TSTP Solution File: GEO195+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO195+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Fri Sep 16 20:35:31 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO195+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 07:01:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(apart_point_and_line_type, type, (
% 0.21/0.42 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.42 tptp_fun_Y_1: $i)).
% 0.21/0.42 tff(intersection_point_type, type, (
% 0.21/0.42 intersection_point: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_X_2_type, type, (
% 0.21/0.42 tptp_fun_X_2: $i)).
% 0.21/0.42 tff(distinct_points_type, type, (
% 0.21/0.42 distinct_points: ( $i * $i ) > $o)).
% 0.21/0.42 tff(convergent_lines_type, type, (
% 0.21/0.42 convergent_lines: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_Z_0_type, type, (
% 0.21/0.42 tptp_fun_Z_0: $i)).
% 0.21/0.42 tff(distinct_lines_type, type, (
% 0.21/0.42 distinct_lines: ( $i * $i ) > $o)).
% 0.21/0.42 tff(1,assumption,(distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2))), introduced(assumption)).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (![X: $i] : (~distinct_points(X, X))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.42 tff(7,plain,(
% 0.21/0.42 ![X: $i] : (~distinct_points(X, X))),
% 0.21/0.42 inference(skolemize,[status(sab)],[6])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (![X: $i] : (~distinct_points(X, X))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.42 tff(11,plain,(~distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(12,assumption,(apart_point_and_line(intersection_point(Y!1, X!2), X!2)), introduced(assumption)).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 ((apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.21/0.42 tff(15,assumption,(convergent_lines(X!2, X!2)), introduced(assumption)).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(19,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart3')).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.42 tff(21,plain,(
% 0.21/0.42 ![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.42 inference(skolemize,[status(sab)],[20])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 (![X: $i] : (~convergent_lines(X, X))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!2, X!2))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[23, 22, 15])).
% 0.21/0.42 tff(25,plain,(~convergent_lines(X!2, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 ((~(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)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 ((~![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)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 ((~![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)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(29,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/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (~![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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (~![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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (~![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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (~![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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (~![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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[33, 27])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (~![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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (~![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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[35, 27])).
% 0.21/0.42 tff(37,plain,(
% 0.21/0.42 ~(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))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[36])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (~(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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[37, 26])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0)),
% 0.21/0.42 inference(or_elim,[status(thm)],[38])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (convergent_lines(X!2, Y!1)),
% 0.21/0.42 inference(and_elim,[status(thm)],[39])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.42 tff(46,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.42 tff(49,plain,(
% 0.21/0.42 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[48])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 ((convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[52])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.21/0.42 inference(transitivity,[status(thm)],[53, 51])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[56, 50, 40])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 (convergent_lines(Y!1, X!2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[57, 25])).
% 0.21/0.42 tff(59,assumption,(~distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2))), introduced(assumption)).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) <=> (apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))))), rewrite(((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))))), rewrite((convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.43 tff(65,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.43 tff(68,plain,(
% 0.21/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[67])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2)) | (~convergent_lines(Y!1, X!2)) | (~(apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2)) | (~convergent_lines(Y!1, X!2)) | (~(apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2)) | (~convergent_lines(Y!1, X!2)) | (~(apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2)) | (~convergent_lines(Y!1, X!2)) | (~(apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[72, 69, 59, 58, 14])).
% 0.21/0.43 tff(74,plain,(distinct_points(intersection_point(Y!1, X!2), intersection_point(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[74, 11])).
% 0.21/0.43 tff(76,assumption,(distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))), introduced(assumption)).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[77, 8, 76])).
% 0.21/0.43 tff(79,plain,(~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 ((~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))) <=> (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[82])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[83, 81])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[85, 80])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[88, 69, 40, 79])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 ((apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 ((apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[92, 89])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.21/0.43 inference(or_elim,[status(thm)],[38])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 0.21/0.43 inference(or_elim,[status(thm)],[38])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | apart_point_and_line(Z, Y)) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))))), rewrite((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[99])).
% 0.21/0.43 tff(101,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq1')).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.21/0.43 tff(104,plain,(
% 0.21/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[103])).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), 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)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[107])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[108, 106])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2)) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 (distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[111, 105, 95, 94])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.44 tff(118,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.21/0.44 tff(121,plain,(
% 0.21/0.44 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.44 inference(skolemize,[status(sab)],[120])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (distinct_lines(X!2, Y!1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[125, 122, 40])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[127])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (^[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))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.44 tff(134,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/GEO008+0.ax','cu1')).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.21/0.44 tff(137,plain,(
% 0.21/0.44 ![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))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[136])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[138, 128])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))) | (~distinct_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))) | (~distinct_lines(X!2, Y!1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 ((apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))) | (~distinct_lines(X!2, Y!1))) <=> (apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))) | (~distinct_lines(X!2, Y!1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))) | (~distinct_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))) | (~distinct_lines(X!2, Y!1))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[141])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))) | (~distinct_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))) | (~distinct_lines(X!2, Y!1)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[142, 140])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))) | (~distinct_lines(X!2, Y!1)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(145,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Y!1, X!2))) | (~distinct_lines(X!2, Y!1))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 (apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[145, 139, 126, 112])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 (apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[146, 93, 91])).
% 0.21/0.45 tff(148,plain,
% 0.21/0.45 (apart_point_and_line(intersection_point(Y!1, X!2), Y!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[147, 75])).
% 0.21/0.45 tff(149,plain,
% 0.21/0.45 ((apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1)) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(150,plain,
% 0.21/0.45 (apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.21/0.45 tff(151,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[72, 69, 11, 58, 150])).
% 0.21/0.45 % SZS output end Proof
%------------------------------------------------------------------------------