TSTP Solution File: GEO226+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO226+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 20:35:53 EDT 2022
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO226+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.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 07:07:20 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.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(distinct_points_type, type, (
% 0.13/0.41 distinct_points: ( $i * $i ) > $o)).
% 0.13/0.41 tff(intersection_point_type, type, (
% 0.13/0.41 intersection_point: ( $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_M_0_type, type, (
% 0.13/0.41 tptp_fun_M_0: $i)).
% 0.13/0.41 tff(tptp_fun_L_1_type, type, (
% 0.13/0.41 tptp_fun_L_1: $i)).
% 0.13/0.41 tff(apart_point_and_line_type, type, (
% 0.13/0.41 apart_point_and_line: ( $i * $i ) > $o)).
% 0.13/0.41 tff(point_type, type, (
% 0.13/0.41 point: $i > $o)).
% 0.13/0.41 tff(convergent_lines_type, type, (
% 0.13/0.41 convergent_lines: ( $i * $i ) > $o)).
% 0.13/0.41 tff(line_type, type, (
% 0.13/0.41 line: $i > $o)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (^[X: $i] : refl((~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0))))) <=> (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0))))) <=> ![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (^[X: $i] : rewrite((~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0))))) <=> (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(4,plain,
% 0.13/0.41 (![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0))))) <=> ![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (((line(L!1) & line(M!0) & convergent_lines(L!1, M!0)) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0)))))) <=> (line(L!1) & line(M!0) & convergent_lines(L!1, M!0) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(6,plain,
% 0.13/0.41 ((~(~(line(L!1) & line(M!0) & convergent_lines(L!1, M!0)))) <=> (line(L!1) & line(M!0) & convergent_lines(L!1, M!0))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 (((~(~(line(L!1) & line(M!0) & convergent_lines(L!1, M!0)))) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0)))))) <=> ((line(L!1) & line(M!0) & convergent_lines(L!1, M!0)) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0))))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[6])).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 (((~(~(line(L!1) & line(M!0) & convergent_lines(L!1, M!0)))) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0)))))) <=> (line(L!1) & line(M!0) & convergent_lines(L!1, M!0) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[7, 5])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 ((~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))) <=> (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 ((~![L: $i, M: $i] : (((line(L) & line(M)) & convergent_lines(L, M)) => ?[X: $i] : (point(X) => ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))) <=> (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(11,axiom,(~![L: $i, M: $i] : (((line(L) & line(M)) & convergent_lines(L, M)) => ?[X: $i] : (point(X) => ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.13/0.41 tff(15,plain,
% 0.13/0.41 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[15, 9])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[17, 9])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (line(L!1) & line(M!0) & convergent_lines(L!1, M!0) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 (![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0)))))),
% 0.13/0.41 inference(and_elim,[status(thm)],[19])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 (![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[20, 4])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 (![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 ((~![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))) | (~((~point(intersection_point(L!1, M!0))) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (~((~point(intersection_point(L!1, M!0))) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (((~point(intersection_point(L!1, M!0))) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)))) | (apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (convergent_lines(L!1, M!0)),
% 0.13/0.41 inference(and_elim,[status(thm)],[19])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (^[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)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (![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))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (^[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))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.41 tff(33,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')).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.41 tff(36,plain,(
% 0.20/0.41 ![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))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[35])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (((~![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(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!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(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 ((distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)))) <=> ((~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((~(apart_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), L!1))) <=> (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 ((distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), L!1)))) <=> (distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), L!1)))) <=> ((~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[41, 39])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (((~![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(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), L!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(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (((~![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(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), L!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(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[43, 38])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), L!1))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[46, 37, 27, 26])).
% 0.20/0.42 tff(48,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(49,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)],[48])).
% 0.20/0.42 tff(50,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(51,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.42 tff(53,plain,(
% 0.20/0.42 ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.42 inference(skolemize,[status(sab)],[52])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[55, 54, 47])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------