TSTP Solution File: GEO196+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO196+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 20:35:32 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO196+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 06:55:04 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(convergent_lines_type, type, (
% 0.21/0.45 convergent_lines: ( $i * $i ) > $o)).
% 0.21/0.45 tff(tptp_fun_U_1_type, type, (
% 0.21/0.45 tptp_fun_U_1: $i)).
% 0.21/0.45 tff(unorthogonal_lines_type, type, (
% 0.21/0.45 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.21/0.45 tff(orthogonal_through_point_type, type, (
% 0.21/0.45 orthogonal_through_point: ( $i * $i ) > $i)).
% 0.21/0.45 tff(intersection_point_type, type, (
% 0.21/0.45 intersection_point: ( $i * $i ) > $i)).
% 0.21/0.45 tff(tptp_fun_V_0_type, type, (
% 0.21/0.45 tptp_fun_V_0: $i)).
% 0.21/0.45 tff(distinct_lines_type, type, (
% 0.21/0.45 distinct_lines: ( $i * $i ) > $o)).
% 0.21/0.45 tff(distinct_points_type, type, (
% 0.21/0.45 distinct_points: ( $i * $i ) > $o)).
% 0.21/0.45 tff(tptp_fun_Y_2_type, type, (
% 0.21/0.45 tptp_fun_Y_2: $i)).
% 0.21/0.45 tff(tptp_fun_X_3_type, type, (
% 0.21/0.45 tptp_fun_X_3: $i)).
% 0.21/0.45 tff(apart_point_and_line_type, type, (
% 0.21/0.45 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.45 tff(incident_point_and_line_type, type, (
% 0.21/0.45 incident_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.45 tff(1,plain,
% 0.21/0.45 (^[A: $i, L: $i] : refl((~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> (~unorthogonal_lines(orthogonal_through_point(L, A), L)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(2,plain,
% 0.21/0.45 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L)) <=> ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(4,axiom,(![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ooc1')).
% 0.21/0.45 tff(5,plain,
% 0.21/0.45 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.45 tff(6,plain,(
% 0.21/0.45 ![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.21/0.45 inference(skolemize,[status(sab)],[5])).
% 0.21/0.45 tff(7,plain,
% 0.21/0.45 (![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.45 tff(8,plain,
% 0.21/0.45 ((~![A: $i, L: $i] : (~unorthogonal_lines(orthogonal_through_point(L, A), L))) | (~unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(9,plain,
% 0.21/0.45 (~unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.45 tff(10,plain,
% 0.21/0.45 (^[L: $i, M: $i, N: $i] : refl((unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(11,plain,
% 0.21/0.45 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.45 tff(12,plain,
% 0.21/0.45 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(13,plain,
% 0.21/0.45 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.45 tff(14,plain,
% 0.21/0.45 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(16,plain,
% 0.21/0.45 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.45 tff(17,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.45 tff(20,plain,(
% 0.21/0.45 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[19])).
% 0.21/0.45 tff(21,plain,
% 0.21/0.45 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.45 tff(22,plain,
% 0.21/0.45 (![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.21/0.45 tff(23,plain,
% 0.21/0.45 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(24,plain,
% 0.21/0.45 ((unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1))) <=> (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(25,plain,
% 0.21/0.45 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[24])).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[25, 23])).
% 0.21/0.46 tff(27,plain,
% 0.21/0.46 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | (unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(28,plain,
% 0.21/0.46 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(L, N) | unorthogonal_lines(L, M) | (~convergent_lines(M, N)))) | unorthogonal_lines(orthogonal_through_point(U!1, intersection_point(U!1, V!0)), U!1) | (~convergent_lines(U!1, U!1))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.46 tff(29,plain,
% 0.21/0.46 (~convergent_lines(U!1, U!1)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[28, 22, 9])).
% 0.21/0.46 tff(30,plain,
% 0.21/0.46 (^[X: $i, Y: $i] : refl((incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(31,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.46 tff(32,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(33,axiom,(![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a4')).
% 0.21/0.46 tff(34,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.46 tff(35,plain,(
% 0.21/0.46 ![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[34])).
% 0.21/0.46 tff(36,plain,
% 0.21/0.46 (![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.21/0.46 tff(37,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(intersection_point(U!1, V!0), Y!2) <=> (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(38,plain,
% 0.21/0.46 (incident_point_and_line(intersection_point(U!1, V!0), Y!2) <=> (~apart_point_and_line(intersection_point(U!1, V!0), Y!2))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.21/0.46 tff(39,assumption,(~apart_point_and_line(intersection_point(U!1, V!0), X!3)), introduced(assumption)).
% 0.21/0.46 tff(40,assumption,(~(incident_point_and_line(intersection_point(U!1, V!0), X!3) <=> (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))), introduced(assumption)).
% 0.21/0.46 tff(41,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(intersection_point(U!1, V!0), X!3) <=> (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(42,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[41, 36, 40])).
% 0.21/0.46 tff(43,plain,(incident_point_and_line(intersection_point(U!1, V!0), X!3) <=> (~apart_point_and_line(intersection_point(U!1, V!0), X!3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(44,plain,
% 0.21/0.46 ((~(incident_point_and_line(intersection_point(U!1, V!0), X!3) <=> (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))) | incident_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), X!3)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(45,plain,
% 0.21/0.46 (incident_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), X!3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.21/0.46 tff(46,plain,
% 0.21/0.46 (incident_point_and_line(intersection_point(U!1, V!0), X!3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[45, 39])).
% 0.21/0.46 tff(47,plain,
% 0.21/0.46 ((~(~((~incident_point_and_line(intersection_point(U!1, V!0), X!3)) | (~incident_point_and_line(intersection_point(U!1, V!0), Y!2))))) <=> ((~incident_point_and_line(intersection_point(U!1, V!0), X!3)) | (~incident_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(48,plain,
% 0.21/0.46 ((incident_point_and_line(intersection_point(U!1, V!0), X!3) & incident_point_and_line(intersection_point(U!1, V!0), Y!2)) <=> (~((~incident_point_and_line(intersection_point(U!1, V!0), X!3)) | (~incident_point_and_line(intersection_point(U!1, V!0), Y!2))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(49,plain,
% 0.21/0.46 ((~(incident_point_and_line(intersection_point(U!1, V!0), X!3) & incident_point_and_line(intersection_point(U!1, V!0), Y!2))) <=> (~(~((~incident_point_and_line(intersection_point(U!1, V!0), X!3)) | (~incident_point_and_line(intersection_point(U!1, V!0), Y!2)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[48])).
% 0.21/0.46 tff(50,plain,
% 0.21/0.46 ((~(incident_point_and_line(intersection_point(U!1, V!0), X!3) & incident_point_and_line(intersection_point(U!1, V!0), Y!2))) <=> ((~incident_point_and_line(intersection_point(U!1, V!0), X!3)) | (~incident_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[49, 47])).
% 0.21/0.46 tff(51,plain,
% 0.21/0.46 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(52,plain,
% 0.21/0.46 ((~![X: $i, Y: $i, U: $i, V: $i] : ((((convergent_lines(X, Y) & convergent_lines(U, V)) & incident_point_and_line(intersection_point(X, Y), U)) & incident_point_and_line(intersection_point(X, Y), V)) => (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(53,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : ((((convergent_lines(X, Y) & convergent_lines(U, V)) & incident_point_and_line(intersection_point(X, Y), U)) & incident_point_and_line(intersection_point(X, Y), V)) => (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.46 tff(54,plain,
% 0.21/0.46 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.21/0.46 tff(57,plain,
% 0.21/0.46 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[56, 51])).
% 0.21/0.46 tff(58,plain,
% 0.21/0.46 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[57, 51])).
% 0.21/0.46 tff(59,plain,
% 0.21/0.46 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & incident_point_and_line(intersection_point(X, Y), U) & incident_point_and_line(intersection_point(X, Y), V))) | (incident_point_and_line(intersection_point(U, V), X) & incident_point_and_line(intersection_point(U, V), Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[59, 51])).
% 0.21/0.46 tff(61,plain,(
% 0.21/0.46 ~((~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & incident_point_and_line(intersection_point(X!3, Y!2), U!1) & incident_point_and_line(intersection_point(X!3, Y!2), V!0))) | (incident_point_and_line(intersection_point(U!1, V!0), X!3) & incident_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[60])).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 (~(incident_point_and_line(intersection_point(U!1, V!0), X!3) & incident_point_and_line(intersection_point(U!1, V!0), Y!2))),
% 0.21/0.46 inference(or_elim,[status(thm)],[61])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 ((~incident_point_and_line(intersection_point(U!1, V!0), X!3)) | (~incident_point_and_line(intersection_point(U!1, V!0), Y!2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[62, 50])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 (~incident_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[63, 46])).
% 0.21/0.46 tff(65,plain,
% 0.21/0.46 ((~(incident_point_and_line(intersection_point(U!1, V!0), Y!2) <=> (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) | incident_point_and_line(intersection_point(U!1, V!0), Y!2) | apart_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(66,plain,
% 0.21/0.46 ((~(incident_point_and_line(intersection_point(U!1, V!0), Y!2) <=> (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) | apart_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.21/0.46 tff(67,plain,
% 0.21/0.46 (apart_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[66, 38])).
% 0.21/0.46 tff(68,assumption,(~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))), introduced(assumption)).
% 0.21/0.46 tff(69,assumption,(apart_point_and_line(intersection_point(U!1, V!0), Y!2)), introduced(assumption)).
% 0.21/0.46 tff(70,plain,
% 0.21/0.46 (convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & incident_point_and_line(intersection_point(X!3, Y!2), U!1) & incident_point_and_line(intersection_point(X!3, Y!2), V!0)),
% 0.21/0.46 inference(or_elim,[status(thm)],[61])).
% 0.21/0.46 tff(71,plain,
% 0.21/0.46 (convergent_lines(X!3, Y!2)),
% 0.21/0.46 inference(and_elim,[status(thm)],[70])).
% 0.21/0.46 tff(72,plain,
% 0.21/0.46 (^[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))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(73,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.46 tff(74,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(75,plain,
% 0.21/0.46 (^[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))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(76,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[75])).
% 0.21/0.46 tff(77,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci4')).
% 0.21/0.46 tff(78,plain,
% 0.21/0.46 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.46 tff(79,plain,
% 0.21/0.46 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.21/0.46 tff(80,plain,(
% 0.21/0.46 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[79])).
% 0.21/0.46 tff(81,plain,
% 0.21/0.46 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.21/0.46 tff(82,plain,
% 0.21/0.46 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(83,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(84,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.46 tff(85,plain,
% 0.21/0.46 (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[84, 81, 71])).
% 0.21/0.46 tff(86,plain,
% 0.21/0.46 (^[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))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(87,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.46 tff(88,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(89,plain,
% 0.21/0.46 (^[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)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.46 tff(91,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/GEO006+0.ax','ceq1')).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.21/0.46 tff(94,plain,(
% 0.21/0.46 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[93])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.21/0.46 tff(96,plain,
% 0.21/0.46 (((~![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(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) <=> ((~![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(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 ((distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2))) <=> (apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(98,plain,
% 0.21/0.46 (((~![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(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) <=> ((~![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(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.46 tff(99,plain,
% 0.21/0.46 (((~![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(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) <=> ((~![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(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[98, 96])).
% 0.21/0.46 tff(100,plain,
% 0.21/0.46 ((~![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(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(101,plain,
% 0.21/0.46 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[101, 95, 85, 69, 68])).
% 0.21/0.46 tff(103,plain,(distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 (distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[103, 67])).
% 0.21/0.46 tff(105,plain,
% 0.21/0.46 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(intersection_point(X!3, Y!2), V!0) <=> (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (incident_point_and_line(intersection_point(X!3, Y!2), V!0) <=> (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[105, 36])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 (incident_point_and_line(intersection_point(X!3, Y!2), V!0)),
% 0.21/0.46 inference(and_elim,[status(thm)],[70])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 ((~(incident_point_and_line(intersection_point(X!3, Y!2), V!0) <=> (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))) | (~incident_point_and_line(intersection_point(X!3, Y!2), V!0)) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 ((~(incident_point_and_line(intersection_point(X!3, Y!2), V!0) <=> (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))) | (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.21/0.46 tff(111,plain,
% 0.21/0.46 (convergent_lines(U!1, V!0)),
% 0.21/0.46 inference(and_elim,[status(thm)],[70])).
% 0.21/0.46 tff(112,plain,
% 0.21/0.46 (((~![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(113,plain,
% 0.21/0.46 ((~![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)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(114,plain,
% 0.21/0.46 ((~![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))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.46 tff(115,plain,
% 0.21/0.46 (~apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[114, 81, 111])).
% 0.21/0.46 tff(116,plain,
% 0.21/0.46 (^[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))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(117,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 (^[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))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[119])).
% 0.21/0.47 tff(121,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci3')).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.21/0.47 tff(124,plain,(
% 0.21/0.47 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[123])).
% 0.21/0.47 tff(125,plain,
% 0.21/0.47 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.21/0.47 tff(126,plain,
% 0.21/0.47 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[128, 125, 71])).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 (^[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_lines(U, V)) | (~distinct_points(X, Y))) <=> (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_lines(U, V)) | (~distinct_points(X, Y))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 (![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_lines(U, V)) | (~distinct_points(X, Y))) <=> ![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))))), rewrite((~(~((~distinct_lines(U, V)) | (~distinct_points(X, Y))))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_lines(U, V)) | (~distinct_points(X, Y))))), ((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_lines(U, V)) | (~distinct_points(X, Y)))))), 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_lines(U, V)) | (~distinct_points(X, Y)))) <=> (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_lines(U, V)) | (~distinct_points(X, Y)))), ((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_lines(U, V)) | (~distinct_points(X, Y)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(135,plain,
% 0.21/0.47 (^[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))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[135])).
% 0.21/0.47 tff(137,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/GEO006+0.ax','cu1')).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.21/0.47 tff(140,plain,(
% 0.21/0.47 ![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))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[139])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.21/0.47 tff(142,plain,
% 0.21/0.47 (![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_lines(U, V)) | (~distinct_points(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!3, Y!2), X!3) | 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(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, X!3)) | apart_point_and_line(intersection_point(U!1, V!0), 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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | 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(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, X!3)) | apart_point_and_line(intersection_point(U!1, V!0), X!3))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 ((apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, X!3)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))) <=> (apart_point_and_line(intersection_point(X!3, Y!2), X!3) | 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(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, X!3)) | apart_point_and_line(intersection_point(U!1, V!0), X!3))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(145,plain,
% 0.21/0.47 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, X!3)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!3, Y!2), X!3) | 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(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, X!3)) | apart_point_and_line(intersection_point(U!1, V!0), X!3)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[144])).
% 0.21/0.47 tff(146,plain,
% 0.21/0.47 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, X!3)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | 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(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, X!3)) | apart_point_and_line(intersection_point(U!1, V!0), X!3))),
% 0.21/0.47 inference(transitivity,[status(thm)],[145, 143])).
% 0.21/0.47 tff(147,plain,
% 0.21/0.47 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, X!3)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(148,plain,
% 0.21/0.47 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | 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(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, X!3)) | apart_point_and_line(intersection_point(U!1, V!0), X!3)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 ((~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, X!3))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[148, 142, 129, 115, 110, 39])).
% 0.21/0.47 tff(150,plain,
% 0.21/0.47 (~distinct_lines(V!0, X!3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[149, 104])).
% 0.21/0.47 tff(151,plain,
% 0.21/0.47 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(152,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[151])).
% 0.21/0.47 tff(153,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(154,plain,
% 0.21/0.47 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(155,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[154])).
% 0.21/0.47 tff(156,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.21/0.47 tff(157,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.21/0.47 tff(158,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.21/0.47 tff(159,plain,(
% 0.21/0.47 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[158])).
% 0.21/0.47 tff(160,plain,
% 0.21/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[159, 152])).
% 0.21/0.47 tff(161,plain,
% 0.21/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, X!3) | convergent_lines(U!1, X!3))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | distinct_lines(V!0, X!3) | convergent_lines(U!1, X!3))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(162,plain,
% 0.21/0.47 ((distinct_lines(V!0, X!3) | convergent_lines(U!1, X!3) | (~convergent_lines(U!1, V!0))) <=> ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, X!3) | convergent_lines(U!1, X!3))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(163,plain,
% 0.21/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, X!3) | convergent_lines(U!1, X!3) | (~convergent_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, X!3) | convergent_lines(U!1, X!3)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[162])).
% 0.21/0.47 tff(164,plain,
% 0.21/0.47 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, X!3) | convergent_lines(U!1, X!3) | (~convergent_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | distinct_lines(V!0, X!3) | convergent_lines(U!1, X!3))),
% 0.21/0.47 inference(transitivity,[status(thm)],[163, 161])).
% 0.21/0.47 tff(165,plain,
% 0.21/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, X!3) | convergent_lines(U!1, X!3) | (~convergent_lines(U!1, V!0)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(166,plain,
% 0.21/0.47 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | distinct_lines(V!0, X!3) | convergent_lines(U!1, X!3)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.21/0.47 tff(167,plain,
% 0.21/0.47 (distinct_lines(V!0, X!3) | convergent_lines(U!1, X!3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[166, 160, 111])).
% 0.21/0.47 tff(168,plain,
% 0.21/0.47 (convergent_lines(U!1, X!3)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[167, 150])).
% 0.21/0.47 tff(169,plain,
% 0.21/0.47 ((~![X: $i, Y: $i] : (incident_point_and_line(X, Y) <=> (~apart_point_and_line(X, Y)))) | (incident_point_and_line(intersection_point(X!3, Y!2), U!1) <=> (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(170,plain,
% 0.21/0.47 (incident_point_and_line(intersection_point(X!3, Y!2), U!1) <=> (~apart_point_and_line(intersection_point(X!3, Y!2), U!1))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[169, 36])).
% 0.21/0.47 tff(171,plain,
% 0.21/0.47 (incident_point_and_line(intersection_point(X!3, Y!2), U!1)),
% 0.21/0.47 inference(and_elim,[status(thm)],[70])).
% 0.21/0.47 tff(172,plain,
% 0.21/0.47 ((~(incident_point_and_line(intersection_point(X!3, Y!2), U!1) <=> (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))) | (~incident_point_and_line(intersection_point(X!3, Y!2), U!1)) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(173,plain,
% 0.21/0.47 ((~(incident_point_and_line(intersection_point(X!3, Y!2), U!1) <=> (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)))) | (~apart_point_and_line(intersection_point(X!3, Y!2), U!1))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.21/0.47 tff(174,plain,
% 0.21/0.47 (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[173, 170])).
% 0.21/0.47 tff(175,plain,
% 0.21/0.47 (((~![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(176,plain,
% 0.21/0.47 ((~![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)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(177,plain,
% 0.21/0.47 ((~![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))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.21/0.47 tff(178,plain,
% 0.21/0.47 (~apart_point_and_line(intersection_point(U!1, V!0), U!1)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[177, 125, 111])).
% 0.21/0.47 tff(179,plain,
% 0.21/0.47 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_lines(X!3, U!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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_lines(X!3, U!1)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 ((apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_lines(X!3, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))) <=> (apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_lines(X!3, U!1)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(181,plain,
% 0.21/0.47 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_lines(X!3, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_lines(X!3, U!1))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[180])).
% 0.21/0.47 tff(182,plain,
% 0.21/0.48 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_lines(X!3, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_lines(X!3, U!1)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[181, 179])).
% 0.21/0.48 tff(183,plain,
% 0.21/0.48 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_lines(X!3, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(184,plain,
% 0.21/0.48 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_lines(X!3, U!1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.21/0.48 tff(185,plain,
% 0.21/0.48 ((~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | apart_point_and_line(intersection_point(U!1, V!0), X!3) | (~distinct_lines(X!3, U!1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[184, 142, 129, 178, 174])).
% 0.21/0.48 tff(186,plain,
% 0.21/0.48 (~distinct_lines(X!3, U!1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[185, 104, 39])).
% 0.21/0.48 tff(187,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!3, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, X!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(X!3, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, X!3)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(188,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!3, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, X!3)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(189,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(X!3, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, X!3))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.21/0.48 tff(190,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[189, 160, 186, 29, 168])).
% 0.21/0.48 tff(191,plain,(apart_point_and_line(intersection_point(U!1, V!0), X!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 (((~![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(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))) <=> ((~![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(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(193,plain,
% 0.21/0.48 ((distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3))) <=> (apart_point_and_line(intersection_point(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(194,plain,
% 0.21/0.48 (((~![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(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))) <=> ((~![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(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[193])).
% 0.21/0.48 tff(195,plain,
% 0.21/0.48 (((~![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(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))) <=> ((~![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(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[194, 192])).
% 0.21/0.48 tff(196,plain,
% 0.21/0.48 ((~![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(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(197,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.21/0.48 tff(198,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[197, 95, 129, 68, 191])).
% 0.21/0.48 tff(199,plain,(distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(200,plain,
% 0.21/0.48 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (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(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, U!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_lines(U, V)) | (~distinct_points(X, Y)))) | 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(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, U!1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(201,plain,
% 0.21/0.48 ((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(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))) <=> (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(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, U!1)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(202,plain,
% 0.21/0.48 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (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(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(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_lines(U, V)) | (~distinct_points(X, Y)))) | (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(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, U!1))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[201])).
% 0.21/0.48 tff(203,plain,
% 0.21/0.48 (((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (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(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(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_lines(U, V)) | (~distinct_points(X, Y)))) | 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(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, U!1)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[202, 200])).
% 0.21/0.48 tff(204,plain,
% 0.21/0.48 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | (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(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(205,plain,
% 0.21/0.48 ((~![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_lines(U, V)) | (~distinct_points(X, Y)))) | 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(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, U!1))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.21/0.48 tff(206,plain,
% 0.21/0.48 ((~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, U!1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[205, 142, 115, 178, 174, 110])).
% 0.21/0.48 tff(207,plain,
% 0.21/0.48 (~distinct_lines(V!0, U!1)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[206, 199])).
% 0.21/0.48 tff(208,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(209,plain,
% 0.21/0.48 ((distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0))) <=> ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(210,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[209])).
% 0.21/0.48 tff(211,plain,
% 0.21/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1))),
% 0.21/0.48 inference(transitivity,[status(thm)],[210, 208])).
% 0.21/0.48 tff(212,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(213,plain,
% 0.21/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.21/0.48 tff(214,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[213, 160, 111, 207, 29])).
% 0.21/0.48 % SZS output end Proof
%------------------------------------------------------------------------------