TSTP Solution File: GEO199+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO199+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 20:35:34 EDT 2022
% Result : Theorem 0.13s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO199+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 07:13:34 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.42 % SZS status Theorem
% 0.13/0.42 % SZS output start Proof
% 0.13/0.42 tff(distinct_points_type, type, (
% 0.13/0.42 distinct_points: ( $i * $i ) > $o)).
% 0.13/0.42 tff(intersection_point_type, type, (
% 0.13/0.42 intersection_point: ( $i * $i ) > $i)).
% 0.13/0.42 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.42 tptp_fun_Y_1: $i)).
% 0.13/0.42 tff(tptp_fun_X_2_type, type, (
% 0.13/0.42 tptp_fun_X_2: $i)).
% 0.13/0.42 tff(distinct_lines_type, type, (
% 0.13/0.42 distinct_lines: ( $i * $i ) > $o)).
% 0.13/0.42 tff(convergent_lines_type, type, (
% 0.13/0.42 convergent_lines: ( $i * $i ) > $o)).
% 0.13/0.42 tff(apart_point_and_line_type, type, (
% 0.13/0.42 apart_point_and_line: ( $i * $i ) > $o)).
% 0.13/0.42 tff(tptp_fun_Z_0_type, type, (
% 0.13/0.42 tptp_fun_Z_0: $i)).
% 0.13/0.42 tff(1,assumption,(convergent_lines(X!2, X!2)), introduced(assumption)).
% 0.13/0.42 tff(2,plain,
% 0.13/0.42 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(3,plain,
% 0.13/0.42 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.42 tff(4,plain,
% 0.13/0.42 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.13/0.42 tff(6,plain,
% 0.13/0.42 (![X: $i] : (~convergent_lines(X, X))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.42 tff(7,plain,(
% 0.13/0.42 ![X: $i] : (~convergent_lines(X, X))),
% 0.13/0.42 inference(skolemize,[status(sab)],[6])).
% 0.13/0.42 tff(8,plain,
% 0.13/0.42 (![X: $i] : (~convergent_lines(X, X))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.42 tff(9,plain,
% 0.13/0.42 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!2, X!2))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(10,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.13/0.42 tff(11,plain,(~convergent_lines(X!2, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.42 tff(12,assumption,(~distinct_lines(Y!1, X!2)), introduced(assumption)).
% 0.13/0.42 tff(13,plain,
% 0.13/0.42 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(14,plain,
% 0.13/0.42 ((~![X: $i, Y: $i, Z: $i] : ((((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) & (~apart_point_and_line(intersection_point(X, Y), Z))) => (~apart_point_and_line(intersection_point(Y, X), Z)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(15,axiom,(~![X: $i, Y: $i, Z: $i] : ((((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) & (~apart_point_and_line(intersection_point(X, Y), Z))) => (~apart_point_and_line(intersection_point(Y, X), Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.13/0.42 tff(16,plain,
% 0.13/0.42 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.42 tff(17,plain,
% 0.13/0.42 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.13/0.42 tff(18,plain,
% 0.13/0.42 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.42 tff(19,plain,
% 0.13/0.42 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.13/0.42 tff(20,plain,
% 0.13/0.42 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.13/0.42 tff(21,plain,
% 0.13/0.42 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.42 tff(22,plain,
% 0.13/0.42 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(intersection_point(Y, X), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z) & (~apart_point_and_line(intersection_point(X, Y), Z)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.13/0.42 tff(23,plain,(
% 0.13/0.42 ~((~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0) & (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[22])).
% 0.13/0.42 tff(24,plain,
% 0.13/0.42 (convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0) & (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))),
% 0.13/0.42 inference(or_elim,[status(thm)],[23])).
% 0.13/0.42 tff(25,plain,
% 0.13/0.42 (convergent_lines(X!2, Y!1)),
% 0.13/0.42 inference(and_elim,[status(thm)],[24])).
% 0.13/0.42 tff(26,plain,
% 0.13/0.42 (^[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))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(27,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.42 tff(28,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(29,plain,
% 0.13/0.42 (^[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)))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(30,plain,
% 0.13/0.42 (![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)))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.42 tff(31,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')).
% 0.13/0.42 tff(32,plain,
% 0.13/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.13/0.42 tff(33,plain,
% 0.13/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.13/0.42 tff(34,plain,(
% 0.13/0.42 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[33])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 ((distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.42 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | distinct_lines(Y!1, X!2) | convergent_lines(X!2, X!2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[41, 35, 25, 12, 11])).
% 0.20/0.42 tff(43,plain,(distinct_lines(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(44,assumption,(~convergent_lines(Y!1, X!2)), introduced(assumption)).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.42 tff(50,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.42 tff(53,plain,(
% 0.20/0.42 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[52])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ((convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1))) <=> ((~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2))),
% 0.20/0.42 inference(transitivity,[status(thm)],[57, 55])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2) | (~convergent_lines(X!2, Y!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, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!2, Y!1)) | convergent_lines(Y!1, X!2) | convergent_lines(X!2, X!2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[60, 54, 25, 44, 11])).
% 0.20/0.42 tff(62,plain,(convergent_lines(Y!1, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.43 tff(68,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')).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.43 tff(71,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[70])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), X!2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[75, 72])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(Y!1, X!2), X!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[76, 62])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.43 tff(83,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')).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.43 tff(86,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[85])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 ((~convergent_lines(Y!1, X!2)) | (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[90, 87])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(Y!1, X!2), Y!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[91, 62])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), X!2))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(X!2, Y!1), X!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[95, 87, 25])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!2, Y!1)) | (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(X!2, Y!1), Y!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[99, 72, 25])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (^[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))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.43 tff(108,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')).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.20/0.43 tff(111,plain,(
% 0.20/0.43 ![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))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[110])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[112, 102])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 ((apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, X!2))) <=> (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, X!2)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, X!2)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[116, 114])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))) | (~distinct_lines(Y!1, X!2)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!2, Y!1), Y!1) | apart_point_and_line(intersection_point(X!2, Y!1), X!2) | apart_point_and_line(intersection_point(Y!1, X!2), Y!1) | apart_point_and_line(intersection_point(Y!1, X!2), X!2) | (~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 ((~distinct_lines(Y!1, X!2)) | (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[119, 113, 100, 96, 92, 77])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 (~distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[120, 43])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.20/0.44 inference(and_elim,[status(thm)],[24])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (apart_point_and_line(intersection_point(Y!1, X!2), Z!0)),
% 0.20/0.44 inference(or_elim,[status(thm)],[23])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.44 tff(129,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')).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.20/0.44 tff(132,plain,(
% 0.20/0.44 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[131])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 (((~![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(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))) <=> ((~![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(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 ((distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0))) <=> ((~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 (((~![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(Y!1, X!2), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[135])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 (((~![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(Y!1, X!2), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[136, 134])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 ((~![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(Y!1, X!2), intersection_point(X!2, Y!1)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(Y!1, X!2), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), Z!0) | distinct_points(intersection_point(Y!1, X!2), intersection_point(X!2, Y!1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[139, 133, 123, 122, 121])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------