TSTP Solution File: GEO187+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO187+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:35:25 EDT 2022
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO187+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 06:58:19 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(apart_point_and_line_type, type, (
% 0.21/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.40 tff(line_connecting_type, type, (
% 0.21/0.40 line_connecting: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.21/0.40 tptp_fun_Y_2: $i)).
% 0.21/0.40 tff(tptp_fun_X_3_type, type, (
% 0.21/0.40 tptp_fun_X_3: $i)).
% 0.21/0.40 tff(tptp_fun_V_0_type, type, (
% 0.21/0.40 tptp_fun_V_0: $i)).
% 0.21/0.40 tff(distinct_lines_type, type, (
% 0.21/0.40 distinct_lines: ( $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_U_1_type, type, (
% 0.21/0.40 tptp_fun_U_1: $i)).
% 0.21/0.40 tff(distinct_points_type, type, (
% 0.21/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & distinct_points(U, V) & (~apart_point_and_line(X, line_connecting(U, V))) & (~apart_point_and_line(Y, line_connecting(U, V))))) | ((~apart_point_and_line(U, line_connecting(X, Y))) & (~apart_point_and_line(V, line_connecting(X, Y)))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & distinct_points(U, V) & (~apart_point_and_line(X, line_connecting(U, V))) & (~apart_point_and_line(Y, line_connecting(U, V))))) | ((~apart_point_and_line(U, line_connecting(X, Y))) & (~apart_point_and_line(V, line_connecting(X, Y))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 ((~![X: $i, Y: $i, U: $i, V: $i] : ((((distinct_points(X, Y) & distinct_points(U, V)) & (~apart_point_and_line(X, line_connecting(U, V)))) & (~apart_point_and_line(Y, line_connecting(U, V)))) => ((~apart_point_and_line(U, line_connecting(X, Y))) & (~apart_point_and_line(V, line_connecting(X, Y)))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & distinct_points(U, V) & (~apart_point_and_line(X, line_connecting(U, V))) & (~apart_point_and_line(Y, line_connecting(U, V))))) | ((~apart_point_and_line(U, line_connecting(X, Y))) & (~apart_point_and_line(V, line_connecting(X, Y))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(3,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : ((((distinct_points(X, Y) & distinct_points(U, V)) & (~apart_point_and_line(X, line_connecting(U, V)))) & (~apart_point_and_line(Y, line_connecting(U, V)))) => ((~apart_point_and_line(U, line_connecting(X, Y))) & (~apart_point_and_line(V, line_connecting(X, Y)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.40 tff(4,plain,
% 0.21/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & distinct_points(U, V) & (~apart_point_and_line(X, line_connecting(U, V))) & (~apart_point_and_line(Y, line_connecting(U, V))))) | ((~apart_point_and_line(U, line_connecting(X, Y))) & (~apart_point_and_line(V, line_connecting(X, Y)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & distinct_points(U, V) & (~apart_point_and_line(X, line_connecting(U, V))) & (~apart_point_and_line(Y, line_connecting(U, V))))) | ((~apart_point_and_line(U, line_connecting(X, Y))) & (~apart_point_and_line(V, line_connecting(X, Y)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & distinct_points(U, V) & (~apart_point_and_line(X, line_connecting(U, V))) & (~apart_point_and_line(Y, line_connecting(U, V))))) | ((~apart_point_and_line(U, line_connecting(X, Y))) & (~apart_point_and_line(V, line_connecting(X, Y)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & distinct_points(U, V) & (~apart_point_and_line(X, line_connecting(U, V))) & (~apart_point_and_line(Y, line_connecting(U, V))))) | ((~apart_point_and_line(U, line_connecting(X, Y))) & (~apart_point_and_line(V, line_connecting(X, Y)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & distinct_points(U, V) & (~apart_point_and_line(X, line_connecting(U, V))) & (~apart_point_and_line(Y, line_connecting(U, V))))) | ((~apart_point_and_line(U, line_connecting(X, Y))) & (~apart_point_and_line(V, line_connecting(X, Y)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & distinct_points(U, V) & (~apart_point_and_line(X, line_connecting(U, V))) & (~apart_point_and_line(Y, line_connecting(U, V))))) | ((~apart_point_and_line(U, line_connecting(X, Y))) & (~apart_point_and_line(V, line_connecting(X, Y)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & distinct_points(U, V) & (~apart_point_and_line(X, line_connecting(U, V))) & (~apart_point_and_line(Y, line_connecting(U, V))))) | ((~apart_point_and_line(U, line_connecting(X, Y))) & (~apart_point_and_line(V, line_connecting(X, Y)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.40 tff(11,plain,(
% 0.21/0.40 ~((~(distinct_points(X!3, Y!2) & distinct_points(U!1, V!0) & (~apart_point_and_line(X!3, line_connecting(U!1, V!0))) & (~apart_point_and_line(Y!2, line_connecting(U!1, V!0))))) | ((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) & (~apart_point_and_line(V!0, line_connecting(X!3, Y!2)))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[10])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (distinct_points(X!3, Y!2) & distinct_points(U!1, V!0) & (~apart_point_and_line(X!3, line_connecting(U!1, V!0))) & (~apart_point_and_line(Y!2, line_connecting(U!1, V!0)))),
% 0.21/0.40 inference(or_elim,[status(thm)],[11])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (distinct_points(X!3, Y!2)),
% 0.21/0.40 inference(and_elim,[status(thm)],[12])).
% 0.21/0.40 tff(14,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(15,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)],[14])).
% 0.21/0.40 tff(16,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(17,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(18,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)],[17])).
% 0.21/0.40 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')).
% 0.21/0.40 tff(20,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)],[19, 18])).
% 0.21/0.40 tff(21,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)],[20, 16])).
% 0.21/0.40 tff(22,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)],[21])).
% 0.21/0.40 tff(23,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)],[22, 15])).
% 0.21/0.40 tff(24,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!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(25,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!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(26,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!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (^[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)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (^[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)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.40 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')).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.21/0.40 tff(36,plain,(
% 0.21/0.40 ![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[35])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.21/0.40 tff(38,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!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(39,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!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(40,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!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[40, 37, 13])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (~apart_point_and_line(Y!2, line_connecting(U!1, V!0))),
% 0.21/0.40 inference(and_elim,[status(thm)],[12])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 (~apart_point_and_line(X!3, line_connecting(U!1, V!0))),
% 0.21/0.40 inference(and_elim,[status(thm)],[12])).
% 0.21/0.40 tff(44,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(45,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)],[44])).
% 0.21/0.40 tff(46,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(47,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)],[46])).
% 0.21/0.40 tff(48,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(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 (^[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))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.40 tff(51,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','cu1')).
% 0.21/0.40 tff(52,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))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.40 tff(53,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))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.21/0.40 tff(54,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))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[53])).
% 0.21/0.40 tff(55,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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.21/0.40 tff(56,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)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.21/0.41 tff(57,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(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | (~distinct_points(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!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)))) | apart_point_and_line(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | (~distinct_points(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 ((apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_points(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)))) <=> (apart_point_and_line(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | (~distinct_points(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(59,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!2, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_points(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!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)))) | (apart_point_and_line(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | (~distinct_points(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.41 tff(60,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!2, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_points(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!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)))) | apart_point_and_line(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | (~distinct_points(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[59, 57])).
% 0.21/0.41 tff(61,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!2, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_points(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(62,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(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | (~distinct_points(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[62, 56, 13, 43, 42, 41, 27])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (distinct_points(U!1, V!0)),
% 0.21/0.41 inference(and_elim,[status(thm)],[12])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | ((~distinct_points(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Y, line_connecting(X, Y))))) | (~distinct_points(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (~apart_point_and_line(V!0, line_connecting(U!1, V!0))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[67, 37, 64])).
% 0.21/0.41 tff(69,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(70,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)],[69])).
% 0.21/0.41 tff(71,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(72,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(73,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)],[72])).
% 0.21/0.41 tff(74,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')).
% 0.21/0.41 tff(75,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)],[74, 73])).
% 0.21/0.41 tff(76,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)],[75, 71])).
% 0.21/0.41 tff(77,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)],[76])).
% 0.21/0.41 tff(78,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)],[77, 70])).
% 0.21/0.41 tff(79,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(V!0, line_connecting(X!3, Y!2))) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!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(V!0, line_connecting(X!3, Y!2))) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 ((distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(X!3, Y!2)))) <=> ((~apart_point_and_line(V!0, line_connecting(X!3, Y!2))) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(81,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!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))))) <=> ((~![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(V!0, line_connecting(X!3, Y!2))) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[80])).
% 0.21/0.41 tff(82,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!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))))) <=> ((~![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(V!0, line_connecting(X!3, Y!2))) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[81, 79])).
% 0.21/0.41 tff(83,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!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(84,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(V!0, line_connecting(X!3, Y!2))) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[84, 78, 68, 63])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0))))) <=> ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | ((~distinct_points(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 ((~![X: $i, Y: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(X, line_connecting(X, Y))))) | (~distinct_points(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (~apart_point_and_line(U!1, line_connecting(U!1, V!0))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[88, 23, 64])).
% 0.21/0.42 tff(90,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(U!1, line_connecting(X!3, Y!2))) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!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(U!1, line_connecting(X!3, Y!2))) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 ((distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(X!3, Y!2)))) <=> ((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(92,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!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(X!3, Y!2))))) <=> ((~![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(U!1, line_connecting(X!3, Y!2))) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[91])).
% 0.21/0.42 tff(93,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!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(X!3, Y!2))))) <=> ((~![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(U!1, line_connecting(X!3, Y!2))) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[92, 90])).
% 0.21/0.42 tff(94,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!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(X!3, Y!2))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(95,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(U!1, line_connecting(X!3, Y!2))) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (~apart_point_and_line(U!1, line_connecting(X!3, Y!2))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[95, 78, 89, 63])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 ((~(~(apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2))))) <=> (apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) & (~apart_point_and_line(V!0, line_connecting(X!3, Y!2)))) <=> (~(apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((~((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) & (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))))) <=> (~(~(apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[98])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 ((~((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) & (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))))) <=> (apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[99, 97])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (~((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) & (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))))),
% 0.21/0.42 inference(or_elim,[status(thm)],[11])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[102, 96, 85])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------