TSTP Solution File: GEO191+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO191+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 20:35:28 EDT 2022
% Result : Theorem 0.16s 0.39s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GEO191+2 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n008.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 06:54:10 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.31 Usage: tptp [options] [-file:]file
% 0.16/0.31 -h, -? prints this message.
% 0.16/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.31 -m, -model generate model.
% 0.16/0.31 -p, -proof generate proof.
% 0.16/0.31 -c, -core generate unsat core of named formulas.
% 0.16/0.31 -st, -statistics display statistics.
% 0.16/0.31 -t:timeout set timeout (in second).
% 0.16/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.31 -<param>:<value> configuration parameter and value.
% 0.16/0.31 -o:<output-file> file to place output in.
% 0.16/0.39 % SZS status Theorem
% 0.16/0.39 % SZS output start Proof
% 0.16/0.39 tff(apart_point_and_line_type, type, (
% 0.16/0.39 apart_point_and_line: ( $i * $i ) > $o)).
% 0.16/0.39 tff(tptp_fun_V_0_type, type, (
% 0.16/0.39 tptp_fun_V_0: $i)).
% 0.16/0.39 tff(intersection_point_type, type, (
% 0.16/0.39 intersection_point: ( $i * $i ) > $i)).
% 0.16/0.39 tff(tptp_fun_Y_2_type, type, (
% 0.16/0.39 tptp_fun_Y_2: $i)).
% 0.16/0.39 tff(tptp_fun_X_3_type, type, (
% 0.16/0.39 tptp_fun_X_3: $i)).
% 0.16/0.39 tff(distinct_points_type, type, (
% 0.16/0.39 distinct_points: ( $i * $i ) > $o)).
% 0.16/0.39 tff(tptp_fun_U_1_type, type, (
% 0.16/0.39 tptp_fun_U_1: $i)).
% 0.16/0.39 tff(convergent_lines_type, type, (
% 0.16/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.16/0.39 tff(distinct_lines_type, type, (
% 0.16/0.39 distinct_lines: ( $i * $i ) > $o)).
% 0.16/0.39 tff(1,assumption,(distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2))), introduced(assumption)).
% 0.16/0.39 tff(2,plain,
% 0.16/0.39 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(3,plain,
% 0.16/0.39 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.16/0.39 tff(4,plain,
% 0.16/0.39 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.16/0.39 tff(6,plain,
% 0.16/0.39 (![X: $i] : (~distinct_points(X, X))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.16/0.39 tff(7,plain,(
% 0.16/0.39 ![X: $i] : (~distinct_points(X, X))),
% 0.16/0.39 inference(skolemize,[status(sab)],[6])).
% 0.16/0.39 tff(8,plain,
% 0.16/0.39 (![X: $i] : (~distinct_points(X, X))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.16/0.39 tff(9,plain,
% 0.16/0.39 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(10,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.16/0.39 tff(11,plain,(~distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.39 tff(12,plain,
% 0.16/0.39 ((~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))))) <=> (~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(13,plain,
% 0.16/0.39 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U))))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(14,plain,
% 0.16/0.39 ((~![X: $i, Y: $i, U: $i, V: $i] : (((convergent_lines(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(intersection_point(X, Y), U) | apart_point_and_line(intersection_point(X, Y), V))) => (apart_point_and_line(intersection_point(U, V), X) | apart_point_and_line(intersection_point(U, V), Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U))))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(15,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((convergent_lines(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(intersection_point(X, Y), U) | apart_point_and_line(intersection_point(X, Y), V))) => (apart_point_and_line(intersection_point(U, V), X) | apart_point_and_line(intersection_point(U, V), Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.16/0.39 tff(16,plain,
% 0.16/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.16/0.39 tff(17,plain,
% 0.16/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.16/0.39 tff(18,plain,
% 0.16/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.16/0.39 tff(19,plain,
% 0.16/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.16/0.39 tff(20,plain,
% 0.16/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.16/0.39 tff(21,plain,
% 0.16/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.16/0.39 tff(22,plain,
% 0.16/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(intersection_point(U, V), Y) | apart_point_and_line(intersection_point(U, V), X) | (~(convergent_lines(X, Y) & convergent_lines(U, V) & (apart_point_and_line(intersection_point(X, Y), V) | apart_point_and_line(intersection_point(X, Y), U)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.16/0.39 tff(23,plain,(
% 0.16/0.39 ~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))))),
% 0.16/0.39 inference(skolemize,[status(sab)],[22])).
% 0.16/0.39 tff(24,plain,
% 0.16/0.39 (~(apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[23, 12])).
% 0.16/0.39 tff(25,plain,
% 0.16/0.39 (convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))),
% 0.16/0.39 inference(or_elim,[status(thm)],[24])).
% 0.16/0.39 tff(26,plain,
% 0.16/0.39 (convergent_lines(X!3, Y!2)),
% 0.16/0.39 inference(and_elim,[status(thm)],[25])).
% 0.16/0.39 tff(27,plain,
% 0.16/0.39 (^[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)))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(28,plain,
% 0.16/0.39 (![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))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.16/0.39 tff(29,plain,
% 0.16/0.39 (![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))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(30,plain,
% 0.16/0.39 (^[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))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(31,plain,
% 0.16/0.39 (![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))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.16/0.39 tff(32,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')).
% 0.16/0.39 tff(33,plain,
% 0.16/0.39 (![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))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.16/0.39 tff(34,plain,
% 0.16/0.39 (![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))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.16/0.39 tff(35,plain,(
% 0.16/0.39 ![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))))),
% 0.16/0.39 inference(skolemize,[status(sab)],[34])).
% 0.16/0.39 tff(36,plain,
% 0.16/0.39 (![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))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.16/0.39 tff(37,plain,
% 0.16/0.39 (((~![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!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))) <=> ((~![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!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(38,plain,
% 0.16/0.39 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))) <=> ((~convergent_lines(X!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(39,plain,
% 0.16/0.39 ((~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))) <=> (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(40,plain,
% 0.16/0.39 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))) <=> (distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[39])).
% 0.16/0.39 tff(41,plain,
% 0.16/0.39 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))) <=> ((~convergent_lines(X!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))),
% 0.16/0.39 inference(transitivity,[status(thm)],[40, 38])).
% 0.16/0.39 tff(42,plain,
% 0.16/0.39 (((~![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!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))) <=> ((~![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!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[41])).
% 0.16/0.39 tff(43,plain,
% 0.16/0.39 (((~![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!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))) <=> ((~![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!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))),
% 0.16/0.40 inference(transitivity,[status(thm)],[42, 37])).
% 0.16/0.40 tff(44,plain,
% 0.16/0.40 ((~![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!3, Y!2), intersection_point(X!3, Y!2)) | (~convergent_lines(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(45,plain,
% 0.16/0.40 ((~![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!3, Y!2)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.16/0.40 tff(46,plain,
% 0.16/0.40 (distinct_points(intersection_point(X!3, Y!2), intersection_point(X!3, Y!2)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[45, 36, 26])).
% 0.16/0.40 tff(47,plain,
% 0.16/0.40 (~(apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[46, 11])).
% 0.16/0.40 tff(48,plain,
% 0.16/0.40 ((apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(49,plain,
% 0.16/0.40 (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.16/0.40 tff(50,plain,
% 0.16/0.40 ((apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(51,plain,
% 0.16/0.40 (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.16/0.40 tff(52,assumption,(distinct_lines(X!3, X!3)), introduced(assumption)).
% 0.16/0.40 tff(53,plain,
% 0.16/0.40 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(54,plain,
% 0.16/0.40 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.16/0.40 tff(55,plain,
% 0.16/0.40 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(56,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart2')).
% 0.16/0.40 tff(57,plain,
% 0.16/0.40 (![X: $i] : (~distinct_lines(X, X))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.16/0.40 tff(58,plain,(
% 0.16/0.40 ![X: $i] : (~distinct_lines(X, X))),
% 0.16/0.40 inference(skolemize,[status(sab)],[57])).
% 0.16/0.40 tff(59,plain,
% 0.16/0.40 (![X: $i] : (~distinct_lines(X, X))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.16/0.40 tff(60,plain,
% 0.16/0.40 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(X!3, X!3))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(61,plain,
% 0.16/0.40 ($false),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[60, 59, 52])).
% 0.16/0.40 tff(62,plain,(~distinct_lines(X!3, X!3)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.40 tff(63,plain,
% 0.16/0.40 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(64,plain,
% 0.16/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[63])).
% 0.16/0.40 tff(65,plain,
% 0.16/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(66,plain,
% 0.16/0.40 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(67,plain,
% 0.16/0.40 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.16/0.40 tff(68,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.16/0.40 tff(69,plain,
% 0.16/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.16/0.40 tff(70,plain,
% 0.16/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.16/0.40 tff(71,plain,(
% 0.16/0.40 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.40 inference(skolemize,[status(sab)],[70])).
% 0.16/0.40 tff(72,plain,
% 0.16/0.40 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.16/0.40 tff(73,plain,
% 0.16/0.40 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!3, Y!2)) | distinct_lines(X!3, Y!2))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!3, Y!2)) | distinct_lines(X!3, Y!2))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(74,plain,
% 0.16/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(X!3, Y!2)) | distinct_lines(X!3, Y!2))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(75,plain,
% 0.16/0.40 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(X!3, Y!2)) | distinct_lines(X!3, Y!2)),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.16/0.40 tff(76,plain,
% 0.16/0.40 (distinct_lines(X!3, Y!2)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[75, 72, 26])).
% 0.16/0.40 tff(77,plain,
% 0.16/0.40 (^[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))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(78,plain,
% 0.16/0.40 (![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)))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.16/0.40 tff(79,plain,
% 0.16/0.40 (![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)))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(80,plain,
% 0.16/0.40 (^[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)))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(81,plain,
% 0.16/0.40 (![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)))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[80])).
% 0.16/0.40 tff(82,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')).
% 0.16/0.40 tff(83,plain,
% 0.16/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.16/0.40 tff(84,plain,
% 0.16/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.16/0.40 tff(85,plain,(
% 0.16/0.40 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.16/0.40 inference(skolemize,[status(sab)],[84])).
% 0.16/0.40 tff(86,plain,
% 0.16/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.16/0.40 tff(87,plain,
% 0.16/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | ((~distinct_lines(X!3, Y!2)) | distinct_lines(X!3, X!3) | distinct_lines(Y!2, X!3))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (~distinct_lines(X!3, Y!2)) | distinct_lines(X!3, X!3) | distinct_lines(Y!2, X!3))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(88,plain,
% 0.16/0.40 ((distinct_lines(Y!2, X!3) | distinct_lines(X!3, X!3) | (~distinct_lines(X!3, Y!2))) <=> ((~distinct_lines(X!3, Y!2)) | distinct_lines(X!3, X!3) | distinct_lines(Y!2, X!3))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(89,plain,
% 0.16/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!2, X!3) | distinct_lines(X!3, X!3) | (~distinct_lines(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | ((~distinct_lines(X!3, Y!2)) | distinct_lines(X!3, X!3) | distinct_lines(Y!2, X!3)))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[88])).
% 0.16/0.40 tff(90,plain,
% 0.16/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!2, X!3) | distinct_lines(X!3, X!3) | (~distinct_lines(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (~distinct_lines(X!3, Y!2)) | distinct_lines(X!3, X!3) | distinct_lines(Y!2, X!3))),
% 0.16/0.40 inference(transitivity,[status(thm)],[89, 87])).
% 0.16/0.40 tff(91,plain,
% 0.16/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!2, X!3) | distinct_lines(X!3, X!3) | (~distinct_lines(X!3, Y!2)))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(92,plain,
% 0.16/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (~distinct_lines(X!3, Y!2)) | distinct_lines(X!3, X!3) | distinct_lines(Y!2, X!3)),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.16/0.40 tff(93,plain,
% 0.16/0.40 (distinct_lines(X!3, X!3) | distinct_lines(Y!2, X!3)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[92, 86, 76])).
% 0.16/0.40 tff(94,plain,
% 0.16/0.40 (distinct_lines(Y!2, X!3)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[93, 62])).
% 0.16/0.40 tff(95,plain,
% 0.16/0.40 (~apart_point_and_line(intersection_point(U!1, V!0), X!3)),
% 0.16/0.40 inference(or_elim,[status(thm)],[24])).
% 0.16/0.40 tff(96,plain,
% 0.16/0.40 (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 0.16/0.40 inference(or_elim,[status(thm)],[24])).
% 0.16/0.40 tff(97,plain,
% 0.16/0.40 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(98,plain,
% 0.16/0.40 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[97])).
% 0.16/0.40 tff(99,plain,
% 0.16/0.40 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(100,plain,
% 0.16/0.40 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[99])).
% 0.16/0.40 tff(101,plain,
% 0.16/0.40 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(102,plain,
% 0.16/0.40 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(103,plain,
% 0.16/0.40 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[102])).
% 0.16/0.40 tff(104,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','cu1')).
% 0.16/0.40 tff(105,plain,
% 0.16/0.40 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.16/0.40 tff(106,plain,
% 0.16/0.40 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.16/0.40 tff(107,plain,(
% 0.16/0.40 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.16/0.40 inference(skolemize,[status(sab)],[106])).
% 0.16/0.40 tff(108,plain,
% 0.16/0.40 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.16/0.40 tff(109,plain,
% 0.16/0.40 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[108, 98])).
% 0.16/0.40 tff(110,plain,
% 0.16/0.40 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(111,plain,
% 0.16/0.40 ((apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | (~distinct_lines(Y!2, X!3))) <=> (apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(112,plain,
% 0.16/0.40 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | (~distinct_lines(Y!2, X!3)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3))))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[111])).
% 0.16/0.40 tff(113,plain,
% 0.16/0.40 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | (~distinct_lines(Y!2, X!3)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3)))),
% 0.16/0.40 inference(transitivity,[status(thm)],[112, 110])).
% 0.16/0.40 tff(114,plain,
% 0.16/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | (~distinct_lines(Y!2, X!3)))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(115,plain,
% 0.16/0.41 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~distinct_lines(Y!2, X!3))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.16/0.41 tff(116,plain,
% 0.16/0.41 (~distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[115, 109, 96, 95, 94, 51, 49])).
% 0.16/0.41 tff(117,plain,
% 0.16/0.41 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(118,plain,
% 0.16/0.41 ((apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2))) <=> (apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(119,plain,
% 0.16/0.41 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2))))),
% 0.16/0.41 inference(monotonicity,[status(thm)],[118])).
% 0.16/0.41 tff(120,plain,
% 0.16/0.41 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))),
% 0.16/0.41 inference(transitivity,[status(thm)],[119, 117])).
% 0.16/0.41 tff(121,plain,
% 0.16/0.41 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2)))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(122,plain,
% 0.16/0.41 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))) | (~distinct_lines(X!3, Y!2))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.16/0.41 tff(123,plain,
% 0.16/0.41 (~distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[122, 109, 96, 95, 76])).
% 0.16/0.41 tff(124,plain,
% 0.16/0.41 (convergent_lines(U!1, V!0)),
% 0.16/0.41 inference(and_elim,[status(thm)],[25])).
% 0.16/0.41 tff(125,plain,
% 0.16/0.41 (((~![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(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!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(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(126,plain,
% 0.16/0.41 ((distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)))) <=> ((~convergent_lines(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(127,plain,
% 0.16/0.41 ((~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))) <=> (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(128,plain,
% 0.16/0.41 ((distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)))) <=> (distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))),
% 0.16/0.41 inference(monotonicity,[status(thm)],[127])).
% 0.16/0.41 tff(129,plain,
% 0.16/0.41 ((distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)))) <=> ((~convergent_lines(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))),
% 0.16/0.41 inference(transitivity,[status(thm)],[128, 126])).
% 0.16/0.41 tff(130,plain,
% 0.16/0.41 (((~![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(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!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(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)))))),
% 0.16/0.41 inference(monotonicity,[status(thm)],[129])).
% 0.16/0.41 tff(131,plain,
% 0.16/0.41 (((~![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(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!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(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))),
% 0.16/0.41 inference(transitivity,[status(thm)],[130, 125])).
% 0.16/0.41 tff(132,plain,
% 0.16/0.41 ((~![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(U!1, V!0), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(133,plain,
% 0.16/0.41 ((~![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(U!1, V!0)) | distinct_points(intersection_point(U!1, V!0), intersection_point(U!1, V!0)) | (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 0.16/0.41 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.16/0.41 tff(134,plain,
% 0.16/0.41 (~(apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[133, 36, 124, 123])).
% 0.16/0.41 tff(135,plain,
% 0.16/0.41 ((apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(136,plain,
% 0.16/0.41 (~apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.16/0.42 tff(137,plain,
% 0.16/0.42 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(138,plain,
% 0.16/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[137])).
% 0.16/0.42 tff(139,plain,
% 0.16/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(140,plain,
% 0.16/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | apart_point_and_line(Z, Y)) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))))), rewrite((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(141,plain,
% 0.16/0.42 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[140])).
% 0.16/0.42 tff(142,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq1')).
% 0.16/0.42 tff(143,plain,
% 0.16/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.16/0.42 tff(144,plain,
% 0.16/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.16/0.42 tff(145,plain,(
% 0.16/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.16/0.42 inference(skolemize,[status(sab)],[144])).
% 0.16/0.42 tff(146,plain,
% 0.16/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.16/0.42 tff(147,plain,
% 0.16/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(148,plain,
% 0.16/0.42 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))) <=> (apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(149,plain,
% 0.16/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[148])).
% 0.16/0.42 tff(150,plain,
% 0.16/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)))),
% 0.16/0.42 inference(transitivity,[status(thm)],[149, 147])).
% 0.16/0.42 tff(151,plain,
% 0.16/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))),
% 0.16/0.42 inference(quant_inst,[status(thm)],[])).
% 0.16/0.42 tff(152,plain,
% 0.16/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.16/0.42 tff(153,plain,
% 0.16/0.42 ((~apart_point_and_line(intersection_point(X!3, Y!2), V!0)) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[152, 146, 136])).
% 0.16/0.42 tff(154,plain,
% 0.16/0.42 (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)),
% 0.16/0.42 inference(unit_resolution,[status(thm)],[153, 116])).
% 0.16/0.42 tff(155,plain,
% 0.16/0.42 (((~![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(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!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(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(156,plain,
% 0.16/0.42 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))) <=> ((~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(157,plain,
% 0.16/0.42 ((~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))) <=> (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(158,plain,
% 0.16/0.42 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))) <=> (distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[157])).
% 0.16/0.42 tff(159,plain,
% 0.16/0.42 ((distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)))) <=> ((~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)))),
% 0.16/0.42 inference(transitivity,[status(thm)],[158, 156])).
% 0.16/0.42 tff(160,plain,
% 0.16/0.42 (((~![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(X!3, Y!2), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!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(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[159])).
% 0.16/0.42 tff(161,plain,
% 0.16/0.42 (((~![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(X!3, Y!2), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!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(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0)))),
% 0.16/0.42 inference(transitivity,[status(thm)],[160, 155])).
% 0.16/0.42 tff(162,plain,
% 0.16/0.42 ((~![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(X!3, Y!2), intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))))),
% 0.16/0.42 inference(quant_inst,[status(thm)],[])).
% 0.16/0.42 tff(163,plain,
% 0.16/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))),
% 0.16/0.42 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.16/0.42 tff(164,plain,
% 0.16/0.42 ((~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))) | distinct_points(intersection_point(X!3, Y!2), intersection_point(U!1, V!0))),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[163, 36, 124])).
% 0.16/0.43 tff(165,plain,
% 0.16/0.43 (~(apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1))),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[164, 116])).
% 0.16/0.43 tff(166,plain,
% 0.16/0.43 ((apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1))),
% 0.16/0.43 inference(tautology,[status(thm)],[])).
% 0.16/0.43 tff(167,plain,
% 0.16/0.43 (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.16/0.43 tff(168,plain,
% 0.16/0.43 (apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(X!3, Y!2), U!1)),
% 0.16/0.43 inference(and_elim,[status(thm)],[25])).
% 0.16/0.43 tff(169,plain,
% 0.16/0.43 ($false),
% 0.16/0.43 inference(unit_resolution,[status(thm)],[168, 167, 154])).
% 0.16/0.43 % SZS output end Proof
%------------------------------------------------------------------------------