TSTP Solution File: GEO226+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO226+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 0.15s 0.34s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : GEO226+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29 % Computer : n011.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Wed Aug 31 07:01:56 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.29 Usage: tptp [options] [-file:]file
% 0.09/0.29 -h, -? prints this message.
% 0.09/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.29 -m, -model generate model.
% 0.09/0.29 -p, -proof generate proof.
% 0.09/0.29 -c, -core generate unsat core of named formulas.
% 0.09/0.29 -st, -statistics display statistics.
% 0.09/0.29 -t:timeout set timeout (in second).
% 0.09/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.29 -<param>:<value> configuration parameter and value.
% 0.09/0.29 -o:<output-file> file to place output in.
% 0.15/0.34 % SZS status Theorem
% 0.15/0.34 % SZS output start Proof
% 0.15/0.34 tff(incident_point_and_line_type, type, (
% 0.15/0.34 incident_point_and_line: ( $i * $i ) > $o)).
% 0.15/0.34 tff(tptp_fun_M_0_type, type, (
% 0.15/0.34 tptp_fun_M_0: $i)).
% 0.15/0.34 tff(intersection_point_type, type, (
% 0.15/0.34 intersection_point: ( $i * $i ) > $i)).
% 0.15/0.34 tff(tptp_fun_L_1_type, type, (
% 0.15/0.34 tptp_fun_L_1: $i)).
% 0.15/0.34 tff(point_type, type, (
% 0.15/0.34 point: $i > $o)).
% 0.15/0.34 tff(convergent_lines_type, type, (
% 0.15/0.34 convergent_lines: ( $i * $i ) > $o)).
% 0.15/0.34 tff(line_type, type, (
% 0.15/0.34 line: $i > $o)).
% 0.15/0.34 tff(apart_point_and_line_type, type, (
% 0.15/0.34 apart_point_and_line: ( $i * $i ) > $o)).
% 0.15/0.34 tff(1,plain,
% 0.15/0.34 (^[X: $i] : refl((~((~point(X)) | (~((~incident_point_and_line(X, L!1)) | (~incident_point_and_line(X, M!0)))))) <=> (~((~point(X)) | (~((~incident_point_and_line(X, L!1)) | (~incident_point_and_line(X, M!0)))))))),
% 0.15/0.34 inference(bind,[status(th)],[])).
% 0.15/0.34 tff(2,plain,
% 0.15/0.34 (![X: $i] : (~((~point(X)) | (~((~incident_point_and_line(X, L!1)) | (~incident_point_and_line(X, M!0)))))) <=> ![X: $i] : (~((~point(X)) | (~((~incident_point_and_line(X, L!1)) | (~incident_point_and_line(X, M!0))))))),
% 0.15/0.34 inference(quant_intro,[status(thm)],[1])).
% 0.15/0.34 tff(3,plain,
% 0.15/0.34 (^[X: $i] : rewrite((~((~point(X)) | (incident_point_and_line(X, L!1) & incident_point_and_line(X, M!0)))) <=> (~((~point(X)) | (~((~incident_point_and_line(X, L!1)) | (~incident_point_and_line(X, M!0)))))))),
% 0.15/0.34 inference(bind,[status(th)],[])).
% 0.15/0.34 tff(4,plain,
% 0.15/0.34 (![X: $i] : (~((~point(X)) | (incident_point_and_line(X, L!1) & incident_point_and_line(X, M!0)))) <=> ![X: $i] : (~((~point(X)) | (~((~incident_point_and_line(X, L!1)) | (~incident_point_and_line(X, M!0))))))),
% 0.15/0.34 inference(quant_intro,[status(thm)],[3])).
% 0.15/0.34 tff(5,plain,
% 0.15/0.34 (((line(L!1) & line(M!0) & convergent_lines(L!1, M!0)) & ![X: $i] : (~((~point(X)) | (incident_point_and_line(X, L!1) & incident_point_and_line(X, M!0))))) <=> (line(L!1) & line(M!0) & convergent_lines(L!1, M!0) & ![X: $i] : (~((~point(X)) | (incident_point_and_line(X, L!1) & incident_point_and_line(X, M!0)))))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(6,plain,
% 0.15/0.34 ((~(~(line(L!1) & line(M!0) & convergent_lines(L!1, M!0)))) <=> (line(L!1) & line(M!0) & convergent_lines(L!1, M!0))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(7,plain,
% 0.15/0.34 (((~(~(line(L!1) & line(M!0) & convergent_lines(L!1, M!0)))) & ![X: $i] : (~((~point(X)) | (incident_point_and_line(X, L!1) & incident_point_and_line(X, M!0))))) <=> ((line(L!1) & line(M!0) & convergent_lines(L!1, M!0)) & ![X: $i] : (~((~point(X)) | (incident_point_and_line(X, L!1) & incident_point_and_line(X, M!0)))))),
% 0.15/0.34 inference(monotonicity,[status(thm)],[6])).
% 0.15/0.34 tff(8,plain,
% 0.15/0.34 (((~(~(line(L!1) & line(M!0) & convergent_lines(L!1, M!0)))) & ![X: $i] : (~((~point(X)) | (incident_point_and_line(X, L!1) & incident_point_and_line(X, M!0))))) <=> (line(L!1) & line(M!0) & convergent_lines(L!1, M!0) & ![X: $i] : (~((~point(X)) | (incident_point_and_line(X, L!1) & incident_point_and_line(X, M!0)))))),
% 0.15/0.34 inference(transitivity,[status(thm)],[7, 5])).
% 0.15/0.34 tff(9,plain,
% 0.15/0.34 ((~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | (incident_point_and_line(X, L) & incident_point_and_line(X, M))))) <=> (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | (incident_point_and_line(X, L) & incident_point_and_line(X, M)))))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(10,plain,
% 0.15/0.34 ((~![L: $i, M: $i] : (((line(L) & line(M)) & convergent_lines(L, M)) => ?[X: $i] : (point(X) => (incident_point_and_line(X, L) & incident_point_and_line(X, M))))) <=> (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | (incident_point_and_line(X, L) & incident_point_and_line(X, M)))))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(11,axiom,(~![L: $i, M: $i] : (((line(L) & line(M)) & convergent_lines(L, M)) => ?[X: $i] : (point(X) => (incident_point_and_line(X, L) & incident_point_and_line(X, M))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.15/0.34 tff(12,plain,
% 0.15/0.34 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | (incident_point_and_line(X, L) & incident_point_and_line(X, M))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.15/0.34 tff(13,plain,
% 0.15/0.34 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | (incident_point_and_line(X, L) & incident_point_and_line(X, M))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.15/0.34 tff(14,plain,
% 0.15/0.34 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | (incident_point_and_line(X, L) & incident_point_and_line(X, M))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.15/0.34 tff(15,plain,
% 0.15/0.34 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | (incident_point_and_line(X, L) & incident_point_and_line(X, M))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.15/0.34 tff(16,plain,
% 0.15/0.34 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | (incident_point_and_line(X, L) & incident_point_and_line(X, M))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[15, 9])).
% 0.15/0.34 tff(17,plain,
% 0.15/0.34 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | (incident_point_and_line(X, L) & incident_point_and_line(X, M))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.15/0.34 tff(18,plain,
% 0.15/0.34 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | (incident_point_and_line(X, L) & incident_point_and_line(X, M))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[17, 9])).
% 0.15/0.34 tff(19,plain,
% 0.15/0.34 (line(L!1) & line(M!0) & convergent_lines(L!1, M!0) & ![X: $i] : (~((~point(X)) | (incident_point_and_line(X, L!1) & incident_point_and_line(X, M!0))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.15/0.34 tff(20,plain,
% 0.15/0.34 (![X: $i] : (~((~point(X)) | (incident_point_and_line(X, L!1) & incident_point_and_line(X, M!0))))),
% 0.15/0.34 inference(and_elim,[status(thm)],[19])).
% 0.15/0.34 tff(21,plain,
% 0.15/0.34 (![X: $i] : (~((~point(X)) | (~((~incident_point_and_line(X, L!1)) | (~incident_point_and_line(X, M!0))))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[20, 4])).
% 0.15/0.34 tff(22,plain,
% 0.15/0.34 (![X: $i] : (~((~point(X)) | (~((~incident_point_and_line(X, L!1)) | (~incident_point_and_line(X, M!0))))))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.15/0.34 tff(23,plain,
% 0.15/0.34 ((~![X: $i] : (~((~point(X)) | (~((~incident_point_and_line(X, L!1)) | (~incident_point_and_line(X, M!0))))))) | (~((~point(intersection_point(L!1, M!0))) | (~((~incident_point_and_line(intersection_point(L!1, M!0), L!1)) | (~incident_point_and_line(intersection_point(L!1, M!0), M!0))))))),
% 0.15/0.34 inference(quant_inst,[status(thm)],[])).
% 0.15/0.34 tff(24,plain,
% 0.15/0.34 (~((~point(intersection_point(L!1, M!0))) | (~((~incident_point_and_line(intersection_point(L!1, M!0), L!1)) | (~incident_point_and_line(intersection_point(L!1, M!0), M!0)))))),
% 0.15/0.34 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.15/0.34 tff(25,plain,
% 0.15/0.34 (((~point(intersection_point(L!1, M!0))) | (~((~incident_point_and_line(intersection_point(L!1, M!0), L!1)) | (~incident_point_and_line(intersection_point(L!1, M!0), M!0))))) | ((~incident_point_and_line(intersection_point(L!1, M!0), L!1)) | (~incident_point_and_line(intersection_point(L!1, M!0), M!0)))),
% 0.15/0.34 inference(tautology,[status(thm)],[])).
% 0.15/0.34 tff(26,plain,
% 0.15/0.34 ((~incident_point_and_line(intersection_point(L!1, M!0), L!1)) | (~incident_point_and_line(intersection_point(L!1, M!0), M!0))),
% 0.15/0.34 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.15/0.34 tff(27,plain,
% 0.15/0.34 (^[X: $i, Y: $i] : refl((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))))),
% 0.15/0.34 inference(bind,[status(th)],[])).
% 0.15/0.34 tff(28,plain,
% 0.15/0.34 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.15/0.34 inference(quant_intro,[status(thm)],[27])).
% 0.15/0.34 tff(29,plain,
% 0.15/0.34 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(30,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.15/0.34 tff(31,plain,
% 0.15/0.34 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.15/0.34 tff(32,plain,(
% 0.15/0.34 ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.15/0.34 inference(skolemize,[status(sab)],[31])).
% 0.15/0.34 tff(33,plain,
% 0.15/0.34 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.15/0.34 tff(34,plain,
% 0.15/0.34 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(intersection_point(L!1, M!0), M!0) <=> (~apart_point_and_line(intersection_point(L!1, M!0), M!0)))),
% 0.15/0.34 inference(quant_inst,[status(thm)],[])).
% 0.15/0.34 tff(35,plain,
% 0.15/0.34 (incident_point_and_line(intersection_point(L!1, M!0), M!0) <=> (~apart_point_and_line(intersection_point(L!1, M!0), M!0))),
% 0.15/0.34 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.15/0.34 tff(36,plain,
% 0.15/0.34 (convergent_lines(L!1, M!0)),
% 0.15/0.34 inference(and_elim,[status(thm)],[19])).
% 0.15/0.34 tff(37,plain,
% 0.15/0.34 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.15/0.34 inference(bind,[status(th)],[])).
% 0.15/0.34 tff(38,plain,
% 0.15/0.34 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.15/0.34 inference(quant_intro,[status(thm)],[37])).
% 0.15/0.34 tff(39,plain,
% 0.15/0.34 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(40,plain,
% 0.15/0.34 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.15/0.34 inference(bind,[status(th)],[])).
% 0.15/0.34 tff(41,plain,
% 0.15/0.34 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.15/0.34 inference(quant_intro,[status(thm)],[40])).
% 0.15/0.34 tff(42,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.15/0.34 tff(43,plain,
% 0.15/0.34 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.15/0.34 tff(44,plain,
% 0.15/0.34 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.15/0.34 tff(45,plain,(
% 0.15/0.34 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.15/0.34 inference(skolemize,[status(sab)],[44])).
% 0.15/0.34 tff(46,plain,
% 0.15/0.34 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.15/0.34 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.15/0.34 tff(47,plain,
% 0.15/0.34 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), M!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), M!0)))),
% 0.15/0.34 inference(rewrite,[status(thm)],[])).
% 0.15/0.34 tff(48,plain,
% 0.15/0.34 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), M!0)))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(49,plain,
% 0.15/0.35 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), M!0))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.15/0.35 tff(50,plain,
% 0.15/0.35 (~apart_point_and_line(intersection_point(L!1, M!0), M!0)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[49, 46, 36])).
% 0.15/0.35 tff(51,plain,
% 0.15/0.35 ((~(incident_point_and_line(intersection_point(L!1, M!0), M!0) <=> (~apart_point_and_line(intersection_point(L!1, M!0), M!0)))) | incident_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), M!0)),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(52,plain,
% 0.15/0.35 ((~(incident_point_and_line(intersection_point(L!1, M!0), M!0) <=> (~apart_point_and_line(intersection_point(L!1, M!0), M!0)))) | incident_point_and_line(intersection_point(L!1, M!0), M!0)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.15/0.35 tff(53,plain,
% 0.15/0.35 (incident_point_and_line(intersection_point(L!1, M!0), M!0)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[52, 35])).
% 0.15/0.35 tff(54,plain,
% 0.15/0.35 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(intersection_point(L!1, M!0), L!1) <=> (~apart_point_and_line(intersection_point(L!1, M!0), L!1)))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(55,plain,
% 0.15/0.35 (incident_point_and_line(intersection_point(L!1, M!0), L!1) <=> (~apart_point_and_line(intersection_point(L!1, M!0), L!1))),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[54, 33])).
% 0.15/0.35 tff(56,plain,
% 0.15/0.35 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(57,plain,
% 0.15/0.35 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[56])).
% 0.15/0.35 tff(58,plain,
% 0.15/0.35 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(59,plain,
% 0.15/0.35 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.15/0.35 inference(bind,[status(th)],[])).
% 0.15/0.35 tff(60,plain,
% 0.15/0.35 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.15/0.35 inference(quant_intro,[status(thm)],[59])).
% 0.15/0.35 tff(61,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.15/0.35 tff(62,plain,
% 0.15/0.35 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.15/0.35 tff(63,plain,
% 0.15/0.35 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.15/0.35 tff(64,plain,(
% 0.15/0.35 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.15/0.35 inference(skolemize,[status(sab)],[63])).
% 0.15/0.35 tff(65,plain,
% 0.15/0.35 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.15/0.35 tff(66,plain,
% 0.15/0.35 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), L!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), L!1)))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(67,plain,
% 0.15/0.35 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), L!1)))),
% 0.15/0.35 inference(quant_inst,[status(thm)],[])).
% 0.15/0.35 tff(68,plain,
% 0.15/0.35 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(L!1, M!0)) | (~apart_point_and_line(intersection_point(L!1, M!0), L!1))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.15/0.35 tff(69,plain,
% 0.15/0.35 (~apart_point_and_line(intersection_point(L!1, M!0), L!1)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[68, 65, 36])).
% 0.15/0.35 tff(70,plain,
% 0.15/0.35 ((~(incident_point_and_line(intersection_point(L!1, M!0), L!1) <=> (~apart_point_and_line(intersection_point(L!1, M!0), L!1)))) | incident_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), L!1)),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(71,plain,
% 0.15/0.35 ((~(incident_point_and_line(intersection_point(L!1, M!0), L!1) <=> (~apart_point_and_line(intersection_point(L!1, M!0), L!1)))) | incident_point_and_line(intersection_point(L!1, M!0), L!1)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.15/0.35 tff(72,plain,
% 0.15/0.35 (incident_point_and_line(intersection_point(L!1, M!0), L!1)),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[71, 55])).
% 0.15/0.35 tff(73,plain,
% 0.15/0.35 ((~((~incident_point_and_line(intersection_point(L!1, M!0), L!1)) | (~incident_point_and_line(intersection_point(L!1, M!0), M!0)))) | (~incident_point_and_line(intersection_point(L!1, M!0), L!1)) | (~incident_point_and_line(intersection_point(L!1, M!0), M!0))),
% 0.15/0.35 inference(tautology,[status(thm)],[])).
% 0.15/0.35 tff(74,plain,
% 0.15/0.35 ($false),
% 0.15/0.35 inference(unit_resolution,[status(thm)],[73, 72, 53, 26])).
% 0.15/0.35 % SZS output end Proof
%------------------------------------------------------------------------------