TSTP Solution File: GEO257+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO257+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 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 20:36:07 EDT 2022
% Result : Theorem 0.17s 0.47s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO257+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 31 07:21:19 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.17/0.47 % SZS status Theorem
% 0.17/0.47 % SZS output start Proof
% 0.17/0.47 tff(left_apart_point_type, type, (
% 0.17/0.47 left_apart_point: ( $i * $i ) > $o)).
% 0.17/0.47 tff(reverse_line_type, type, (
% 0.17/0.47 reverse_line: $i > $i)).
% 0.17/0.47 tff(line_connecting_type, type, (
% 0.17/0.47 line_connecting: ( $i * $i ) > $i)).
% 0.17/0.47 tff(tptp_fun_C_1_type, type, (
% 0.17/0.47 tptp_fun_C_1: $i)).
% 0.17/0.47 tff(tptp_fun_A_3_type, type, (
% 0.17/0.47 tptp_fun_A_3: $i)).
% 0.17/0.47 tff(tptp_fun_D_0_type, type, (
% 0.17/0.47 tptp_fun_D_0: $i)).
% 0.17/0.47 tff(distinct_lines_type, type, (
% 0.17/0.47 distinct_lines: ( $i * $i ) > $o)).
% 0.17/0.47 tff(tptp_fun_L_4_type, type, (
% 0.17/0.47 tptp_fun_L_4: $i)).
% 0.17/0.47 tff(apart_point_and_line_type, type, (
% 0.17/0.47 apart_point_and_line: ( $i * $i ) > $o)).
% 0.17/0.47 tff(distinct_points_type, type, (
% 0.17/0.47 distinct_points: ( $i * $i ) > $o)).
% 0.17/0.47 tff(tptp_fun_B_2_type, type, (
% 0.17/0.47 tptp_fun_B_2: $i)).
% 0.17/0.47 tff(before_on_line_type, type, (
% 0.17/0.47 before_on_line: ( $i * $i * $i ) > $o)).
% 0.17/0.47 tff(unequally_directed_lines_type, type, (
% 0.17/0.47 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.17/0.47 tff(1,assumption,(distinct_lines(L!4, line_connecting(A!3, C!1))), introduced(assumption)).
% 0.17/0.47 tff(2,plain,
% 0.17/0.47 (^[A: $i, L: $i] : refl((apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))))),
% 0.17/0.47 inference(bind,[status(th)],[])).
% 0.17/0.47 tff(3,plain,
% 0.17/0.47 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.17/0.47 inference(quant_intro,[status(thm)],[2])).
% 0.17/0.47 tff(4,plain,
% 0.17/0.47 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(5,axiom,(![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','apt_def')).
% 0.17/0.47 tff(6,plain,
% 0.17/0.47 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.17/0.47 tff(7,plain,(
% 0.17/0.47 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.17/0.47 inference(skolemize,[status(sab)],[6])).
% 0.17/0.47 tff(8,plain,
% 0.17/0.47 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.17/0.47 tff(9,plain,
% 0.17/0.47 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (apart_point_and_line(C!1, line_connecting(A!3, C!1)) <=> (left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1)))))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(10,plain,
% 0.17/0.47 (apart_point_and_line(C!1, line_connecting(A!3, C!1)) <=> (left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.17/0.47 tff(11,plain,
% 0.17/0.47 ((~(before_on_line(L!4, A!3, C!1) | (~(before_on_line(L!4, A!3, B!2) & before_on_line(L!4, B!2, C!1))) | (~(distinct_points(A!3, C!1) & distinct_points(B!2, C!1) & (~apart_point_and_line(C!1, L!4)) & left_apart_point(D!0, L!4))))) <=> (~(before_on_line(L!4, A!3, C!1) | (~(before_on_line(L!4, A!3, B!2) & before_on_line(L!4, B!2, C!1))) | (~(distinct_points(A!3, C!1) & distinct_points(B!2, C!1) & (~apart_point_and_line(C!1, L!4)) & left_apart_point(D!0, L!4)))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(12,plain,
% 0.17/0.47 ((~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & (~apart_point_and_line(C, L)) & left_apart_point(D, L))))) <=> (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & (~apart_point_and_line(C, L)) & left_apart_point(D, L)))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(13,plain,
% 0.17/0.47 ((~![L: $i, A: $i, B: $i, C: $i, D: $i] : ((((distinct_points(A, C) & distinct_points(B, C)) & (~apart_point_and_line(C, L))) & left_apart_point(D, L)) => ((before_on_line(L, A, B) & before_on_line(L, B, C)) => before_on_line(L, A, C)))) <=> (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & (~apart_point_and_line(C, L)) & left_apart_point(D, L)))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(14,axiom,(~![L: $i, A: $i, B: $i, C: $i, D: $i] : ((((distinct_points(A, C) & distinct_points(B, C)) & (~apart_point_and_line(C, L))) & left_apart_point(D, L)) => ((before_on_line(L, A, B) & before_on_line(L, B, C)) => before_on_line(L, A, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.17/0.47 tff(15,plain,
% 0.17/0.47 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & (~apart_point_and_line(C, L)) & left_apart_point(D, L))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.17/0.47 tff(16,plain,
% 0.17/0.47 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & (~apart_point_and_line(C, L)) & left_apart_point(D, L))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.17/0.47 tff(17,plain,
% 0.17/0.47 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & (~apart_point_and_line(C, L)) & left_apart_point(D, L))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.17/0.47 tff(18,plain,
% 0.17/0.47 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & (~apart_point_and_line(C, L)) & left_apart_point(D, L))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.17/0.47 tff(19,plain,
% 0.17/0.47 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & (~apart_point_and_line(C, L)) & left_apart_point(D, L))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.17/0.47 tff(20,plain,
% 0.17/0.47 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & (~apart_point_and_line(C, L)) & left_apart_point(D, L))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.17/0.47 tff(21,plain,
% 0.17/0.47 (~![L: $i, A: $i, B: $i, C: $i, D: $i] : (before_on_line(L, A, C) | (~(before_on_line(L, A, B) & before_on_line(L, B, C))) | (~(distinct_points(A, C) & distinct_points(B, C) & (~apart_point_and_line(C, L)) & left_apart_point(D, L))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.17/0.47 tff(22,plain,(
% 0.17/0.47 ~(before_on_line(L!4, A!3, C!1) | (~(before_on_line(L!4, A!3, B!2) & before_on_line(L!4, B!2, C!1))) | (~(distinct_points(A!3, C!1) & distinct_points(B!2, C!1) & (~apart_point_and_line(C!1, L!4)) & left_apart_point(D!0, L!4))))),
% 0.17/0.47 inference(skolemize,[status(sab)],[21])).
% 0.17/0.47 tff(23,plain,
% 0.17/0.47 (~(before_on_line(L!4, A!3, C!1) | (~(before_on_line(L!4, A!3, B!2) & before_on_line(L!4, B!2, C!1))) | (~(distinct_points(A!3, C!1) & distinct_points(B!2, C!1) & (~apart_point_and_line(C!1, L!4)) & left_apart_point(D!0, L!4))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[22, 11])).
% 0.17/0.47 tff(24,plain,
% 0.17/0.47 (distinct_points(A!3, C!1) & distinct_points(B!2, C!1) & (~apart_point_and_line(C!1, L!4)) & left_apart_point(D!0, L!4)),
% 0.17/0.47 inference(or_elim,[status(thm)],[23])).
% 0.17/0.47 tff(25,plain,
% 0.17/0.47 (distinct_points(A!3, C!1)),
% 0.17/0.47 inference(and_elim,[status(thm)],[24])).
% 0.17/0.47 tff(26,plain,
% 0.17/0.47 (^[A: $i, B: $i] : refl(((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B))))) <=> ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B))))))),
% 0.17/0.47 inference(bind,[status(th)],[])).
% 0.17/0.47 tff(27,plain,
% 0.17/0.47 (![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B))))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))),
% 0.17/0.47 inference(quant_intro,[status(thm)],[26])).
% 0.17/0.47 tff(28,plain,
% 0.17/0.47 (^[A: $i, B: $i] : rewrite(((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B))))))),
% 0.17/0.47 inference(bind,[status(th)],[])).
% 0.17/0.47 tff(29,plain,
% 0.17/0.47 (![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))),
% 0.17/0.47 inference(quant_intro,[status(thm)],[28])).
% 0.17/0.47 tff(30,plain,
% 0.17/0.47 (![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(31,plain,
% 0.17/0.47 (^[A: $i, B: $i] : rewrite((distinct_points(A, B) => ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))))),
% 0.17/0.47 inference(bind,[status(th)],[])).
% 0.17/0.47 tff(32,plain,
% 0.17/0.47 (![A: $i, B: $i] : (distinct_points(A, B) => ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B))))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.17/0.47 inference(quant_intro,[status(thm)],[31])).
% 0.17/0.47 tff(33,axiom,(![A: $i, B: $i] : (distinct_points(A, B) => ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oagco5')).
% 0.17/0.47 tff(34,plain,
% 0.17/0.47 (![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.17/0.47 tff(35,plain,
% 0.17/0.47 (![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.17/0.47 tff(36,plain,(
% 0.17/0.47 ![A: $i, B: $i] : ((~distinct_points(A, B)) | ((~apart_point_and_line(A, line_connecting(A, B))) & (~apart_point_and_line(B, line_connecting(A, B)))))),
% 0.17/0.47 inference(skolemize,[status(sab)],[35])).
% 0.17/0.47 tff(37,plain,
% 0.17/0.47 (![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.17/0.47 tff(38,plain,
% 0.17/0.47 (![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.17/0.47 tff(39,plain,
% 0.17/0.47 (((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | ((~distinct_points(A!3, C!1)) | (~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1)))))) <=> ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | (~distinct_points(A!3, C!1)) | (~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1)))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(40,plain,
% 0.17/0.47 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | ((~distinct_points(A!3, C!1)) | (~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1)))))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(41,plain,
% 0.17/0.47 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | (~(apart_point_and_line(B, line_connecting(A, B)) | apart_point_and_line(A, line_connecting(A, B)))))) | (~distinct_points(A!3, C!1)) | (~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.17/0.47 tff(42,plain,
% 0.17/0.47 (~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1)))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[41, 38, 25])).
% 0.17/0.47 tff(43,plain,
% 0.17/0.47 ((apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1))) | (~apart_point_and_line(C!1, line_connecting(A!3, C!1)))),
% 0.17/0.47 inference(tautology,[status(thm)],[])).
% 0.17/0.47 tff(44,plain,
% 0.17/0.47 (~apart_point_and_line(C!1, line_connecting(A!3, C!1))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.17/0.47 tff(45,plain,
% 0.17/0.47 ((~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) <=> (left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1)))))) | apart_point_and_line(C!1, line_connecting(A!3, C!1)) | (~(left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1)))))),
% 0.17/0.47 inference(tautology,[status(thm)],[])).
% 0.17/0.47 tff(46,plain,
% 0.17/0.47 ((~(apart_point_and_line(C!1, line_connecting(A!3, C!1)) <=> (left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1)))))) | (~(left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1)))))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.17/0.47 tff(47,plain,
% 0.17/0.47 (~(left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[46, 10])).
% 0.17/0.47 tff(48,plain,
% 0.17/0.47 ((left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1)))) | (~left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))))),
% 0.17/0.47 inference(tautology,[status(thm)],[])).
% 0.17/0.47 tff(49,plain,
% 0.17/0.47 (~left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1)))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.17/0.47 tff(50,plain,
% 0.17/0.47 ((left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1)))) | (~left_apart_point(C!1, line_connecting(A!3, C!1)))),
% 0.17/0.47 inference(tautology,[status(thm)],[])).
% 0.17/0.47 tff(51,plain,
% 0.17/0.47 (~left_apart_point(C!1, line_connecting(A!3, C!1))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.17/0.47 tff(52,plain,
% 0.17/0.47 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (apart_point_and_line(A!3, line_connecting(A!3, C!1)) <=> (left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(53,plain,
% 0.17/0.47 (apart_point_and_line(A!3, line_connecting(A!3, C!1)) <=> (left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))))),
% 0.17/0.47 inference(unit_resolution,[status(thm)],[52, 8])).
% 0.17/0.48 tff(54,plain,
% 0.17/0.48 ((apart_point_and_line(C!1, line_connecting(A!3, C!1)) | apart_point_and_line(A!3, line_connecting(A!3, C!1))) | (~apart_point_and_line(A!3, line_connecting(A!3, C!1)))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(55,plain,
% 0.17/0.48 (~apart_point_and_line(A!3, line_connecting(A!3, C!1))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[54, 42])).
% 0.17/0.48 tff(56,plain,
% 0.17/0.48 ((~(apart_point_and_line(A!3, line_connecting(A!3, C!1)) <=> (left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))))) | apart_point_and_line(A!3, line_connecting(A!3, C!1)) | (~(left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(57,plain,
% 0.17/0.48 ((~(apart_point_and_line(A!3, line_connecting(A!3, C!1)) <=> (left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))))) | (~(left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.17/0.48 tff(58,plain,
% 0.17/0.48 (~(left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[57, 53])).
% 0.17/0.48 tff(59,plain,
% 0.17/0.48 ((left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))) | (~left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(60,plain,
% 0.17/0.48 (~left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.17/0.48 tff(61,plain,
% 0.17/0.48 ((left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1)))) | (~left_apart_point(A!3, line_connecting(A!3, C!1)))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(62,plain,
% 0.17/0.48 (~left_apart_point(A!3, line_connecting(A!3, C!1))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.17/0.48 tff(63,plain,
% 0.17/0.48 (^[L: $i, A: $i, B: $i] : refl((before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))))) <=> (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(64,plain,
% 0.17/0.48 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[63])).
% 0.17/0.48 tff(65,plain,
% 0.17/0.48 (^[L: $i, A: $i, B: $i] : rewrite((before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B))))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(66,plain,
% 0.17/0.48 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[65])).
% 0.17/0.48 tff(67,plain,
% 0.17/0.48 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 0.17/0.48 inference(rewrite,[status(thm)],[])).
% 0.17/0.48 tff(68,plain,
% 0.17/0.48 (^[L: $i, A: $i, B: $i] : rewrite((before_on_line(L, A, B) <=> (((distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L))))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B))))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(69,plain,
% 0.17/0.48 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L))))) & (~unequally_directed_lines(L, line_connecting(A, B))))) <=> ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[68])).
% 0.17/0.48 tff(70,axiom,(![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (((distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L))))) & (~unequally_directed_lines(L, line_connecting(A, B)))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','bf_def')).
% 0.17/0.48 tff(71,plain,
% 0.17/0.48 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.17/0.48 tff(72,plain,
% 0.17/0.48 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.17/0.48 tff(73,plain,(
% 0.17/0.48 ![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (distinct_points(A, B) & (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) & (~(left_apart_point(B, L) | left_apart_point(B, reverse_line(L)))) & (~unequally_directed_lines(L, line_connecting(A, B)))))),
% 0.17/0.48 inference(skolemize,[status(sab)],[72])).
% 0.17/0.48 tff(74,plain,
% 0.17/0.48 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.17/0.48 tff(75,plain,
% 0.17/0.48 (![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.17/0.48 tff(76,plain,
% 0.17/0.48 (((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, B!2) <=> (~(left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2)))))) <=> ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, B!2) <=> (~(left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2))))))),
% 0.17/0.48 inference(rewrite,[status(thm)],[])).
% 0.17/0.48 tff(77,plain,
% 0.17/0.48 ((before_on_line(L!4, A!3, B!2) <=> (~(unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, B!2))))) <=> (before_on_line(L!4, A!3, B!2) <=> (~(left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2)))))),
% 0.17/0.48 inference(rewrite,[status(thm)],[])).
% 0.17/0.48 tff(78,plain,
% 0.17/0.48 (((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, B!2) <=> (~(unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, B!2)))))) <=> ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, B!2) <=> (~(left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2))))))),
% 0.17/0.48 inference(monotonicity,[status(thm)],[77])).
% 0.17/0.48 tff(79,plain,
% 0.17/0.48 (((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, B!2) <=> (~(unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, B!2)))))) <=> ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, B!2) <=> (~(left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2))))))),
% 0.17/0.48 inference(transitivity,[status(thm)],[78, 76])).
% 0.17/0.48 tff(80,plain,
% 0.17/0.48 ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, B!2) <=> (~(unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, B!2)))))),
% 0.17/0.48 inference(quant_inst,[status(thm)],[])).
% 0.17/0.48 tff(81,plain,
% 0.17/0.48 ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, B!2) <=> (~(left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2)))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.17/0.48 tff(82,plain,
% 0.17/0.48 (before_on_line(L!4, A!3, B!2) <=> (~(left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[81, 75])).
% 0.17/0.48 tff(83,plain,
% 0.17/0.48 (before_on_line(L!4, A!3, B!2) & before_on_line(L!4, B!2, C!1)),
% 0.17/0.48 inference(or_elim,[status(thm)],[23])).
% 0.17/0.48 tff(84,plain,
% 0.17/0.48 (before_on_line(L!4, A!3, B!2)),
% 0.17/0.48 inference(and_elim,[status(thm)],[83])).
% 0.17/0.48 tff(85,plain,
% 0.17/0.48 ((~(before_on_line(L!4, A!3, B!2) <=> (~(left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2)))))) | (~before_on_line(L!4, A!3, B!2)) | (~(left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2))))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(86,plain,
% 0.17/0.48 ((~(before_on_line(L!4, A!3, B!2) <=> (~(left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2)))))) | (~(left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.17/0.48 tff(87,plain,
% 0.17/0.48 (~(left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2)))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[86, 82])).
% 0.17/0.48 tff(88,plain,
% 0.17/0.48 ((left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2))) | (~left_apart_point(A!3, L!4))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(89,plain,
% 0.17/0.48 (~left_apart_point(A!3, L!4)),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.17/0.48 tff(90,plain,
% 0.17/0.48 ((left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | unequally_directed_lines(L!4, line_connecting(A!3, B!2)) | left_apart_point(B!2, reverse_line(L!4)) | left_apart_point(B!2, L!4) | (~distinct_points(A!3, B!2))) | (~left_apart_point(A!3, reverse_line(L!4)))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(91,plain,
% 0.17/0.48 (~left_apart_point(A!3, reverse_line(L!4))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[90, 87])).
% 0.17/0.48 tff(92,plain,
% 0.17/0.48 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (apart_point_and_line(C!1, L!4) <=> (left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4))))),
% 0.17/0.48 inference(quant_inst,[status(thm)],[])).
% 0.17/0.48 tff(93,plain,
% 0.17/0.48 (apart_point_and_line(C!1, L!4) <=> (left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[92, 8])).
% 0.17/0.48 tff(94,plain,
% 0.17/0.48 (~apart_point_and_line(C!1, L!4)),
% 0.17/0.48 inference(and_elim,[status(thm)],[24])).
% 0.17/0.48 tff(95,plain,
% 0.17/0.48 ((~(apart_point_and_line(C!1, L!4) <=> (left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4))))) | apart_point_and_line(C!1, L!4) | (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4))))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(96,plain,
% 0.17/0.48 ((~(apart_point_and_line(C!1, L!4) <=> (left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4))))) | (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.17/0.48 tff(97,plain,
% 0.17/0.48 (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[96, 93])).
% 0.17/0.48 tff(98,plain,
% 0.17/0.48 ((left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4))) | (~left_apart_point(C!1, reverse_line(L!4)))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(99,plain,
% 0.17/0.48 (~left_apart_point(C!1, reverse_line(L!4))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.17/0.48 tff(100,plain,
% 0.17/0.48 ((left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4))) | (~left_apart_point(C!1, L!4))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(101,plain,
% 0.17/0.48 (~left_apart_point(C!1, L!4)),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.17/0.48 tff(102,plain,
% 0.17/0.48 (^[A: $i, B: $i, L: $i, M: $i] : refl((left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(103,plain,
% 0.17/0.48 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M))) <=> ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[102])).
% 0.17/0.48 tff(104,plain,
% 0.17/0.48 (^[A: $i, B: $i, L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(A, B) & distinct_lines(L, M)) <=> (~((~distinct_points(A, B)) | (~distinct_lines(L, M))))), ((~(distinct_points(A, B) & distinct_lines(L, M))) <=> (~(~((~distinct_points(A, B)) | (~distinct_lines(L, M))))))), rewrite((~(~((~distinct_points(A, B)) | (~distinct_lines(L, M))))) <=> ((~distinct_points(A, B)) | (~distinct_lines(L, M)))), ((~(distinct_points(A, B) & distinct_lines(L, M))) <=> ((~distinct_points(A, B)) | (~distinct_lines(L, M))))), ((left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M)))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | ((~distinct_points(A, B)) | (~distinct_lines(L, M)))))), rewrite((left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | ((~distinct_points(A, B)) | (~distinct_lines(L, M)))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))), ((left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M)))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))))),
% 0.17/0.49 inference(bind,[status(th)],[])).
% 0.17/0.49 tff(105,plain,
% 0.17/0.49 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M)))) <=> ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))),
% 0.17/0.49 inference(quant_intro,[status(thm)],[104])).
% 0.17/0.49 tff(106,plain,
% 0.17/0.49 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M)))) <=> ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(107,plain,
% 0.17/0.49 (^[A: $i, B: $i, L: $i, M: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((left_apart_point(A, L) | left_apart_point(B, L)) <=> (left_apart_point(B, L) | left_apart_point(A, L))), (((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) <=> ((left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, M)))), rewrite(((left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, M)) <=> (left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), (((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) <=> (left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), ((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) <=> ((left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, M)))), rewrite(((left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, M)) <=> (left_apart_point(B, M) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), ((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) <=> (left_apart_point(B, M) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), (((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) <=> ((left_apart_point(B, M) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, reverse_line(L))))), rewrite(((left_apart_point(B, M) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, reverse_line(L))) <=> (left_apart_point(B, M) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), (((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) <=> (left_apart_point(B, M) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), ((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) <=> ((left_apart_point(B, M) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, reverse_line(L))))), rewrite(((left_apart_point(B, M) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, reverse_line(L))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), ((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) <=> (left_apart_point(B, M) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) <=> ((left_apart_point(B, M) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, reverse_line(M))))), rewrite(((left_apart_point(B, M) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(A, reverse_line(M))) <=> (left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) <=> (left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), ((((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M))) <=> ((left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, reverse_line(M))))), rewrite(((left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)) | left_apart_point(B, reverse_line(M))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))), ((((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L)))), (((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M)))) <=> ((distinct_points(A, B) & distinct_lines(L, M)) => (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))))), rewrite(((distinct_points(A, B) & distinct_lines(L, M)) => (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))), (((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M)))) <=> (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))))),
% 0.17/0.49 inference(bind,[status(th)],[])).
% 0.17/0.49 tff(108,plain,
% 0.17/0.49 (![A: $i, B: $i, L: $i, M: $i] : ((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M)))) <=> ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.17/0.49 inference(quant_intro,[status(thm)],[107])).
% 0.17/0.49 tff(109,axiom,(![A: $i, B: $i, L: $i, M: $i] : ((distinct_points(A, B) & distinct_lines(L, M)) => (((((((left_apart_point(A, L) | left_apart_point(B, L)) | left_apart_point(A, M)) | left_apart_point(B, M)) | left_apart_point(A, reverse_line(L))) | left_apart_point(B, reverse_line(L))) | left_apart_point(A, reverse_line(M))) | left_apart_point(B, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oaguc1')).
% 0.17/0.49 tff(110,plain,
% 0.17/0.49 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.17/0.49 tff(111,plain,
% 0.17/0.49 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.17/0.49 tff(112,plain,(
% 0.17/0.49 ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~(distinct_points(A, B) & distinct_lines(L, M))))),
% 0.17/0.49 inference(skolemize,[status(sab)],[111])).
% 0.17/0.49 tff(113,plain,
% 0.17/0.49 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.17/0.49 tff(114,plain,
% 0.17/0.49 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.17/0.49 tff(115,plain,
% 0.17/0.49 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | (~distinct_lines(L!4, line_connecting(A!3, C!1))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | (~distinct_lines(L!4, line_connecting(A!3, C!1))))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(116,plain,
% 0.17/0.49 ((left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(C!1, L!4) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)) | (~distinct_lines(L!4, line_connecting(A!3, C!1)))) <=> (left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | (~distinct_lines(L!4, line_connecting(A!3, C!1))))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(117,plain,
% 0.17/0.49 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(C!1, L!4) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)) | (~distinct_lines(L!4, line_connecting(A!3, C!1))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | (~distinct_lines(L!4, line_connecting(A!3, C!1)))))),
% 0.17/0.49 inference(monotonicity,[status(thm)],[116])).
% 0.17/0.49 tff(118,plain,
% 0.17/0.49 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(C!1, L!4) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)) | (~distinct_lines(L!4, line_connecting(A!3, C!1))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | (~distinct_lines(L!4, line_connecting(A!3, C!1))))),
% 0.17/0.49 inference(transitivity,[status(thm)],[117, 115])).
% 0.17/0.49 tff(119,plain,
% 0.17/0.49 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(C!1, L!4) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)) | (~distinct_lines(L!4, line_connecting(A!3, C!1))))),
% 0.17/0.49 inference(quant_inst,[status(thm)],[])).
% 0.17/0.49 tff(120,plain,
% 0.17/0.49 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, reverse_line(M)) | left_apart_point(B, M) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)) | left_apart_point(A!3, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(line_connecting(A!3, C!1))) | left_apart_point(C!1, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(line_connecting(A!3, C!1))) | (~distinct_lines(L!4, line_connecting(A!3, C!1)))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.17/0.49 tff(121,plain,
% 0.17/0.49 ($false),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[120, 114, 25, 101, 99, 91, 89, 62, 60, 51, 49, 1])).
% 0.17/0.49 tff(122,plain,(~distinct_lines(L!4, line_connecting(A!3, C!1))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.49 tff(123,plain,
% 0.17/0.49 (((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, C!1) <=> (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)))))) <=> ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, C!1) <=> (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1))))))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(124,plain,
% 0.17/0.49 ((before_on_line(L!4, A!3, C!1) <=> (~(unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(C!1, L!4) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1))))) <=> (before_on_line(L!4, A!3, C!1) <=> (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)))))),
% 0.17/0.50 inference(rewrite,[status(thm)],[])).
% 0.17/0.50 tff(125,plain,
% 0.17/0.50 (((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, C!1) <=> (~(unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(C!1, L!4) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)))))) <=> ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, C!1) <=> (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1))))))),
% 0.17/0.50 inference(monotonicity,[status(thm)],[124])).
% 0.17/0.50 tff(126,plain,
% 0.17/0.50 (((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, C!1) <=> (~(unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(C!1, L!4) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)))))) <=> ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, C!1) <=> (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1))))))),
% 0.17/0.50 inference(transitivity,[status(thm)],[125, 123])).
% 0.17/0.50 tff(127,plain,
% 0.17/0.50 ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, C!1) <=> (~(unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(C!1, reverse_line(L!4)) | left_apart_point(C!1, L!4) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)))))),
% 0.17/0.50 inference(quant_inst,[status(thm)],[])).
% 0.17/0.50 tff(128,plain,
% 0.17/0.50 ((~![L: $i, A: $i, B: $i] : (before_on_line(L, A, B) <=> (~(unequally_directed_lines(L, line_connecting(A, B)) | left_apart_point(B, reverse_line(L)) | left_apart_point(B, L) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, L) | (~distinct_points(A, B)))))) | (before_on_line(L!4, A!3, C!1) <=> (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.17/0.50 tff(129,plain,
% 0.17/0.50 (before_on_line(L!4, A!3, C!1) <=> (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1))))),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[128, 75])).
% 0.17/0.50 tff(130,plain,
% 0.17/0.50 (~before_on_line(L!4, A!3, C!1)),
% 0.17/0.50 inference(or_elim,[status(thm)],[23])).
% 0.17/0.50 tff(131,plain,
% 0.17/0.50 ((~(before_on_line(L!4, A!3, C!1) <=> (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)))))) | before_on_line(L!4, A!3, C!1) | (left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)))),
% 0.17/0.50 inference(tautology,[status(thm)],[])).
% 0.17/0.50 tff(132,plain,
% 0.17/0.50 ((~(before_on_line(L!4, A!3, C!1) <=> (~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)))))) | (left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)))),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.17/0.50 tff(133,plain,
% 0.17/0.50 (left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1))),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[132, 129])).
% 0.17/0.50 tff(134,plain,
% 0.17/0.50 ((~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)))) | left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1))),
% 0.17/0.50 inference(tautology,[status(thm)],[])).
% 0.17/0.50 tff(135,plain,
% 0.17/0.50 ((~(left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4) | (~distinct_points(A!3, C!1)))) | left_apart_point(C!1, L!4) | left_apart_point(C!1, reverse_line(L!4)) | unequally_directed_lines(L!4, line_connecting(A!3, C!1)) | left_apart_point(A!3, reverse_line(L!4)) | left_apart_point(A!3, L!4)),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[134, 25])).
% 0.17/0.50 tff(136,plain,
% 0.17/0.50 (unequally_directed_lines(L!4, line_connecting(A!3, C!1))),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[135, 99, 101, 91, 89, 133])).
% 0.17/0.50 tff(137,plain,
% 0.17/0.50 (left_apart_point(D!0, L!4)),
% 0.17/0.50 inference(and_elim,[status(thm)],[24])).
% 0.17/0.50 tff(138,plain,
% 0.17/0.50 (^[A: $i, L: $i, M: $i] : refl((left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L))) <=> (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L))))),
% 0.17/0.50 inference(bind,[status(th)],[])).
% 0.17/0.50 tff(139,plain,
% 0.17/0.50 (![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L))) <=> ![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))),
% 0.17/0.50 inference(quant_intro,[status(thm)],[138])).
% 0.17/0.50 tff(140,plain,
% 0.17/0.50 (^[A: $i, L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((left_apart_point(A, L) & unequally_directed_lines(L, M)) <=> (~((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M))))), ((~(left_apart_point(A, L) & unequally_directed_lines(L, M))) <=> (~(~((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M))))))), rewrite((~(~((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M))))) <=> ((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M)))), ((~(left_apart_point(A, L) & unequally_directed_lines(L, M))) <=> ((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M))))), ((left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))) <=> (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | ((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M)))))), rewrite((left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | ((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M)))) <=> (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))), ((left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))) <=> (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))))),
% 0.17/0.50 inference(bind,[status(th)],[])).
% 0.17/0.50 tff(141,plain,
% 0.17/0.50 (![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))) <=> ![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))),
% 0.17/0.50 inference(quant_intro,[status(thm)],[140])).
% 0.17/0.50 tff(142,plain,
% 0.17/0.50 (![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))) <=> ![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.17/0.50 inference(rewrite,[status(thm)],[])).
% 0.17/0.50 tff(143,plain,
% 0.17/0.50 (^[A: $i, L: $i, M: $i] : rewrite(((left_apart_point(A, L) & unequally_directed_lines(L, M)) => (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)))) <=> (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))))),
% 0.17/0.50 inference(bind,[status(th)],[])).
% 0.17/0.50 tff(144,plain,
% 0.17/0.50 (![A: $i, L: $i, M: $i] : ((left_apart_point(A, L) & unequally_directed_lines(L, M)) => (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)))) <=> ![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.17/0.50 inference(quant_intro,[status(thm)],[143])).
% 0.17/0.50 tff(145,axiom,(![A: $i, L: $i, M: $i] : ((left_apart_point(A, L) & unequally_directed_lines(L, M)) => (distinct_lines(L, M) | left_apart_point(A, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oagsub2')).
% 0.17/0.50 tff(146,plain,
% 0.17/0.50 (![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.17/0.50 tff(147,plain,
% 0.17/0.50 (![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.17/0.50 tff(148,plain,(
% 0.17/0.50 ![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.17/0.50 inference(skolemize,[status(sab)],[147])).
% 0.17/0.50 tff(149,plain,
% 0.17/0.50 (![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.17/0.50 tff(150,plain,
% 0.17/0.50 (![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[149, 139])).
% 0.17/0.50 tff(151,plain,
% 0.17/0.50 (((~![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)))) <=> ((~![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)))),
% 0.17/0.50 inference(rewrite,[status(thm)],[])).
% 0.17/0.50 tff(152,plain,
% 0.17/0.50 ((left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4))) <=> ((~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)))),
% 0.17/0.50 inference(rewrite,[status(thm)],[])).
% 0.17/0.50 tff(153,plain,
% 0.17/0.50 (((~![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))) | (left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4)))) <=> ((~![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1))))),
% 0.17/0.50 inference(monotonicity,[status(thm)],[152])).
% 0.17/0.50 tff(154,plain,
% 0.17/0.50 (((~![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))) | (left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4)))) <=> ((~![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)))),
% 0.17/0.50 inference(transitivity,[status(thm)],[153, 151])).
% 0.17/0.50 tff(155,plain,
% 0.17/0.50 ((~![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))) | (left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1)) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4)))),
% 0.17/0.50 inference(quant_inst,[status(thm)],[])).
% 0.17/0.50 tff(156,plain,
% 0.17/0.50 ((~![A: $i, L: $i, M: $i] : (left_apart_point(A, reverse_line(M)) | distinct_lines(L, M) | (~unequally_directed_lines(L, M)) | (~left_apart_point(A, L)))) | (~unequally_directed_lines(L!4, line_connecting(A!3, C!1))) | (~left_apart_point(D!0, L!4)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1))),
% 0.17/0.50 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.17/0.50 tff(157,plain,
% 0.17/0.50 (left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))) | distinct_lines(L!4, line_connecting(A!3, C!1))),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[156, 150, 137, 136])).
% 0.17/0.50 tff(158,plain,
% 0.17/0.50 (left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[157, 122])).
% 0.17/0.51 tff(159,plain,
% 0.17/0.51 ((left_apart_point(D!0, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))) | (~left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1))))),
% 0.17/0.51 inference(tautology,[status(thm)],[])).
% 0.17/0.51 tff(160,plain,
% 0.17/0.51 (left_apart_point(D!0, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))),
% 0.17/0.51 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.17/0.51 tff(161,plain,
% 0.17/0.51 (^[A: $i, L: $i] : refl((~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))))),
% 0.17/0.51 inference(bind,[status(th)],[])).
% 0.17/0.51 tff(162,plain,
% 0.17/0.51 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.17/0.51 inference(quant_intro,[status(thm)],[161])).
% 0.17/0.51 tff(163,plain,
% 0.17/0.51 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.17/0.51 inference(rewrite,[status(thm)],[])).
% 0.17/0.51 tff(164,axiom,(![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag10')).
% 0.17/0.51 tff(165,plain,
% 0.17/0.51 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.17/0.51 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.17/0.51 tff(166,plain,(
% 0.17/0.51 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.17/0.51 inference(skolemize,[status(sab)],[165])).
% 0.17/0.51 tff(167,plain,
% 0.17/0.51 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.17/0.51 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.17/0.51 tff(168,plain,
% 0.17/0.51 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(D!0, line_connecting(A!3, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(A!3, C!1)))))),
% 0.17/0.51 inference(quant_inst,[status(thm)],[])).
% 0.17/0.51 tff(169,plain,
% 0.17/0.51 ($false),
% 0.17/0.51 inference(unit_resolution,[status(thm)],[168, 167, 160])).
% 0.17/0.51 % SZS output end Proof
%------------------------------------------------------------------------------