TSTP Solution File: GEO205+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 20:35:38 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 07:04:45 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(apart_point_and_line_type, type, (
% 0.20/0.42 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.42 tff(tptp_fun_Z_0_type, type, (
% 0.20/0.42 tptp_fun_Z_0: $i)).
% 0.20/0.42 tff(intersection_point_type, type, (
% 0.20/0.42 intersection_point: ( $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_X_2_type, type, (
% 0.20/0.42 tptp_fun_X_2: $i)).
% 0.20/0.42 tff(distinct_points_type, type, (
% 0.20/0.42 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.42 tff(convergent_lines_type, type, (
% 0.20/0.42 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.42 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.42 tptp_fun_Y_1: $i)).
% 0.20/0.42 tff(distinct_lines_type, type, (
% 0.20/0.42 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.42 tff(1,assumption,(distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0))), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.42 tff(7,plain,(
% 0.20/0.42 ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.42 inference(skolemize,[status(sab)],[6])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.42 tff(11,plain,(~distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & (~distinct_lines(Y, Z)))) | (convergent_lines(X, Z) & (~distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & (~distinct_lines(Y, Z)))) | (convergent_lines(X, Z) & (~distinct_points(intersection_point(X, Y), intersection_point(X, Z))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : ((convergent_lines(X, Y) & (~distinct_lines(Y, Z))) => (convergent_lines(X, Z) & (~distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & (~distinct_lines(Y, Z)))) | (convergent_lines(X, Z) & (~distinct_points(intersection_point(X, Y), intersection_point(X, Z))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(14,axiom,(~![X: $i, Y: $i, Z: $i] : ((convergent_lines(X, Y) & (~distinct_lines(Y, Z))) => (convergent_lines(X, Z) & (~distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & (~distinct_lines(Y, Z)))) | (convergent_lines(X, Z) & (~distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & (~distinct_lines(Y, Z)))) | (convergent_lines(X, Z) & (~distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & (~distinct_lines(Y, Z)))) | (convergent_lines(X, Z) & (~distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & (~distinct_lines(Y, Z)))) | (convergent_lines(X, Z) & (~distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & (~distinct_lines(Y, Z)))) | (convergent_lines(X, Z) & (~distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & (~distinct_lines(Y, Z)))) | (convergent_lines(X, Z) & (~distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (~![X: $i, Y: $i, Z: $i] : ((~(convergent_lines(X, Y) & (~distinct_lines(Y, Z)))) | (convergent_lines(X, Z) & (~distinct_points(intersection_point(X, Y), intersection_point(X, Z)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.20/0.42 tff(22,plain,(
% 0.20/0.42 ~((~(convergent_lines(X!2, Y!1) & (~distinct_lines(Y!1, Z!0)))) | (convergent_lines(X!2, Z!0) & (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[21])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (convergent_lines(X!2, Y!1) & (~distinct_lines(Y!1, Z!0))),
% 0.20/0.42 inference(or_elim,[status(thm)],[22])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (~distinct_lines(Y!1, Z!0)),
% 0.20/0.42 inference(and_elim,[status(thm)],[23])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.42 tff(30,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.42 tff(33,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.42 inference(skolemize,[status(sab)],[32])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(Y!1, Z!0)) | distinct_lines(Y!1, Z!0))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(Y!1, Z!0)) | distinct_lines(Y!1, Z!0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(Y!1, Z!0)) | distinct_lines(Y!1, Z!0))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(Y!1, Z!0)) | distinct_lines(Y!1, Z!0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (~convergent_lines(Y!1, Z!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[37, 34, 24])).
% 0.20/0.42 tff(39,assumption,(~convergent_lines(X!2, Z!0)), introduced(assumption)).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (convergent_lines(X!2, Y!1)),
% 0.20/0.42 inference(and_elim,[status(thm)],[23])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(42,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.43 tff(46,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart6')).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.43 tff(49,plain,(
% 0.20/0.43 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[48])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(X!2, Z!0) | convergent_lines(Y!1, Z!0) | (~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, Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(X!2, Y!1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 ((convergent_lines(Y!1, Z!0) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1))) <=> (convergent_lines(X!2, Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(X!2, Y!1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Z!0) | convergent_lines(X!2, Z!0) | (~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, Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(X!2, Y!1))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[52])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Z!0) | convergent_lines(X!2, Z!0) | (~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, Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(X!2, Y!1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[53, 51])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Z!0) | convergent_lines(X!2, Z!0) | (~convergent_lines(X!2, Y!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(X!2, Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(X!2, Y!1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[56, 50, 40, 39, 38])).
% 0.20/0.43 tff(58,plain,(convergent_lines(X!2, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (![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)))) <=> ![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (![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)))) <=> ![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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (^[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))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.43 tff(64,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/sandbox2/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.20/0.43 tff(67,plain,(
% 0.20/0.43 ![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))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[66])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (((~![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, Z!0)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))))) <=> ((~![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, Z!0)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))) <=> ((~convergent_lines(X!2, Z!0)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 ((~(apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2))) <=> (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 ((distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2)))) <=> (distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 ((distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2)))) <=> ((~convergent_lines(X!2, Z!0)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (((~![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, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), 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, Z!0)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[73])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (((~![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, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), 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, Z!0)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[74, 69])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 ((~![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, Z!0), intersection_point(X!2, Z!0)) | (~convergent_lines(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), X!2))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 ((~![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, Z!0)) | distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (distinct_points(intersection_point(X!2, Z!0), intersection_point(X!2, Z!0)) | (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[77, 68, 58])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (~(apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[78, 11])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 ((apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(X!2, Z!0), Z!0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 ((apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0)) | (~apart_point_and_line(intersection_point(X!2, Z!0), X!2))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(X!2, Z!0), X!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.20/0.43 tff(84,assumption,(distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))), introduced(assumption)).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[85, 8, 84])).
% 0.20/0.44 tff(87,plain,(~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 (((~![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)) | (~(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)))) <=> ((~![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)) | (~(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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 ((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)) | (~(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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 ((~(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), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 ((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), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[90])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 ((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)) | (~(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)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[91, 89])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (((~![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)) | (~(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))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (((~![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)) | (~(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)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[93, 88])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 ((~![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))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 ((~![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)) | (~(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))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[96, 68, 40, 87])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 ((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), Y!1))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 ((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))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (((~![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(X!2, Y!1)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (distinct_lines(X!2, Y!1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[104, 34, 40])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 ((~(~((~convergent_lines(X!2, Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> ((~convergent_lines(X!2, Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 ((convergent_lines(X!2, Z!0) & (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) <=> (~((~convergent_lines(X!2, Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 ((~(convergent_lines(X!2, Z!0) & (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> (~(~((~convergent_lines(X!2, Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 ((~(convergent_lines(X!2, Z!0) & (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> ((~convergent_lines(X!2, Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[108, 106])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (~(convergent_lines(X!2, Z!0) & (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 0.20/0.44 inference(or_elim,[status(thm)],[22])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 ((~convergent_lines(X!2, Z!0)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[111, 58])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (^[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_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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (![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_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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[115])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (^[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))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[118])).
% 0.20/0.44 tff(120,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','cu1')).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.20/0.45 tff(123,plain,(
% 0.20/0.45 ![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))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[122])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[124, 114])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), 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(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 ((apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Z!0), 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_lines(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0)))) <=> ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Z!0), 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_lines(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | ((~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[127])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Z!0), 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_lines(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_lines(U, V)) | (~distinct_points(X, Y)))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1))),
% 0.20/0.45 inference(transitivity,[status(thm)],[128, 126])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!2, Z!0), Y!1) | apart_point_and_line(intersection_point(X!2, Z!0), 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_lines(X!2, Y!1)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Z!0))) | (~distinct_lines(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 (apart_point_and_line(intersection_point(X!2, Z!0), 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) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[131, 125, 112, 105])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 (apart_point_and_line(intersection_point(X!2, Z!0), X!2) | apart_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[132, 101, 99])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (apart_point_and_line(intersection_point(X!2, Z!0), Y!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[133, 83])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.45 tff(140,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq2')).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.20/0.45 tff(143,plain,(
% 0.20/0.45 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[142])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Y!1, Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(Y!1, Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 ((distinct_lines(Y!1, Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1))) <=> (distinct_lines(Y!1, Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Y!1, Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Y!1, Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Y!1, Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(Y!1, Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0))),
% 0.20/0.45 inference(transitivity,[status(thm)],[147, 145])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Y!1, Z!0) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(Y!1, Z!0) | (~apart_point_and_line(intersection_point(X!2, Z!0), Y!1)) | apart_point_and_line(intersection_point(X!2, Z!0), Z!0)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[150, 144, 24, 134, 81])).
% 0.20/0.45 % SZS output end Proof
%------------------------------------------------------------------------------