TSTP Solution File: GEO192+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO192+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 20:35:29 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO192+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 07:11:18 EDT 2022
% 0.13/0.34 % 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.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(distinct_lines_type, type, (
% 0.19/0.42 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_Z_0_type, type, (
% 0.19/0.42 tptp_fun_Z_0: $i)).
% 0.19/0.42 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.42 tptp_fun_Y_1: $i)).
% 0.19/0.42 tff(apart_point_and_line_type, type, (
% 0.19/0.42 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.42 tff(intersection_point_type, type, (
% 0.19/0.42 intersection_point: ( $i * $i ) > $i)).
% 0.19/0.42 tff(tptp_fun_X_2_type, type, (
% 0.19/0.42 tptp_fun_X_2: $i)).
% 0.19/0.42 tff(distinct_points_type, type, (
% 0.19/0.42 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.42 tff(convergent_lines_type, type, (
% 0.19/0.42 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.42 tff(1,assumption,(distinct_lines(Z!0, Z!0)), introduced(assumption)).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(5,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart2')).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.42 tff(7,plain,(
% 0.19/0.42 ![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.42 inference(skolemize,[status(sab)],[6])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(Z!0, Z!0))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.42 tff(11,plain,(~distinct_lines(Z!0, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(12,assumption,(distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))), introduced(assumption)).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(16,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 (![X: $i] : (~distinct_points(X, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.42 tff(18,plain,(
% 0.19/0.42 ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.42 inference(skolemize,[status(sab)],[17])).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 (![X: $i] : (~distinct_points(X, X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.42 tff(20,plain,
% 0.19/0.42 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.19/0.42 tff(22,plain,(~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 ((~((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> (~((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))) <=> (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (apart_point_and_line(intersection_point(X, Y), Z) => (distinct_lines(X, Z) & distinct_lines(Y, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(26,axiom,(~![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (apart_point_and_line(intersection_point(X, Y), Z) => (distinct_lines(X, Z) & distinct_lines(Y, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 (~![X: $i, Y: $i, Z: $i] : ((distinct_lines(X, Z) & distinct_lines(Y, Z)) | (~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Z)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.19/0.43 tff(34,plain,(
% 0.19/0.43 ~((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[33])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 (~((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[34, 23])).
% 0.19/0.43 tff(36,plain,
% 0.19/0.43 (convergent_lines(X!2, Y!1)),
% 0.19/0.43 inference(or_elim,[status(thm)],[35])).
% 0.19/0.43 tff(37,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(38,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.43 tff(39,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(40,plain,
% 0.19/0.43 (^[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))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(41,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.43 tff(42,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')).
% 0.19/0.43 tff(43,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.43 tff(44,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.19/0.43 tff(45,plain,(
% 0.19/0.43 ![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))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[44])).
% 0.19/0.43 tff(46,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.19/0.43 tff(47,plain,
% 0.19/0.43 (((~![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 ((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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 ((~(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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 ((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))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 ((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))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[50, 48])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (((~![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)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 (((~![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))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[52, 47])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 ((~![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))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 ((~![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)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (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)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[55, 46, 36])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (~(apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[56, 22])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 ((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))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.19/0.43 inference(or_elim,[status(thm)],[35])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.43 tff(66,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq2')).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.43 tff(69,plain,(
% 0.19/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[68])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.44 tff(71,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(72,plain,
% 0.19/0.44 ((distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))) <=> ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(73,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[72])).
% 0.19/0.44 tff(74,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.19/0.44 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.44 tff(75,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(76,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.44 tff(77,plain,
% 0.19/0.44 (distinct_lines(Z!0, Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[76, 70, 60])).
% 0.19/0.44 tff(78,plain,
% 0.19/0.44 (distinct_lines(Z!0, Y!1)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[77, 59])).
% 0.19/0.44 tff(79,plain,
% 0.19/0.44 ((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))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(80,plain,
% 0.19/0.44 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[79, 57])).
% 0.19/0.44 tff(81,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 ((distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))) <=> ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.19/0.44 inference(transitivity,[status(thm)],[83, 81])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 (distinct_lines(Z!0, X!2) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[86, 70, 60])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 (distinct_lines(Z!0, X!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[87, 80])).
% 0.19/0.44 tff(89,plain,
% 0.19/0.44 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(93,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.44 tff(94,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart5')).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.44 tff(96,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.19/0.44 tff(97,plain,(
% 0.19/0.44 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[96])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, X!2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, X!2)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, X!2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 (distinct_lines(X!2, Z!0) | distinct_lines(Z!0, Z!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[101, 98, 88])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 (distinct_lines(X!2, Z!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[102, 11])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 ((~(~((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0))))) <=> ((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 ((distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0)) <=> (~((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 ((~(distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0))) <=> (~(~((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0)))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[105])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 ((~(distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0))) <=> ((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[106, 104])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 (~(distinct_lines(X!2, Z!0) & distinct_lines(Y!1, Z!0))),
% 0.19/0.44 inference(or_elim,[status(thm)],[35])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 ((~distinct_lines(X!2, Z!0)) | (~distinct_lines(Y!1, Z!0))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.44 tff(110,plain,
% 0.19/0.44 (~distinct_lines(Y!1, Z!0)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[109, 103])).
% 0.19/0.44 tff(111,plain,
% 0.19/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Y!1, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, Y!1)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(112,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, Y!1)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(113,plain,
% 0.19/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Y!1, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, Y!1))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.44 tff(114,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[113, 98, 110, 78, 11])).
% 0.19/0.44 % SZS output end Proof
%------------------------------------------------------------------------------