TSTP Solution File: GEO226+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO226+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 0.35s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : GEO226+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n006.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Aug 31 07:02:54 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.15/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.31 Usage: tptp [options] [-file:]file
% 0.15/0.31 -h, -? prints this message.
% 0.15/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.31 -m, -model generate model.
% 0.15/0.31 -p, -proof generate proof.
% 0.15/0.31 -c, -core generate unsat core of named formulas.
% 0.15/0.31 -st, -statistics display statistics.
% 0.15/0.31 -t:timeout set timeout (in second).
% 0.15/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.31 -<param>:<value> configuration parameter and value.
% 0.15/0.31 -o:<output-file> file to place output in.
% 0.15/0.35 % SZS status Theorem
% 0.15/0.35 % SZS output start Proof
% 0.15/0.35 tff(apart_point_and_line_type, type, (
% 0.15/0.35 apart_point_and_line: ( $i * $i ) > $o)).
% 0.15/0.35 tff(tptp_fun_M_0_type, type, (
% 0.15/0.35 tptp_fun_M_0: $i)).
% 0.15/0.35 tff(intersection_point_type, type, (
% 0.15/0.35 intersection_point: ( $i * $i ) > $i)).
% 0.15/0.35 tff(tptp_fun_L_1_type, type, (
% 0.15/0.35 tptp_fun_L_1: $i)).
% 0.15/0.35 tff(point_type, type, (
% 0.15/0.35 point: $i > $o)).
% 0.15/0.35 tff(convergent_lines_type, type, (
% 0.15/0.35 convergent_lines: ( $i * $i ) > $o)).
% 0.15/0.35 tff(line_type, type, (
% 0.15/0.35 line: $i > $o)).
% 0.15/0.35 tff(1,plain,
% 0.15/0.35 (((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))))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(2,plain,
% 0.15/0.35 ((~(~(line(L!1) & line(M!0) & convergent_lines(L!1, M!0)))) <=> (line(L!1) & line(M!0) & convergent_lines(L!1, M!0))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(3,plain,
% 0.15/0.35 (((~(~(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))))))),
% 0.15/0.35 inference(monotonicity,[status(thm)],[2])).
% 0.15/0.35 tff(4,plain,
% 0.15/0.35 (((~(~(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))))))),
% 0.15/0.35 inference(transitivity,[status(thm)],[3, 1])).
% 0.15/0.35 tff(5,plain,
% 0.15/0.35 ((~![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))))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(6,plain,
% 0.15/0.35 ((~![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))))))),
% 0.15/0.35 inference(rewrite,[status(thm)],[])).
% 0.15/0.35 tff(7,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/sandbox2/benchmark/theBenchmark.p','con')).
% 0.15/0.35 tff(8,plain,
% 0.15/0.35 (~![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)))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.15/0.35 tff(9,plain,
% 0.15/0.35 (~![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)))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.15/0.35 tff(10,plain,
% 0.15/0.35 (~![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)))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.15/0.35 tff(11,plain,
% 0.15/0.35 (~![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)))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.15/0.35 tff(12,plain,
% 0.15/0.35 (~![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)))))),
% 0.15/0.35 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.15/0.35 tff(13,plain,
% 0.15/0.35 (~![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)))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.15/0.36 tff(14,plain,
% 0.15/0.36 (~![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)))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.15/0.36 tff(15,plain,
% 0.15/0.36 (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)))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.15/0.36 tff(16,plain,
% 0.15/0.36 (convergent_lines(L!1, M!0)),
% 0.15/0.36 inference(and_elim,[status(thm)],[15])).
% 0.15/0.36 tff(17,plain,
% 0.15/0.36 (^[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))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(18,plain,
% 0.15/0.36 (![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)))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[17])).
% 0.15/0.36 tff(19,plain,
% 0.15/0.36 (![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)))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(20,plain,
% 0.15/0.36 (^[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))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(21,plain,
% 0.15/0.36 (![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)))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[20])).
% 0.15/0.36 tff(22,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.15/0.36 tff(23,plain,
% 0.15/0.36 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.15/0.36 tff(24,plain,
% 0.15/0.36 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.15/0.36 tff(25,plain,(
% 0.15/0.36 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.15/0.36 inference(skolemize,[status(sab)],[24])).
% 0.15/0.36 tff(26,plain,
% 0.15/0.36 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.15/0.36 tff(27,plain,
% 0.15/0.36 (((~![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)))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(28,plain,
% 0.15/0.36 ((~![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)))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(29,plain,
% 0.15/0.36 ((~![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))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.15/0.36 tff(30,plain,
% 0.15/0.36 (~apart_point_and_line(intersection_point(L!1, M!0), L!1)),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[29, 26, 16])).
% 0.15/0.36 tff(31,plain,
% 0.15/0.36 (^[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))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(32,plain,
% 0.15/0.36 (![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)))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[31])).
% 0.15/0.36 tff(33,plain,
% 0.15/0.36 (![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)))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(34,plain,
% 0.15/0.36 (^[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))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(35,plain,
% 0.15/0.36 (![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)))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[34])).
% 0.15/0.36 tff(36,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.15/0.36 tff(37,plain,
% 0.15/0.36 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.15/0.36 tff(38,plain,
% 0.15/0.36 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.15/0.36 tff(39,plain,(
% 0.15/0.36 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.15/0.36 inference(skolemize,[status(sab)],[38])).
% 0.15/0.36 tff(40,plain,
% 0.15/0.36 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.15/0.36 tff(41,plain,
% 0.15/0.36 (((~![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)))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(42,plain,
% 0.15/0.36 ((~![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)))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(43,plain,
% 0.15/0.36 ((~![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))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.15/0.36 tff(44,plain,
% 0.15/0.36 (~apart_point_and_line(intersection_point(L!1, M!0), M!0)),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[43, 40, 16])).
% 0.15/0.36 tff(45,plain,
% 0.15/0.36 ((~(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)),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(46,plain,
% 0.15/0.36 (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[45, 44, 30])).
% 0.15/0.36 tff(47,plain,
% 0.15/0.36 (((~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))),
% 0.15/0.36 inference(tautology,[status(thm)],[])).
% 0.15/0.36 tff(48,plain,
% 0.15/0.36 ((~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)))),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.15/0.36 tff(49,plain,
% 0.15/0.36 (^[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))))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(50,plain,
% 0.15/0.36 (![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)))))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[49])).
% 0.15/0.36 tff(51,plain,
% 0.15/0.36 (^[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))))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(52,plain,
% 0.15/0.36 (![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)))))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[51])).
% 0.15/0.36 tff(53,plain,
% 0.15/0.36 (![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0)))))),
% 0.15/0.36 inference(and_elim,[status(thm)],[15])).
% 0.15/0.36 tff(54,plain,
% 0.15/0.36 (![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.15/0.36 tff(55,plain,
% 0.15/0.36 (![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.15/0.36 tff(56,plain,
% 0.15/0.36 ((~![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))) | (~((~point(intersection_point(L!1, M!0))) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)))))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(57,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[56, 55, 48])).
% 0.15/0.36 % SZS output end Proof
%------------------------------------------------------------------------------