TSTP Solution File: GEO237+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO237+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 20:35:58 EDT 2022
% Result : Theorem 0.14s 0.34s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GEO237+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.00/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.29 % Computer : n021.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Wed Aug 31 07:04:26 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.08/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.29 Usage: tptp [options] [-file:]file
% 0.08/0.29 -h, -? prints this message.
% 0.08/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.08/0.29 -m, -model generate model.
% 0.08/0.29 -p, -proof generate proof.
% 0.08/0.29 -c, -core generate unsat core of named formulas.
% 0.08/0.29 -st, -statistics display statistics.
% 0.08/0.29 -t:timeout set timeout (in second).
% 0.08/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.08/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.29 -<param>:<value> configuration parameter and value.
% 0.08/0.29 -o:<output-file> file to place output in.
% 0.14/0.34 % SZS status Theorem
% 0.14/0.34 % SZS output start Proof
% 0.14/0.34 tff(left_apart_point_type, type, (
% 0.14/0.34 left_apart_point: ( $i * $i ) > $o)).
% 0.14/0.34 tff(reverse_line_type, type, (
% 0.14/0.34 reverse_line: $i > $i)).
% 0.14/0.34 tff(tptp_fun_L_0_type, type, (
% 0.14/0.34 tptp_fun_L_0: $i)).
% 0.14/0.34 tff(tptp_fun_B_2_type, type, (
% 0.14/0.34 tptp_fun_B_2: $i)).
% 0.14/0.34 tff(tptp_fun_A_3_type, type, (
% 0.14/0.34 tptp_fun_A_3: $i)).
% 0.14/0.34 tff(tptp_fun_C_1_type, type, (
% 0.14/0.34 tptp_fun_C_1: $i)).
% 0.14/0.34 tff(divides_points_type, type, (
% 0.14/0.34 divides_points: ( $i * $i * $i ) > $o)).
% 0.14/0.34 tff(apart_point_and_line_type, type, (
% 0.14/0.34 apart_point_and_line: ( $i * $i ) > $o)).
% 0.14/0.34 tff(1,assumption,(left_apart_point(C!1, reverse_line(L!0))), introduced(assumption)).
% 0.14/0.34 tff(2,plain,
% 0.14/0.34 (^[A: $i, B: $i, L: $i] : refl((divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L)))))) <=> (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L)))))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(3,plain,
% 0.14/0.34 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L)))))) <=> ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.34 tff(4,plain,
% 0.14/0.34 (^[A: $i, B: $i, L: $i] : rewrite((divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L)))) <=> (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L)))))))),
% 0.14/0.34 inference(bind,[status(th)],[])).
% 0.14/0.34 tff(5,plain,
% 0.14/0.34 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L)))) <=> ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))),
% 0.14/0.34 inference(quant_intro,[status(thm)],[4])).
% 0.14/0.34 tff(6,plain,
% 0.14/0.34 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L)))) <=> ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(7,axiom,(![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','div_def')).
% 0.14/0.34 tff(8,plain,
% 0.14/0.34 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.14/0.34 tff(9,plain,(
% 0.14/0.34 ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L))))),
% 0.14/0.34 inference(skolemize,[status(sab)],[8])).
% 0.14/0.34 tff(10,plain,
% 0.14/0.34 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.14/0.34 tff(11,plain,
% 0.14/0.34 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))),
% 0.14/0.34 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.14/0.34 tff(12,plain,
% 0.14/0.34 (((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))))))) <=> ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(13,plain,
% 0.14/0.34 ((divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0)))))) <=> (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))))))),
% 0.14/0.34 inference(rewrite,[status(thm)],[])).
% 0.14/0.34 tff(14,plain,
% 0.14/0.34 (((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))))))) <=> ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))))))),
% 0.14/0.34 inference(monotonicity,[status(thm)],[13])).
% 0.14/0.34 tff(15,plain,
% 0.14/0.34 (((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))))))) <=> ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))))))),
% 0.14/0.34 inference(transitivity,[status(thm)],[14, 12])).
% 0.14/0.34 tff(16,plain,
% 0.14/0.34 ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))))))),
% 0.14/0.34 inference(quant_inst,[status(thm)],[])).
% 0.14/0.34 tff(17,plain,
% 0.14/0.34 ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.14/0.35 tff(18,plain,
% 0.14/0.35 (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[17, 11])).
% 0.14/0.35 tff(19,plain,
% 0.14/0.35 ((~(divides_points(L!0, B!2, C!1) | divides_points(L!0, A!3, C!1) | (~divides_points(L!0, A!3, B!2)) | (~apart_point_and_line(C!1, L!0)))) <=> (~(divides_points(L!0, B!2, C!1) | divides_points(L!0, A!3, C!1) | (~divides_points(L!0, A!3, B!2)) | (~apart_point_and_line(C!1, L!0))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(20,plain,
% 0.14/0.35 ((~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))) <=> (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(21,plain,
% 0.14/0.35 ((~![A: $i, B: $i, C: $i, L: $i] : (apart_point_and_line(C, L) => (divides_points(L, A, B) => (divides_points(L, A, C) | divides_points(L, B, C))))) <=> (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(22,axiom,(~![A: $i, B: $i, C: $i, L: $i] : (apart_point_and_line(C, L) => (divides_points(L, A, B) => (divides_points(L, A, C) | divides_points(L, B, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.14/0.35 tff(23,plain,
% 0.14/0.35 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.14/0.35 tff(24,plain,
% 0.14/0.35 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.14/0.35 tff(25,plain,
% 0.14/0.35 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.14/0.35 tff(26,plain,
% 0.14/0.35 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.14/0.35 tff(27,plain,
% 0.14/0.35 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.14/0.35 tff(28,plain,
% 0.14/0.35 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.14/0.35 tff(29,plain,
% 0.14/0.35 (~![A: $i, B: $i, C: $i, L: $i] : (divides_points(L, B, C) | divides_points(L, A, C) | (~divides_points(L, A, B)) | (~apart_point_and_line(C, L)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.14/0.35 tff(30,plain,(
% 0.14/0.35 ~(divides_points(L!0, B!2, C!1) | divides_points(L!0, A!3, C!1) | (~divides_points(L!0, A!3, B!2)) | (~apart_point_and_line(C!1, L!0)))),
% 0.14/0.35 inference(skolemize,[status(sab)],[29])).
% 0.14/0.35 tff(31,plain,
% 0.14/0.35 (~(divides_points(L!0, B!2, C!1) | divides_points(L!0, A!3, C!1) | (~divides_points(L!0, A!3, B!2)) | (~apart_point_and_line(C!1, L!0)))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[30, 19])).
% 0.14/0.35 tff(32,plain,
% 0.14/0.35 (~divides_points(L!0, B!2, C!1)),
% 0.14/0.35 inference(or_elim,[status(thm)],[31])).
% 0.14/0.35 tff(33,plain,
% 0.14/0.35 ((~(divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))))))) | divides_points(L!0, B!2, C!1) | (~((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))))))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(34,plain,
% 0.14/0.35 ((~(divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))))))) | (~((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))))))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.14/0.35 tff(35,plain,
% 0.14/0.35 (~((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[34, 18])).
% 0.14/0.35 tff(36,plain,
% 0.14/0.35 (((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))))) | ((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(37,plain,
% 0.14/0.35 ((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0)))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.14/0.35 tff(38,plain,
% 0.14/0.35 ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0)))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(39,plain,
% 0.14/0.35 ((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0)))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.14/0.35 tff(40,plain,
% 0.14/0.35 (~left_apart_point(B!2, L!0)),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[39, 1])).
% 0.14/0.35 tff(41,plain,
% 0.14/0.35 (((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))) | left_apart_point(B!2, L!0)),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(42,plain,
% 0.14/0.35 ((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.14/0.35 tff(43,plain,
% 0.14/0.35 (((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))))) <=> ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(44,plain,
% 0.14/0.35 ((divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(A!3, reverse_line(L!0))) | (~left_apart_point(C!1, L!0)))))) <=> (divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))))),
% 0.14/0.35 inference(rewrite,[status(thm)],[])).
% 0.14/0.35 tff(45,plain,
% 0.14/0.35 (((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(A!3, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))))))) <=> ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))))))),
% 0.14/0.35 inference(monotonicity,[status(thm)],[44])).
% 0.14/0.35 tff(46,plain,
% 0.14/0.35 (((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(A!3, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))))))) <=> ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))))))),
% 0.14/0.35 inference(transitivity,[status(thm)],[45, 43])).
% 0.14/0.35 tff(47,plain,
% 0.14/0.35 ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(A!3, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))))))),
% 0.14/0.35 inference(quant_inst,[status(thm)],[])).
% 0.14/0.35 tff(48,plain,
% 0.14/0.35 ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))))),
% 0.14/0.35 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.14/0.35 tff(49,plain,
% 0.14/0.35 (divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[48, 11])).
% 0.14/0.35 tff(50,plain,
% 0.14/0.35 (~divides_points(L!0, A!3, C!1)),
% 0.14/0.35 inference(or_elim,[status(thm)],[31])).
% 0.14/0.35 tff(51,plain,
% 0.14/0.35 ((~(divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))))) | divides_points(L!0, A!3, C!1) | (~((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(52,plain,
% 0.14/0.35 ((~(divides_points(L!0, A!3, C!1) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))))) | (~((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.14/0.35 tff(53,plain,
% 0.14/0.35 (~((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))))),
% 0.14/0.35 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.14/0.35 tff(54,plain,
% 0.14/0.35 (((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))) | ((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))),
% 0.14/0.35 inference(tautology,[status(thm)],[])).
% 0.14/0.35 tff(55,plain,
% 0.14/0.35 ((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.14/0.36 tff(56,plain,
% 0.14/0.36 ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0)))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(57,plain,
% 0.14/0.36 ((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.14/0.36 tff(58,plain,
% 0.14/0.36 (~left_apart_point(A!3, L!0)),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[57, 1])).
% 0.14/0.36 tff(59,plain,
% 0.14/0.36 (((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))) | left_apart_point(A!3, L!0)),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(60,plain,
% 0.14/0.36 ((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.14/0.36 tff(61,plain,
% 0.14/0.36 (((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))))) <=> ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))))))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(62,plain,
% 0.14/0.36 ((divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(A!3, reverse_line(L!0))) | (~left_apart_point(B!2, L!0)))))) <=> (divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(63,plain,
% 0.14/0.36 (((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(A!3, reverse_line(L!0))) | (~left_apart_point(B!2, L!0))))))) <=> ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))))))),
% 0.14/0.36 inference(monotonicity,[status(thm)],[62])).
% 0.14/0.36 tff(64,plain,
% 0.14/0.36 (((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(A!3, reverse_line(L!0))) | (~left_apart_point(B!2, L!0))))))) <=> ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))))))),
% 0.14/0.36 inference(transitivity,[status(thm)],[63, 61])).
% 0.14/0.36 tff(65,plain,
% 0.14/0.36 ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(A!3, reverse_line(L!0))) | (~left_apart_point(B!2, L!0))))))),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(66,plain,
% 0.14/0.36 ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.14/0.36 tff(67,plain,
% 0.14/0.36 (divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[66, 11])).
% 0.14/0.36 tff(68,plain,
% 0.14/0.36 (divides_points(L!0, A!3, B!2)),
% 0.14/0.36 inference(or_elim,[status(thm)],[31])).
% 0.14/0.36 tff(69,plain,
% 0.14/0.36 ((~(divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))))) | (~divides_points(L!0, A!3, B!2)) | ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(70,plain,
% 0.14/0.36 ((~(divides_points(L!0, A!3, B!2) <=> ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))))) | ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.14/0.36 tff(71,plain,
% 0.14/0.36 ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[70, 67])).
% 0.14/0.36 tff(72,plain,
% 0.14/0.36 ((~((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))))) | (~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(73,plain,
% 0.14/0.36 ((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.14/0.36 tff(74,plain,
% 0.14/0.36 ($false),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[73, 60, 42])).
% 0.14/0.36 tff(75,plain,(~left_apart_point(C!1, reverse_line(L!0))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.36 tff(76,plain,
% 0.14/0.36 (^[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)))))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(77,plain,
% 0.14/0.36 (![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))))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[76])).
% 0.14/0.36 tff(78,plain,
% 0.14/0.36 (![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))))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(79,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')).
% 0.14/0.36 tff(80,plain,
% 0.14/0.36 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.14/0.36 tff(81,plain,(
% 0.14/0.36 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.14/0.36 inference(skolemize,[status(sab)],[80])).
% 0.14/0.36 tff(82,plain,
% 0.14/0.36 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.14/0.36 tff(83,plain,
% 0.14/0.36 ((~![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!0) <=> (left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0))))),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(84,plain,
% 0.14/0.36 (apart_point_and_line(C!1, L!0) <=> (left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.14/0.36 tff(85,plain,
% 0.14/0.36 (apart_point_and_line(C!1, L!0)),
% 0.14/0.36 inference(or_elim,[status(thm)],[31])).
% 0.14/0.36 tff(86,plain,
% 0.14/0.36 ((~(apart_point_and_line(C!1, L!0) <=> (left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0))))) | (~apart_point_and_line(C!1, L!0)) | (left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0)))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(87,plain,
% 0.14/0.36 ((~(apart_point_and_line(C!1, L!0) <=> (left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0))))) | (left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.14/0.36 tff(88,plain,
% 0.14/0.36 (left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.14/0.36 tff(89,plain,
% 0.14/0.36 ((~(left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0)))) | left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(90,plain,
% 0.14/0.36 (left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.14/0.36 tff(91,plain,
% 0.14/0.36 (left_apart_point(C!1, L!0)),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[90, 75])).
% 0.14/0.36 tff(92,plain,
% 0.14/0.36 (((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))))) | ((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(93,plain,
% 0.14/0.36 ((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[92, 35])).
% 0.14/0.36 tff(94,plain,
% 0.14/0.36 ((~((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0))))) | (~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(95,plain,
% 0.14/0.36 ((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.14/0.36 tff(96,plain,
% 0.14/0.36 (~left_apart_point(B!2, reverse_line(L!0))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[95, 91])).
% 0.14/0.36 tff(97,plain,
% 0.14/0.36 (((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))) | left_apart_point(B!2, reverse_line(L!0))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(98,plain,
% 0.14/0.36 ((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.14/0.36 tff(99,plain,
% 0.14/0.36 (((~((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))))) | ((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(100,plain,
% 0.14/0.36 ((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[99, 53])).
% 0.14/0.36 tff(101,plain,
% 0.14/0.36 ((~((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0))))) | (~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(102,plain,
% 0.14/0.36 ((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.14/0.36 tff(103,plain,
% 0.14/0.36 (~left_apart_point(A!3, reverse_line(L!0))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[102, 91])).
% 0.14/0.36 tff(104,plain,
% 0.14/0.36 (((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))) | left_apart_point(A!3, reverse_line(L!0))),
% 0.14/0.36 inference(tautology,[status(thm)],[])).
% 0.14/0.36 tff(105,plain,
% 0.14/0.36 ((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.14/0.36 tff(106,plain,
% 0.14/0.36 ($false),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[73, 105, 98])).
% 0.14/0.36 % SZS output end Proof
%------------------------------------------------------------------------------