TSTP Solution File: GEO189+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO189+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:35:26 EDT 2022
% Result : Theorem 0.16s 0.35s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GEO189+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n024.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Wed Aug 31 06:52:04 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.16/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.31 Usage: tptp [options] [-file:]file
% 0.16/0.31 -h, -? prints this message.
% 0.16/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.31 -m, -model generate model.
% 0.16/0.31 -p, -proof generate proof.
% 0.16/0.31 -c, -core generate unsat core of named formulas.
% 0.16/0.31 -st, -statistics display statistics.
% 0.16/0.31 -t:timeout set timeout (in second).
% 0.16/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.31 -<param>:<value> configuration parameter and value.
% 0.16/0.31 -o:<output-file> file to place output in.
% 0.16/0.35 % SZS status Theorem
% 0.16/0.35 % SZS output start Proof
% 0.16/0.35 tff(distinct_lines_type, type, (
% 0.16/0.35 distinct_lines: ( $i * $i ) > $o)).
% 0.16/0.35 tff(line_connecting_type, type, (
% 0.16/0.35 line_connecting: ( $i * $i ) > $i)).
% 0.16/0.35 tff(tptp_fun_Y_1_type, type, (
% 0.16/0.35 tptp_fun_Y_1: $i)).
% 0.16/0.35 tff(tptp_fun_X_2_type, type, (
% 0.16/0.35 tptp_fun_X_2: $i)).
% 0.16/0.35 tff(tptp_fun_Z_0_type, type, (
% 0.16/0.35 tptp_fun_Z_0: $i)).
% 0.16/0.35 tff(apart_point_and_line_type, type, (
% 0.16/0.35 apart_point_and_line: ( $i * $i ) > $o)).
% 0.16/0.35 tff(distinct_points_type, type, (
% 0.16/0.35 distinct_points: ( $i * $i ) > $o)).
% 0.16/0.35 tff(1,plain,
% 0.16/0.35 ((~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Y, line_connecting(X, Z))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~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) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y)))))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(2,plain,
% 0.16/0.35 ((~![X: $i, Y: $i, Z: $i] : ((((distinct_points(X, Y) & distinct_points(X, Z)) & distinct_points(Y, Z)) & (~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) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y)))))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(3,axiom,(~![X: $i, Y: $i, Z: $i] : ((((distinct_points(X, Y) & distinct_points(X, Z)) & distinct_points(Y, Z)) & (~apart_point_and_line(Z, line_connecting(X, Y)))) => (~apart_point_and_line(Y, line_connecting(X, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.16/0.35 tff(4,plain,
% 0.16/0.35 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Y, line_connecting(X, Z))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.16/0.35 tff(5,plain,
% 0.16/0.35 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Y, line_connecting(X, Z))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.16/0.35 tff(6,plain,
% 0.16/0.35 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Y, line_connecting(X, Z))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.16/0.35 tff(7,plain,
% 0.16/0.35 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Y, line_connecting(X, Z))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.16/0.35 tff(8,plain,
% 0.16/0.35 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Y, line_connecting(X, Z))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.16/0.35 tff(9,plain,
% 0.16/0.35 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Y, line_connecting(X, Z))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.16/0.35 tff(10,plain,
% 0.16/0.35 (~![X: $i, Y: $i, Z: $i] : ((~apart_point_and_line(Y, line_connecting(X, Z))) | (~(distinct_points(X, Y) & distinct_points(X, Z) & distinct_points(Y, Z) & (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.16/0.35 tff(11,plain,(
% 0.16/0.35 ~((~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))) | (~(distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & distinct_points(Y!1, Z!0) & (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))))),
% 0.16/0.35 inference(skolemize,[status(sab)],[10])).
% 0.16/0.35 tff(12,plain,
% 0.16/0.35 (distinct_points(X!2, Y!1) & distinct_points(X!2, Z!0) & distinct_points(Y!1, Z!0) & (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))),
% 0.16/0.35 inference(or_elim,[status(thm)],[11])).
% 0.16/0.35 tff(13,plain,
% 0.16/0.35 (distinct_points(X!2, Z!0)),
% 0.16/0.35 inference(and_elim,[status(thm)],[12])).
% 0.16/0.35 tff(14,plain,
% 0.16/0.35 (^[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)))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(15,plain,
% 0.16/0.35 (![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))))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[14])).
% 0.16/0.35 tff(16,plain,
% 0.16/0.35 (![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))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(17,plain,
% 0.16/0.35 (^[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)))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(18,plain,
% 0.16/0.35 (![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))))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[17])).
% 0.16/0.35 tff(19,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(X, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci1')).
% 0.16/0.35 tff(20,plain,
% 0.16/0.35 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.16/0.35 tff(21,plain,
% 0.16/0.35 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.16/0.35 tff(22,plain,(
% 0.16/0.35 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.16/0.35 inference(skolemize,[status(sab)],[21])).
% 0.16/0.35 tff(23,plain,
% 0.16/0.35 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.16/0.35 tff(24,plain,
% 0.16/0.35 (((~![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))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(25,plain,
% 0.16/0.35 ((~![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))))),
% 0.16/0.35 inference(quant_inst,[status(thm)],[])).
% 0.16/0.35 tff(26,plain,
% 0.16/0.35 ((~![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)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.16/0.35 tff(27,plain,
% 0.16/0.35 (~apart_point_and_line(X!2, line_connecting(X!2, Z!0))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.16/0.35 tff(28,plain,
% 0.16/0.35 (^[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)))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(29,plain,
% 0.16/0.35 (![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))))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[28])).
% 0.16/0.35 tff(30,plain,
% 0.16/0.35 (![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))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(31,plain,
% 0.16/0.35 (^[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)))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(32,plain,
% 0.16/0.35 (![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))))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[31])).
% 0.16/0.35 tff(33,axiom,(![X: $i, Y: $i] : (distinct_points(X, Y) => (~apart_point_and_line(Y, line_connecting(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ci2')).
% 0.16/0.35 tff(34,plain,
% 0.16/0.35 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.16/0.35 tff(35,plain,
% 0.16/0.35 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.16/0.35 tff(36,plain,(
% 0.16/0.35 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.16/0.35 inference(skolemize,[status(sab)],[35])).
% 0.16/0.35 tff(37,plain,
% 0.16/0.35 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.16/0.35 tff(38,plain,
% 0.16/0.35 (((~![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))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(39,plain,
% 0.16/0.35 ((~![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))))),
% 0.16/0.35 inference(quant_inst,[status(thm)],[])).
% 0.16/0.35 tff(40,plain,
% 0.16/0.35 ((~![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)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.16/0.35 tff(41,plain,
% 0.16/0.35 (~apart_point_and_line(Z!0, line_connecting(X!2, Z!0))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[40, 37, 13])).
% 0.16/0.35 tff(42,plain,
% 0.16/0.35 (distinct_points(X!2, Y!1)),
% 0.16/0.35 inference(and_elim,[status(thm)],[12])).
% 0.16/0.35 tff(43,plain,
% 0.16/0.35 (((~![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))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(44,plain,
% 0.16/0.35 ((~![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))))),
% 0.16/0.35 inference(quant_inst,[status(thm)],[])).
% 0.16/0.35 tff(45,plain,
% 0.16/0.35 ((~![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)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.16/0.35 tff(46,plain,
% 0.16/0.35 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[45, 23, 42])).
% 0.16/0.35 tff(47,plain,
% 0.16/0.35 (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.16/0.35 inference(and_elim,[status(thm)],[12])).
% 0.16/0.35 tff(48,plain,
% 0.16/0.35 (^[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))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(49,plain,
% 0.16/0.35 (![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)))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[48])).
% 0.16/0.35 tff(50,plain,
% 0.16/0.35 (^[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)))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(51,plain,
% 0.16/0.35 (![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)))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[50])).
% 0.16/0.35 tff(52,plain,
% 0.16/0.35 (![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))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(53,plain,
% 0.16/0.35 (^[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))))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(54,plain,
% 0.16/0.35 (![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))))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[53])).
% 0.16/0.35 tff(55,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')).
% 0.16/0.35 tff(56,plain,
% 0.16/0.35 (![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))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.16/0.35 tff(57,plain,
% 0.16/0.35 (![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))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.16/0.35 tff(58,plain,(
% 0.16/0.35 ![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))))),
% 0.16/0.35 inference(skolemize,[status(sab)],[57])).
% 0.16/0.35 tff(59,plain,
% 0.16/0.35 (![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)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.16/0.35 tff(60,plain,
% 0.16/0.35 (![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)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.16/0.35 tff(61,plain,
% 0.16/0.35 (((~![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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | 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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | 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))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(62,plain,
% 0.16/0.35 ((apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, 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, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))) <=> (apart_point_and_line(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | 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))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(63,plain,
% 0.16/0.35 (((~![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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, 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, 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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | 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)))))),
% 0.16/0.35 inference(monotonicity,[status(thm)],[62])).
% 0.16/0.35 tff(64,plain,
% 0.16/0.35 (((~![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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, 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, 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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | 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))))),
% 0.16/0.35 inference(transitivity,[status(thm)],[63, 61])).
% 0.16/0.35 tff(65,plain,
% 0.16/0.35 ((~![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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(Z!0, 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, Z!0)) | (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(66,plain,
% 0.16/0.36 ((~![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(Z!0, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Z!0)) | apart_point_and_line(Z!0, line_connecting(X!2, Z!0)) | 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)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.16/0.36 tff(67,plain,
% 0.16/0.36 (~distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[66, 60, 13, 47, 46, 41, 27])).
% 0.16/0.36 tff(68,plain,
% 0.16/0.36 (((~![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))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(69,plain,
% 0.16/0.36 ((~![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))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(70,plain,
% 0.16/0.36 ((~![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)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.16/0.36 tff(71,plain,
% 0.16/0.36 (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[70, 37, 42])).
% 0.16/0.36 tff(72,plain,
% 0.16/0.36 (apart_point_and_line(Y!1, line_connecting(X!2, Z!0))),
% 0.16/0.36 inference(or_elim,[status(thm)],[11])).
% 0.16/0.36 tff(73,plain,
% 0.16/0.36 (^[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))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(74,plain,
% 0.16/0.36 (![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)))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[73])).
% 0.16/0.36 tff(75,plain,
% 0.16/0.36 (![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)))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(76,plain,
% 0.16/0.36 (^[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)))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(77,plain,
% 0.16/0.36 (![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)))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[76])).
% 0.16/0.36 tff(78,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/sandbox/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.16/0.36 tff(79,plain,
% 0.16/0.36 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.16/0.36 tff(80,plain,
% 0.16/0.36 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.16/0.36 tff(81,plain,(
% 0.16/0.36 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.16/0.36 inference(skolemize,[status(sab)],[80])).
% 0.16/0.36 tff(82,plain,
% 0.16/0.36 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.16/0.36 tff(83,plain,
% 0.16/0.36 (((~![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(Y!1, line_connecting(X!2, Z!0))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, 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(Y!1, line_connecting(X!2, Z!0))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(84,plain,
% 0.16/0.36 ((distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)) | 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(Y!1, line_connecting(X!2, Z!0))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(85,plain,
% 0.16/0.36 (((~![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, Z!0), line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(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(Y!1, line_connecting(X!2, Z!0))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))))),
% 0.16/0.36 inference(monotonicity,[status(thm)],[84])).
% 0.16/0.36 tff(86,plain,
% 0.16/0.36 (((~![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, Z!0), line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(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(Y!1, line_connecting(X!2, Z!0))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1)))),
% 0.16/0.36 inference(transitivity,[status(thm)],[85, 83])).
% 0.16/0.36 tff(87,plain,
% 0.16/0.36 ((~![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, Z!0), line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(88,plain,
% 0.16/0.36 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(Y!1, line_connecting(X!2, Z!0))) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | distinct_lines(line_connecting(X!2, Z!0), line_connecting(X!2, Y!1))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.16/0.36 tff(89,plain,
% 0.16/0.36 ($false),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[88, 82, 72, 71, 67])).
% 0.16/0.36 % SZS output end Proof
%------------------------------------------------------------------------------