, line_connecting(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(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[121])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | apart_point_and_line(Z!0, parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | (~apart_point_and_line(Z!0, line_connecting(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(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[122, 120])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | apart_point_and_line(Z!0, parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, parallel_through_point(line_connecting(X!2, Y!1), Z!0)) | distinct_lines(line_connecting(X!2, Y!1), parallel_through_point(line_connecting(X!2, Y!1), Z!0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[125, 119, 109, 108, 99])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------