TSTP Solution File: GEO176+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO176+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 20:35:17 EDT 2022
% Result : Theorem 0.12s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO176+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 06:54:49 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 % SZS output start Proof
% 0.12/0.41 tff(apart_point_and_line_type, type, (
% 0.12/0.41 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.41 tff(tptp_fun_V_0_type, type, (
% 0.12/0.41 tptp_fun_V_0: $i)).
% 0.12/0.41 tff(tptp_fun_X_3_type, type, (
% 0.12/0.41 tptp_fun_X_3: $i)).
% 0.12/0.41 tff(intersection_point_type, type, (
% 0.12/0.41 intersection_point: ( $i * $i ) > $i)).
% 0.12/0.41 tff(tptp_fun_U_1_type, type, (
% 0.12/0.41 tptp_fun_U_1: $i)).
% 0.12/0.41 tff(convergent_lines_type, type, (
% 0.12/0.41 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.41 tff(distinct_points_type, type, (
% 0.12/0.41 distinct_points: ( $i * $i ) > $o)).
% 0.12/0.41 tff(tptp_fun_Y_2_type, type, (
% 0.12/0.41 tptp_fun_Y_2: $i)).
% 0.12/0.41 tff(1,plain,
% 0.12/0.41 ((distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1))) <=> (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(2,plain,
% 0.12/0.41 ((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1)))) <=> (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[1])).
% 0.12/0.41 tff(3,plain,
% 0.12/0.41 (((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1)))) | distinct_points(X!3, intersection_point(U!1, V!0))) <=> ((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1)))) | distinct_points(X!3, intersection_point(U!1, V!0)))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[2])).
% 0.12/0.41 tff(4,plain,
% 0.12/0.41 ((~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1)))) | distinct_points(X!3, intersection_point(U!1, V!0)))) <=> (~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1)))) | distinct_points(X!3, intersection_point(U!1, V!0))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[3])).
% 0.12/0.41 tff(5,plain,
% 0.12/0.41 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(X, V) | apart_point_and_line(X, U)))) | distinct_points(X, intersection_point(U, V)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(X, V) | apart_point_and_line(X, U)))) | distinct_points(X, intersection_point(U, V))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(6,plain,
% 0.12/0.41 ((~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(X, U) | apart_point_and_line(X, V))) => distinct_points(X, intersection_point(U, V)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(X, V) | apart_point_and_line(X, U)))) | distinct_points(X, intersection_point(U, V))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(7,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(X, U) | apart_point_and_line(X, V))) => distinct_points(X, intersection_point(U, V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.12/0.41 tff(8,plain,
% 0.12/0.41 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(X, V) | apart_point_and_line(X, U)))) | distinct_points(X, intersection_point(U, V)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.41 tff(9,plain,
% 0.12/0.41 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(X, V) | apart_point_and_line(X, U)))) | distinct_points(X, intersection_point(U, V)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.41 tff(10,plain,
% 0.12/0.41 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(X, V) | apart_point_and_line(X, U)))) | distinct_points(X, intersection_point(U, V)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.41 tff(11,plain,
% 0.12/0.42 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(X, V) | apart_point_and_line(X, U)))) | distinct_points(X, intersection_point(U, V)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.42 tff(12,plain,
% 0.12/0.42 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(X, V) | apart_point_and_line(X, U)))) | distinct_points(X, intersection_point(U, V)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.12/0.42 tff(13,plain,
% 0.12/0.42 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(X, V) | apart_point_and_line(X, U)))) | distinct_points(X, intersection_point(U, V)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.12/0.42 tff(14,plain,
% 0.12/0.42 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(X, V) | apart_point_and_line(X, U)))) | distinct_points(X, intersection_point(U, V)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.12/0.42 tff(15,plain,(
% 0.12/0.42 ~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1)))) | distinct_points(X!3, intersection_point(U!1, V!0)))),
% 0.12/0.42 inference(skolemize,[status(sab)],[14])).
% 0.12/0.42 tff(16,plain,
% 0.12/0.42 (~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1)))) | distinct_points(X!3, intersection_point(U!1, V!0)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.12/0.42 tff(17,plain,
% 0.12/0.42 (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1))),
% 0.12/0.42 inference(or_elim,[status(thm)],[16])).
% 0.12/0.42 tff(18,plain,
% 0.12/0.42 (convergent_lines(U!1, V!0)),
% 0.12/0.42 inference(and_elim,[status(thm)],[17])).
% 0.12/0.42 tff(19,plain,
% 0.12/0.42 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(20,plain,
% 0.12/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.42 tff(21,plain,
% 0.12/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(22,plain,
% 0.12/0.42 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(23,plain,
% 0.12/0.42 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.42 tff(24,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.12/0.42 tff(25,plain,
% 0.12/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.42 tff(26,plain,
% 0.12/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.42 tff(27,plain,(
% 0.12/0.42 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.42 inference(skolemize,[status(sab)],[26])).
% 0.12/0.42 tff(28,plain,
% 0.12/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.12/0.42 tff(29,plain,
% 0.12/0.42 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(30,plain,
% 0.12/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(31,plain,
% 0.12/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.42 tff(32,plain,
% 0.12/0.42 (~apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[31, 28, 18])).
% 0.12/0.42 tff(33,plain,
% 0.12/0.42 (~distinct_points(X!3, intersection_point(U!1, V!0))),
% 0.12/0.42 inference(or_elim,[status(thm)],[16])).
% 0.12/0.42 tff(34,plain,
% 0.12/0.42 (^[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))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(35,plain,
% 0.12/0.42 (![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)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.42 tff(36,plain,
% 0.12/0.42 (![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)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(37,plain,
% 0.12/0.42 (^[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)))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(38,plain,
% 0.12/0.42 (![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)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.42 tff(39,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/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 0.12/0.42 tff(40,plain,
% 0.12/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.42 tff(41,plain,
% 0.12/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.12/0.42 tff(42,plain,(
% 0.12/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.12/0.42 inference(skolemize,[status(sab)],[41])).
% 0.12/0.42 tff(43,plain,
% 0.12/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.12/0.42 tff(44,plain,
% 0.12/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(X!3, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(X!3, V!0)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(45,plain,
% 0.12/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(X!3, V!0)))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(46,plain,
% 0.12/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~apart_point_and_line(X!3, V!0))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.42 tff(47,plain,
% 0.12/0.42 (~apart_point_and_line(X!3, V!0)),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[46, 43, 33, 32])).
% 0.12/0.42 tff(48,plain,
% 0.12/0.42 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(49,plain,
% 0.12/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.12/0.42 tff(50,plain,
% 0.12/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(51,plain,
% 0.12/0.42 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(52,plain,
% 0.12/0.42 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.42 tff(53,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.12/0.42 tff(54,plain,
% 0.12/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.12/0.42 tff(55,plain,
% 0.12/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.12/0.42 tff(56,plain,(
% 0.12/0.42 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.42 inference(skolemize,[status(sab)],[55])).
% 0.12/0.42 tff(57,plain,
% 0.12/0.42 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.12/0.42 tff(58,plain,
% 0.12/0.42 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(59,plain,
% 0.12/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (~apart_point_and_line(intersection_point(U!1, V!0), U!1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[60, 57, 18])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~apart_point_and_line(X!3, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~apart_point_and_line(X!3, U!1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~apart_point_and_line(X!3, U!1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(X!3, intersection_point(U!1, V!0)) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~apart_point_and_line(X!3, U!1))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (~apart_point_and_line(X!3, U!1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[64, 43, 33, 61])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1)),
% 0.20/0.42 inference(and_elim,[status(thm)],[17])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[66, 65, 47])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------