TSTP Solution File: GEO181+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO181+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 20:35:20 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO181+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 06:57:42 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(distinct_lines_type, type, (
% 0.14/0.39 distinct_lines: ( $i * $i ) > $o)).
% 0.14/0.39 tff(line_connecting_type, type, (
% 0.14/0.39 line_connecting: ( $i * $i ) > $i)).
% 0.14/0.39 tff(tptp_fun_Z_0_type, type, (
% 0.14/0.39 tptp_fun_Z_0: $i)).
% 0.14/0.39 tff(tptp_fun_X_2_type, type, (
% 0.14/0.39 tptp_fun_X_2: $i)).
% 0.14/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.14/0.39 tptp_fun_Y_1: $i)).
% 0.14/0.39 tff(apart_point_and_line_type, type, (
% 0.14/0.39 apart_point_and_line: ( $i * $i ) > $o)).
% 0.14/0.39 tff(distinct_points_type, type, (
% 0.14/0.39 distinct_points: ( $i * $i ) > $o)).
% 0.14/0.39 tff(1,assumption,(~distinct_points(X!2, Z!0)), introduced(assumption)).
% 0.14/0.39 tff(2,plain,
% 0.14/0.39 ((~(apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> (~(apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(3,plain,
% 0.14/0.39 ((~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Y, line_connecting(X, Z)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Y, line_connecting(X, Z)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(4,plain,
% 0.14/0.39 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => apart_point_and_line(Y, line_connecting(X, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Y, line_connecting(X, Z)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(5,axiom,(~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => apart_point_and_line(Y, line_connecting(X, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.14/0.39 tff(6,plain,
% 0.14/0.39 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Y, line_connecting(X, Z)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.39 tff(7,plain,
% 0.14/0.39 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Y, line_connecting(X, Z)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.14/0.39 tff(8,plain,
% 0.14/0.39 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Y, line_connecting(X, Z)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Y, line_connecting(X, Z)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Y, line_connecting(X, Z)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.14/0.39 tff(11,plain,
% 0.14/0.39 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Y, line_connecting(X, Z)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Y, line_connecting(X, Z)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.14/0.39 tff(13,plain,(
% 0.14/0.39 ~(apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.14/0.39 inference(skolemize,[status(sab)],[12])).
% 0.14/0.39 tff(14,plain,
% 0.14/0.39 (~(apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.14/0.39 tff(15,plain,
% 0.14/0.39 (distinct_points(X!2, Y!1)),
% 0.14/0.39 inference(or_elim,[status(thm)],[14])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | distinct_points(Y, Z)) <=> (distinct_points(Y, Z) | distinct_points(X, Z))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))))), rewrite((distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.14/0.40 tff(21,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart4')).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.14/0.40 tff(24,plain,(
% 0.14/0.40 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[23])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(X!2, Y!1)) | distinct_points(X!2, Z!0) | distinct_points(Y!1, Z!0))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | distinct_points(X!2, Z!0) | distinct_points(Y!1, Z!0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 ((distinct_points(Y!1, Z!0) | distinct_points(X!2, Z!0) | (~distinct_points(X!2, Y!1))) <=> ((~distinct_points(X!2, Y!1)) | distinct_points(X!2, Z!0) | distinct_points(Y!1, Z!0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, Z!0) | distinct_points(X!2, Z!0) | (~distinct_points(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(X!2, Y!1)) | distinct_points(X!2, Z!0) | distinct_points(Y!1, Z!0)))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[27])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, Z!0) | distinct_points(X!2, Z!0) | (~distinct_points(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | distinct_points(X!2, Z!0) | distinct_points(Y!1, Z!0))),
% 0.14/0.40 inference(transitivity,[status(thm)],[28, 26])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, Z!0) | distinct_points(X!2, Z!0) | (~distinct_points(X!2, Y!1)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | distinct_points(X!2, Z!0) | distinct_points(Y!1, Z!0)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 (distinct_points(X!2, Z!0) | distinct_points(Y!1, Z!0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[31, 25, 15])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (distinct_points(Y!1, Z!0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[32, 1])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.14/0.40 tff(39,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.14/0.40 tff(42,plain,(
% 0.14/0.40 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[41])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(Y!1, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(Y!1, Z!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(Y!1, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(Y!1, Z!0))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(Y!1, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(Y!1, Z!0))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(Y!1, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 (~apart_point_and_line(Z!0, line_connecting(Y!1, Z!0))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[46, 43, 33])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 (^[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))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(51,plain,
% 0.14/0.40 (^[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)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(52,plain,
% 0.14/0.40 (![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)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.14/0.40 tff(53,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 0.14/0.40 tff(54,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.14/0.40 tff(55,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.14/0.40 tff(56,plain,(
% 0.14/0.40 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[55])).
% 0.14/0.40 tff(57,plain,
% 0.14/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.14/0.40 tff(58,plain,
% 0.14/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(X!2, Z!0) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Y!1, Z!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(X!2, Z!0) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Y!1, Z!0))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(59,plain,
% 0.14/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(X!2, Z!0) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Y!1, Z!0))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(60,plain,
% 0.14/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | distinct_points(X!2, Z!0) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | (~apart_point_and_line(X!2, line_connecting(Y!1, Z!0)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.14/0.40 tff(61,plain,
% 0.14/0.40 (~apart_point_and_line(X!2, line_connecting(Y!1, Z!0))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[60, 57, 1, 47])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (^[X: $i, Y: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (^[X: $i, Y: $i] : rewrite((distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(66,plain,
% 0.21/0.40 (![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y)))) <=> ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.40 tff(67,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.21/0.40 tff(70,plain,(
% 0.21/0.40 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[69])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(Y!1, Z!0)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, Z!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(Y!1, Z!0)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, Z!0))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(Y!1, Z!0)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, Z!0))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(Y!1, Z!0)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, Z!0)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 (~apart_point_and_line(Y!1, line_connecting(Y!1, Z!0))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[74, 71, 33])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[78, 71, 15])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[82, 43, 15])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (^[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))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.41 tff(91,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.21/0.41 tff(94,plain,(
% 0.21/0.41 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[93])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | ((~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, Z!0)) | apart_point_and_line(X!2, line_connecting(Y!1, Z!0)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, Z!0)) | apart_point_and_line(X!2, line_connecting(Y!1, Z!0)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 ((apart_point_and_line(Y!1, line_connecting(Y!1, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0)))) <=> ((~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, Z!0)) | apart_point_and_line(X!2, line_connecting(Y!1, Z!0)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Y!1, line_connecting(Y!1, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | ((~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, Z!0)) | apart_point_and_line(X!2, line_connecting(Y!1, Z!0)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[98])).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Y!1, line_connecting(Y!1, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, Z!0)) | apart_point_and_line(X!2, line_connecting(Y!1, Z!0)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[99, 97])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Y!1, line_connecting(Y!1, Z!0)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, Z!0)) | apart_point_and_line(X!2, line_connecting(Y!1, Z!0)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.41 tff(103,plain,
% 0.21/0.41 (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[102, 96, 15, 83, 79, 75, 61])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 (apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.21/0.41 inference(or_elim,[status(thm)],[14])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.41 tff(110,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.21/0.41 tff(113,plain,(
% 0.21/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[112])).
% 0.21/0.41 tff(114,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.21/0.41 tff(115,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(116,plain,
% 0.21/0.41 ((distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0)) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))) <=> ((~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(117,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0)) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[116])).
% 0.21/0.41 tff(118,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0)) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[117, 115])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0)) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(Y!1, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, Z!0))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[120, 114, 104, 47, 103])).
% 0.21/0.42 tff(122,plain,(distinct_points(X!2, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[125, 43])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[126, 122])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 ((distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))) <=> ((~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[129])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[130, 128])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 (apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[133, 114, 104])).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 (distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[134, 127])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 (((~![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)))) | ((~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(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)))) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 ((apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)))) <=> ((~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 (((~![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(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(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)))) | ((~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[137])).
% 0.21/0.42 tff(139,plain,
% 0.21/0.42 (((~![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(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(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)))) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[138, 136])).
% 0.21/0.42 tff(140,plain,
% 0.21/0.42 ((~![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(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(141,plain,
% 0.21/0.42 ((~![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)))) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.21/0.42 tff(142,plain,
% 0.21/0.42 (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[141, 96, 15, 83, 79])).
% 0.21/0.42 tff(143,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(144,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(145,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.42 tff(146,plain,
% 0.21/0.42 ((~distinct_points(X!2, Z!0)) | (~apart_point_and_line(X!2, line_connecting(X!2, Z!0)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[145, 71])).
% 0.21/0.42 tff(147,plain,
% 0.21/0.42 (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[146, 122])).
% 0.21/0.42 tff(148,plain,
% 0.21/0.42 (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))),
% 0.21/0.42 inference(or_elim,[status(thm)],[14])).
% 0.21/0.42 tff(149,plain,
% 0.21/0.42 (((~![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(Y!1, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(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(Y!1, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(150,plain,
% 0.21/0.42 ((apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))) <=> (apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(151,plain,
% 0.21/0.42 (((~![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(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(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(Y!1, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[150])).
% 0.21/0.42 tff(152,plain,
% 0.21/0.42 (((~![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(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(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(Y!1, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[151, 149])).
% 0.21/0.42 tff(153,plain,
% 0.21/0.42 ((~![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(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Z!0)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 ((~![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(Y!1, line_connecting(X!2, Z!0)) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 (apart_point_and_line(X!2, line_connecting(X!2, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[154, 96, 148, 15, 83, 79])).
% 0.21/0.43 tff(156,plain,
% 0.21/0.43 (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[155, 147])).
% 0.21/0.43 tff(157,plain,
% 0.21/0.43 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(158,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[157])).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(160,plain,
% 0.21/0.43 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(161,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[160])).
% 0.21/0.43 tff(162,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart5')).
% 0.21/0.43 tff(163,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.21/0.43 tff(164,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.21/0.43 tff(165,plain,(
% 0.21/0.43 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[164])).
% 0.21/0.43 tff(166,plain,
% 0.21/0.43 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.21/0.43 tff(167,plain,
% 0.21/0.43 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(168,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(169,plain,
% 0.21/0.43 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(X!2, Z!0)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.21/0.43 tff(170,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[169, 166, 156, 142, 135])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------