TSTP Solution File: GEO225+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO225+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 20:35:52 EDT 2022
% Result : Theorem 0.14s 0.34s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GEO225+1 : TPTP v8.1.0. Released v3.3.0.
% 0.05/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.29 % Computer : n027.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 07:18:32 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.14/0.34 % SZS status Theorem
% 0.14/0.34 % SZS output start Proof
% 0.14/0.34 tff(apart_point_and_line_type, type, (
% 0.14/0.34 apart_point_and_line: ( $i * $i ) > $o)).
% 0.14/0.34 tff(line_connecting_type, type, (
% 0.14/0.34 line_connecting: ( $i * $i ) > $i)).
% 0.14/0.34 tff(tptp_fun_B_0_type, type, (
% 0.14/0.34 tptp_fun_B_0: $i)).
% 0.14/0.34 tff(tptp_fun_A_1_type, type, (
% 0.14/0.34 tptp_fun_A_1: $i)).
% 0.14/0.34 tff(line_type, type, (
% 0.14/0.34 line: $i > $o)).
% 0.14/0.34 tff(distinct_points_type, type, (
% 0.14/0.34 distinct_points: ( $i * $i ) > $o)).
% 0.14/0.34 tff(point_type, type, (
% 0.14/0.34 point: $i > $o)).
% 0.14/0.34 tff(1,plain,
% 0.14/0.34 (((point(A!1) & point(B!0) & distinct_points(A!1, B!0)) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X)))))) <=> (point(A!1) & point(B!0) & distinct_points(A!1, B!0) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X))))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(2,plain,
% 0.14/0.34 ((~(~(point(A!1) & point(B!0) & distinct_points(A!1, B!0)))) <=> (point(A!1) & point(B!0) & distinct_points(A!1, B!0))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(3,plain,
% 0.14/0.34 (((~(~(point(A!1) & point(B!0) & distinct_points(A!1, B!0)))) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X)))))) <=> ((point(A!1) & point(B!0) & distinct_points(A!1, B!0)) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X))))))),
% 0.14/0.34 inference(monotonicity,[status(thm)],[2])).
% 0.14/0.34 tff(4,plain,
% 0.14/0.34 (((~(~(point(A!1) & point(B!0) & distinct_points(A!1, B!0)))) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X)))))) <=> (point(A!1) & point(B!0) & distinct_points(A!1, B!0) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X))))))),
% 0.14/0.34 inference(transitivity,[status(thm)],[3, 1])).
% 0.14/0.34 tff(5,plain,
% 0.14/0.34 ((~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))) <=> (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X))))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(6,plain,
% 0.14/0.34 ((~![A: $i, B: $i] : (((point(A) & point(B)) & distinct_points(A, B)) => ?[X: $i] : (line(X) => ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))) <=> (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X))))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(7,axiom,(~![A: $i, B: $i] : (((point(A) & point(B)) & distinct_points(A, B)) => ?[X: $i] : (line(X) => ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.14/0.34 tff(8,plain,
% 0.14/0.34 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.14/0.34 tff(9,plain,
% 0.14/0.34 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.14/0.34 tff(10,plain,
% 0.14/0.34 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.14/0.34 tff(11,plain,
% 0.14/0.34 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.14/0.34 tff(12,plain,
% 0.14/0.34 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.14/0.34 tff(13,plain,
% 0.14/0.34 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.14/0.34 tff(14,plain,
% 0.14/0.34 (~![A: $i, B: $i] : ((~(point(A) & point(B) & distinct_points(A, B))) | ?[X: $i] : ((~line(X)) | ((~apart_point_and_line(A, X)) & (~apart_point_and_line(B, X)))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.14/0.34 tff(15,plain,
% 0.14/0.34 (point(A!1) & point(B!0) & distinct_points(A!1, B!0) & ![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X)))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.14/0.34 tff(16,plain,
% 0.14/0.34 (distinct_points(A!1, B!0)),
% 0.14/0.34 inference(and_elim,[status(thm)],[15])).
% 0.14/0.34 tff(17,plain,
% 0.14/0.34 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(18,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[17])).
% 0.14/0.34 tff(19,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(20,plain,
% 0.14/0.34 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(21,plain,
% 0.14/0.34 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[20])).
% 0.14/0.34 tff(22,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.14/0.34 tff(23,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.14/0.34 tff(24,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.14/0.34 tff(25,plain,(
% 0.14/0.34 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.34 inference(skolemize,[status(sab)],[24])).
% 0.14/0.34 tff(26,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.14/0.34 tff(27,plain,
% 0.14/0.34 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(28,plain,
% 0.14/0.34 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(29,plain,
% 0.14/0.34 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(A!1, line_connecting(A!1, B!0)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.14/0.34 tff(30,plain,
% 0.14/0.34 (~apart_point_and_line(A!1, line_connecting(A!1, B!0))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[29, 26, 16])).
% 0.14/0.34 tff(31,plain,
% 0.14/0.34 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(32,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[31])).
% 0.14/0.34 tff(33,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(34,plain,
% 0.14/0.34 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(35,plain,
% 0.14/0.34 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[34])).
% 0.14/0.34 tff(36,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.14/0.34 tff(37,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.14/0.34 tff(38,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.14/0.34 tff(39,plain,(
% 0.14/0.34 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.34 inference(skolemize,[status(sab)],[38])).
% 0.14/0.34 tff(40,plain,
% 0.14/0.34 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.14/0.34 tff(41,plain,
% 0.14/0.34 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(42,plain,
% 0.14/0.34 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(43,plain,
% 0.14/0.34 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(A!1, B!0)) | (~apart_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.14/0.34 tff(44,plain,
% 0.14/0.34 (~apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[43, 40, 16])).
% 0.14/0.34 tff(45,plain,
% 0.14/0.34 ((~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0)))) | apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(46,plain,
% 0.14/0.34 (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[45, 44, 30])).
% 0.14/0.34 tff(47,plain,
% 0.14/0.34 (((~line(line_connecting(A!1, B!0))) | (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))))) | (apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0)))),
% 0.14/0.34 inference(tautology,[status(thm)],[])).
% 0.14/0.34 tff(48,plain,
% 0.14/0.34 ((~line(line_connecting(A!1, B!0))) | (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))))),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.14/0.34 tff(49,plain,
% 0.14/0.34 (^[X: $i] : refl((~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X))))) <=> (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X))))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(50,plain,
% 0.14/0.34 (![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X))))) <=> ![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[49])).
% 0.14/0.34 tff(51,plain,
% 0.14/0.34 (^[X: $i] : rewrite((~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X))))) <=> (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X))))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(52,plain,
% 0.14/0.34 (![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X))))) <=> ![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[51])).
% 0.14/0.34 tff(53,plain,
% 0.14/0.34 (![X: $i] : (~((~line(X)) | ((~apart_point_and_line(A!1, X)) & (~apart_point_and_line(B!0, X)))))),
% 0.14/0.34 inference(and_elim,[status(thm)],[15])).
% 0.14/0.34 tff(54,plain,
% 0.14/0.34 (![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.14/0.34 tff(55,plain,
% 0.14/0.34 (![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.14/0.34 tff(56,plain,
% 0.14/0.34 ((~![X: $i] : (~((~line(X)) | (~(apart_point_and_line(A!1, X) | apart_point_and_line(B!0, X)))))) | (~((~line(line_connecting(A!1, B!0))) | (~(apart_point_and_line(A!1, line_connecting(A!1, B!0)) | apart_point_and_line(B!0, line_connecting(A!1, B!0))))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(57,plain,
% 0.14/0.34 ($false),
% 0.14/0.34 inference(unit_resolution,[status(thm)],[56, 55, 48])).
% 0.14/0.34 % SZS output end Proof
%------------------------------------------------------------------------------