TSTP Solution File: GEO197+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO197+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 20:35:33 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO197+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 07:15:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 % SZS output start Proof
% 0.19/0.47 tff(distinct_points_type, type, (
% 0.19/0.47 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.47 tff(intersection_point_type, type, (
% 0.19/0.47 intersection_point: ( $i * $i ) > $i)).
% 0.19/0.47 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.47 tptp_fun_Y_1: $i)).
% 0.19/0.47 tff(tptp_fun_X_2_type, type, (
% 0.19/0.47 tptp_fun_X_2: $i)).
% 0.19/0.47 tff(apart_point_and_line_type, type, (
% 0.19/0.47 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.47 tff(tptp_fun_Z_0_type, type, (
% 0.19/0.47 tptp_fun_Z_0: $i)).
% 0.19/0.47 tff(convergent_lines_type, type, (
% 0.19/0.47 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.47 tff(distinct_lines_type, type, (
% 0.19/0.47 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.47 tff(1,assumption,(distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1))), introduced(assumption)).
% 0.19/0.47 tff(2,plain,
% 0.19/0.47 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(3,plain,
% 0.19/0.47 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.47 tff(4,plain,
% 0.19/0.47 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.19/0.47 tff(6,plain,
% 0.19/0.47 (![X: $i] : (~distinct_points(X, X))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.47 tff(7,plain,(
% 0.19/0.47 ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.47 inference(skolemize,[status(sab)],[6])).
% 0.19/0.47 tff(8,plain,
% 0.19/0.47 (![X: $i] : (~distinct_points(X, X))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.47 tff(9,plain,
% 0.19/0.47 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(10,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.47 tff(11,plain,(~distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(12,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Z, Y), X)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Z, Y), X)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(13,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) & (~apart_point_and_line(intersection_point(X, Y), Z))) => (~apart_point_and_line(intersection_point(Z, Y), X)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Z, Y), X)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(14,axiom,(~![X: $i, Y: $i, Z: $i] : ((((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) & (~apart_point_and_line(intersection_point(X, Y), Z))) => (~apart_point_and_line(intersection_point(Z, Y), X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.47 tff(15,plain,
% 0.19/0.47 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Z, Y), X)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.47 tff(16,plain,
% 0.19/0.47 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Z, Y), X)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.19/0.47 tff(17,plain,
% 0.19/0.47 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Z, Y), X)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.47 tff(18,plain,
% 0.19/0.47 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Z, Y), X)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.19/0.47 tff(19,plain,
% 0.19/0.47 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Z, Y), X)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.19/0.47 tff(20,plain,
% 0.19/0.47 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Z, Y), X)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.47 tff(21,plain,
% 0.19/0.47 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Z, Y), X)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.19/0.47 tff(22,plain,(
% 0.19/0.47 ~((~apart_point_and_line(intersection_point(Z!0, Y!1), X!2)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0) & (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[21])).
% 0.19/0.47 tff(23,plain,
% 0.19/0.47 (apart_point_and_line(intersection_point(Z!0, Y!1), X!2)),
% 0.19/0.47 inference(or_elim,[status(thm)],[22])).
% 0.19/0.47 tff(24,plain,
% 0.19/0.47 ((apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), X!2))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(25,plain,
% 0.19/0.47 (apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.19/0.47 tff(26,plain,
% 0.19/0.47 (convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0) & (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))),
% 0.19/0.47 inference(or_elim,[status(thm)],[22])).
% 0.19/0.47 tff(27,plain,
% 0.19/0.47 (convergent_lines(X!2, Y!1)),
% 0.19/0.47 inference(and_elim,[status(thm)],[26])).
% 0.19/0.47 tff(28,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(29,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.47 tff(30,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(31,plain,
% 0.19/0.47 (^[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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(32,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.47 tff(33,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.19/0.47 tff(34,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.47 tff(36,plain,(
% 0.19/0.47 ![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))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[35])).
% 0.19/0.47 tff(37,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.19/0.47 tff(38,plain,
% 0.19/0.47 (((~![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!2, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!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(X!2, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 ((distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 ((~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2))) <=> (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 ((distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))) <=> (distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.47 tff(42,plain,
% 0.19/0.47 ((distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[41, 39])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 (((~![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(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2))))) <=> ((~![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!2, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 (((~![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(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2))))) <=> ((~![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!2, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[43, 38])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 ((~![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(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), X!2))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(46,plain,
% 0.19/0.47 ((~![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!2, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), X!2) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 (distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[46, 37, 27, 25])).
% 0.19/0.47 tff(48,plain,
% 0.19/0.47 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(49,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | distinct_points(Y, Z)) <=> (distinct_points(Y, Z) | distinct_points(X, Z))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))))), rewrite((distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(52,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.47 tff(53,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart4')).
% 0.19/0.47 tff(54,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.19/0.47 tff(56,plain,(
% 0.19/0.47 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[55])).
% 0.19/0.47 tff(57,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(59,plain,
% 0.19/0.47 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1)))) <=> (distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(60,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~distinct_points(intersection_point(Z!0, Y!1), intersection_point(X!2, Y!1))) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 (distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[63, 57, 47])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 (distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[64, 11])).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 (convergent_lines(Z!0, Y!1)),
% 0.19/0.47 inference(and_elim,[status(thm)],[26])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 (((~![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(Z!0, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!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(Z!0, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(68,plain,
% 0.19/0.47 ((distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~convergent_lines(Z!0, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))) <=> ((~convergent_lines(Z!0, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(69,plain,
% 0.19/0.48 (((~![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(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~convergent_lines(Z!0, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!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(Z!0, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.48 tff(70,plain,
% 0.19/0.48 (((~![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(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~convergent_lines(Z!0, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!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(Z!0, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[69, 67])).
% 0.19/0.48 tff(71,plain,
% 0.19/0.48 ((~![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(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~convergent_lines(Z!0, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(72,plain,
% 0.19/0.48 ((~![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(Z!0, Y!1)) | distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.48 tff(73,plain,
% 0.19/0.48 (distinct_points(intersection_point(Z!0, Y!1), intersection_point(Z!0, Y!1)) | (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[72, 37, 66])).
% 0.19/0.48 tff(74,plain,
% 0.19/0.48 (~(apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[73, 11])).
% 0.19/0.48 tff(75,plain,
% 0.19/0.48 ((apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(76,plain,
% 0.19/0.48 (~apart_point_and_line(intersection_point(Z!0, Y!1), Y!1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.48 tff(77,plain,
% 0.19/0.48 ((apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)) | (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(78,plain,
% 0.19/0.48 (~apart_point_and_line(intersection_point(Z!0, Y!1), Z!0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[77, 74])).
% 0.19/0.48 tff(79,assumption,(distinct_lines(Z!0, Z!0)), introduced(assumption)).
% 0.19/0.48 tff(80,plain,
% 0.19/0.48 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(81,plain,
% 0.19/0.48 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.48 tff(82,plain,
% 0.19/0.48 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(83,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart2')).
% 0.19/0.48 tff(84,plain,
% 0.19/0.48 (![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.48 tff(85,plain,(
% 0.19/0.48 ![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.48 inference(skolemize,[status(sab)],[84])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 (![X: $i] : (~distinct_lines(X, X))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(Z!0, Z!0))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[87, 86, 79])).
% 0.19/0.48 tff(89,plain,(~distinct_lines(Z!0, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.48 tff(95,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.48 tff(98,plain,(
% 0.19/0.48 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.48 inference(skolemize,[status(sab)],[97])).
% 0.19/0.48 tff(99,plain,
% 0.19/0.48 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(Z!0, Y!1)) | distinct_lines(Z!0, Y!1))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(Z!0, Y!1)) | distinct_lines(Z!0, Y!1))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(Z!0, Y!1)) | distinct_lines(Z!0, Y!1))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(Z!0, Y!1)) | distinct_lines(Z!0, Y!1)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.48 tff(103,plain,
% 0.19/0.48 (distinct_lines(Z!0, Y!1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[102, 99, 66])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[104])).
% 0.19/0.48 tff(106,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.48 tff(109,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart5')).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.19/0.48 tff(112,plain,(
% 0.19/0.48 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[111])).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Z!0, Z!0) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Z!0, Z!0) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Z!0, Y!1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(115,plain,
% 0.19/0.48 ((distinct_lines(Y!1, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, Y!1))) <=> (distinct_lines(Z!0, Z!0) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Z!0, Y!1)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Z!0, Z!0) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Z!0, Y!1))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.48 tff(117,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Z!0, Z!0) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Z!0, Y!1)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[116, 114])).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Y!1, Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, Y!1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(119,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Z!0, Z!0) | distinct_lines(Y!1, Z!0) | (~distinct_lines(Z!0, Y!1))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.48 tff(120,plain,
% 0.19/0.48 (distinct_lines(Z!0, Z!0) | distinct_lines(Y!1, Z!0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[119, 113, 103])).
% 0.19/0.48 tff(121,plain,
% 0.19/0.48 (distinct_lines(Y!1, Z!0)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[120, 89])).
% 0.19/0.48 tff(122,plain,
% 0.19/0.48 (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.19/0.48 inference(and_elim,[status(thm)],[26])).
% 0.19/0.48 tff(123,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(124,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.48 tff(125,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(126,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[125])).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(128,plain,
% 0.19/0.48 (^[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))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(129,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.48 tff(130,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/sandbox2/benchmark/Axioms/GEO008+0.ax','cu1')).
% 0.19/0.48 tff(131,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.48 tff(132,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.19/0.48 tff(133,plain,(
% 0.19/0.48 ![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))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[132])).
% 0.19/0.48 tff(134,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.19/0.48 tff(135,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[134, 124])).
% 0.19/0.48 tff(136,plain,
% 0.19/0.48 (((~![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(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_lines(Y!1, Z!0)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))) <=> ((~![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(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_lines(Y!1, Z!0)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(137,plain,
% 0.19/0.48 ((apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, Z!0))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_lines(Y!1, Z!0)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(138,plain,
% 0.19/0.48 (((~![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(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, Z!0)))) <=> ((~![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(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_lines(Y!1, Z!0)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.48 tff(139,plain,
% 0.19/0.48 (((~![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(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, Z!0)))) <=> ((~![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(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_lines(Y!1, Z!0)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[138, 136])).
% 0.19/0.48 tff(140,plain,
% 0.19/0.48 ((~![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(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1))) | (~distinct_lines(Y!1, Z!0)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(141,plain,
% 0.19/0.48 ((~![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(X!2, Y!1), Z!0) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Z!0, Y!1), Z!0) | apart_point_and_line(intersection_point(Z!0, Y!1), Y!1) | (~distinct_lines(Y!1, Z!0)) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(Z!0, Y!1)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.48 tff(142,plain,
% 0.19/0.48 (apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[141, 135, 122, 121, 78, 76, 65])).
% 0.19/0.48 tff(143,plain,
% 0.19/0.48 ((apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(144,plain,
% 0.19/0.48 (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.19/0.48 tff(145,plain,
% 0.19/0.48 (((~![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!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![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!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(146,plain,
% 0.19/0.48 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(147,plain,
% 0.19/0.48 ((~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))) <=> (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(148,plain,
% 0.19/0.48 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[147])).
% 0.19/0.48 tff(149,plain,
% 0.19/0.48 ((distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[148, 146])).
% 0.19/0.48 tff(150,plain,
% 0.19/0.48 (((~![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!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![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!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[149])).
% 0.19/0.48 tff(151,plain,
% 0.19/0.48 (((~![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!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))) <=> ((~![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!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[150, 145])).
% 0.19/0.48 tff(152,plain,
% 0.19/0.48 ((~![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!2, Y!1), intersection_point(X!2, Y!1)) | (~convergent_lines(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(153,plain,
% 0.19/0.48 ((~![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!2, Y!1)) | distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.49 tff(154,plain,
% 0.19/0.49 (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)) | (~(apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[153, 37, 27])).
% 0.19/0.49 tff(155,plain,
% 0.19/0.49 (distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[154, 144])).
% 0.19/0.49 tff(156,plain,
% 0.19/0.49 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(X!2, Y!1), intersection_point(X!2, Y!1)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(157,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[156, 8, 155])).
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------