TSTP Solution File: GEO187+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO187+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO187+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 07:04:17 EDT 2022
% 0.13/0.34 % 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.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(apart_point_and_line_type, type, (
% 0.19/0.46 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.46 tff(line_connecting_type, type, (
% 0.19/0.46 line_connecting: ( $i * $i ) > $i)).
% 0.19/0.46 tff(tptp_fun_Y_2_type, type, (
% 0.19/0.46 tptp_fun_Y_2: $i)).
% 0.19/0.46 tff(tptp_fun_X_3_type, type, (
% 0.19/0.46 tptp_fun_X_3: $i)).
% 0.19/0.46 tff(tptp_fun_U_1_type, type, (
% 0.19/0.46 tptp_fun_U_1: $i)).
% 0.19/0.46 tff(distinct_lines_type, type, (
% 0.19/0.46 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.46 tff(tptp_fun_V_0_type, type, (
% 0.19/0.46 tptp_fun_V_0: $i)).
% 0.19/0.46 tff(distinct_points_type, type, (
% 0.19/0.46 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.46 tff(1,assumption,(distinct_points(X!3, X!3)), introduced(assumption)).
% 0.19/0.46 tff(2,plain,
% 0.19/0.46 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(3,plain,
% 0.19/0.46 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.46 tff(4,plain,
% 0.19/0.46 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.19/0.46 tff(6,plain,
% 0.19/0.46 (![X: $i] : (~distinct_points(X, X))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.46 tff(7,plain,(
% 0.19/0.46 ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.46 inference(skolemize,[status(sab)],[6])).
% 0.19/0.46 tff(8,plain,
% 0.19/0.46 (![X: $i] : (~distinct_points(X, X))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.46 tff(9,plain,
% 0.19/0.46 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(X!3, X!3))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(10,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.46 tff(11,plain,(~distinct_points(X!3, X!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(12,assumption,(~distinct_points(X!3, X!3)), introduced(assumption)).
% 0.19/0.46 tff(13,plain,
% 0.19/0.46 (((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2))) | distinct_points(X!3, X!3)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 ((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.19/0.46 tff(15,assumption,(apart_point_and_line(X!3, line_connecting(X!3, Y!2))), introduced(assumption)).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 ((~![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))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 ((~![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))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(18,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/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.46 tff(19,plain,
% 0.19/0.46 (~![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.46 tff(20,plain,
% 0.19/0.46 (~![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.19/0.46 tff(21,plain,
% 0.19/0.46 (~![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.46 tff(22,plain,
% 0.19/0.46 (~![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.19/0.46 tff(23,plain,
% 0.19/0.46 (~![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.19/0.46 tff(24,plain,
% 0.19/0.46 (~![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 (~![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[24, 16])).
% 0.19/0.46 tff(26,plain,(
% 0.19/0.46 ~((~(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)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[25])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 (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)))),
% 0.19/0.46 inference(or_elim,[status(thm)],[26])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 (distinct_points(X!3, Y!2)),
% 0.19/0.46 inference(and_elim,[status(thm)],[27])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 (^[X: $i, Y: $i, Z: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(Z, X) & distinct_points(Z, Y)) <=> (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))), rewrite(((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))) <=> ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> (distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))))), rewrite((distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.46 tff(36,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con1')).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.46 tff(39,plain,(
% 0.19/0.46 ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[38])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[40, 30])).
% 0.19/0.47 tff(42,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))) | (~((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))) | (~((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))) | (~((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))) | (~((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[44, 41, 28, 15, 14])).
% 0.19/0.47 tff(46,plain,((~apart_point_and_line(X!3, line_connecting(X!3, Y!2))) | distinct_points(X!3, X!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[46, 11])).
% 0.19/0.47 tff(48,assumption,(distinct_points(Y!2, Y!2)), introduced(assumption)).
% 0.19/0.47 tff(49,plain,
% 0.19/0.47 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Y!2, Y!2))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[49, 8, 48])).
% 0.19/0.47 tff(51,plain,(~distinct_points(Y!2, Y!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(52,plain,
% 0.19/0.47 (((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))) | distinct_points(Y!2, Y!2)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 ((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.19/0.47 tff(54,assumption,(apart_point_and_line(Y!2, line_connecting(X!3, Y!2))), introduced(assumption)).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))) | (~((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))) | (~((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(56,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))) | (~((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(57,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))) | (~((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[57, 41, 28, 54, 53])).
% 0.19/0.47 tff(59,plain,(~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(60,plain,
% 0.19/0.47 (~apart_point_and_line(Y!2, line_connecting(U!1, V!0))),
% 0.19/0.47 inference(and_elim,[status(thm)],[27])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 (~apart_point_and_line(X!3, line_connecting(U!1, V!0))),
% 0.19/0.47 inference(and_elim,[status(thm)],[27])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(68,plain,
% 0.19/0.47 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.47 tff(69,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/GEO008+0.ax','cu1')).
% 0.19/0.47 tff(70,plain,
% 0.19/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.47 tff(71,plain,
% 0.19/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.47 tff(72,plain,(
% 0.19/0.47 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[71])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.19/0.47 tff(75,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (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)) | (~distinct_lines(line_connecting(X!3, 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(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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)) | (~distinct_lines(line_connecting(X!3, 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(X!3, Y!2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(76,plain,
% 0.19/0.47 ((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)) | (~distinct_lines(line_connecting(X!3, 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(X!3, Y!2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(77,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (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)) | (~distinct_lines(line_connecting(X!3, 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(X!3, Y!2))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[76])).
% 0.19/0.47 tff(78,plain,
% 0.19/0.47 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (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)) | (~distinct_lines(line_connecting(X!3, 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(X!3, Y!2)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[77, 75])).
% 0.19/0.48 tff(79,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(80,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_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)) | (~distinct_lines(line_connecting(X!3, 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(X!3, Y!2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.48 tff(81,plain,
% 0.19/0.48 ((~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))) | apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[80, 74, 28, 61, 60, 59])).
% 0.19/0.48 tff(82,plain,
% 0.19/0.48 (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[81, 47])).
% 0.19/0.48 tff(83,assumption,(distinct_points(U!1, U!1)), introduced(assumption)).
% 0.19/0.48 tff(84,plain,
% 0.19/0.48 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(U!1, U!1))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(85,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[84, 8, 83])).
% 0.19/0.48 tff(86,plain,(~distinct_points(U!1, U!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 (((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0))) | distinct_points(U!1, U!1)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 ((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.48 tff(89,assumption,(apart_point_and_line(U!1, line_connecting(U!1, V!0))), introduced(assumption)).
% 0.19/0.48 tff(90,plain,
% 0.19/0.48 (distinct_points(U!1, V!0)),
% 0.19/0.48 inference(and_elim,[status(thm)],[27])).
% 0.19/0.48 tff(91,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0))) | (~((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0))) | (~((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(92,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0))) | (~((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0))) | (~((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[93, 41, 90, 89, 88])).
% 0.19/0.48 tff(95,plain,(~apart_point_and_line(U!1, line_connecting(U!1, V!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.48 tff(98,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(99,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.48 tff(101,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/GEO008+0.ax','ceq2')).
% 0.19/0.48 tff(102,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.48 tff(103,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.19/0.48 tff(104,plain,(
% 0.19/0.48 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[103])).
% 0.19/0.48 tff(105,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.19/0.48 tff(106,plain,
% 0.19/0.48 (((~![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))) | 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)))) <=> ((~![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))) | 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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 ((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))) | 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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 (((~![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))) | 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))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 (((~![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))) | 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)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[108, 106])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 ((~![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))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 ((~![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))) | 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))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 ((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) | 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))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[111, 105])).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 ((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[112, 95])).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 (~apart_point_and_line(U!1, line_connecting(X!3, Y!2))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[113, 82])).
% 0.19/0.48 tff(115,assumption,(distinct_points(V!0, V!0)), introduced(assumption)).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(V!0, V!0))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(117,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[116, 8, 115])).
% 0.19/0.48 tff(118,plain,(~distinct_points(V!0, V!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(119,plain,
% 0.19/0.48 (((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0))) | distinct_points(V!0, V!0)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(120,plain,
% 0.19/0.48 ((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.48 tff(121,assumption,(apart_point_and_line(V!0, line_connecting(U!1, V!0))), introduced(assumption)).
% 0.19/0.48 tff(122,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0))) | (~((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0))) | (~((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(123,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0))) | (~((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(124,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0))) | (~((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.48 tff(125,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[124, 41, 90, 121, 120])).
% 0.19/0.48 tff(126,plain,(~apart_point_and_line(V!0, line_connecting(U!1, V!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(128,plain,
% 0.19/0.48 ((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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(129,plain,
% 0.19/0.48 (((~![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))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.48 tff(130,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[129, 127])).
% 0.19/0.48 tff(131,plain,
% 0.19/0.48 ((~![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))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(132,plain,
% 0.19/0.48 ((~![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))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.48 tff(133,plain,
% 0.19/0.48 ((~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))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[132, 105])).
% 0.19/0.48 tff(134,plain,
% 0.19/0.48 ((~apart_point_and_line(V!0, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[133, 126])).
% 0.19/0.48 tff(135,plain,
% 0.19/0.48 (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[134, 82])).
% 0.19/0.48 tff(136,plain,
% 0.19/0.48 ((~(~(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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(137,plain,
% 0.19/0.48 (((~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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(138,plain,
% 0.19/0.48 ((~((~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)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.48 tff(139,plain,
% 0.19/0.48 ((~((~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)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[138, 136])).
% 0.19/0.48 tff(140,plain,
% 0.19/0.48 (~((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) & (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))))),
% 0.19/0.48 inference(or_elim,[status(thm)],[26])).
% 0.19/0.48 tff(141,plain,
% 0.19/0.48 (apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.48 tff(142,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[141, 135, 114])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------