%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO237+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 : Sat Jun 21 05:06:05 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO237+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:47:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(left_apart_point_type, type, (
% 0.19/0.38 left_apart_point: ( $i * $i ) > $o)).
% 0.19/0.38 tff(reverse_line_type, type, (
% 0.19/0.38 reverse_line: $i > $i)).
% 0.19/0.38 tff(tptp_fun_L_0_type, type, (
% 0.19/0.38 tptp_fun_L_0: $i)).
% 0.19/0.38 tff(tptp_fun_B_2_type, type, (
% 0.19/0.38 tptp_fun_B_2: $i)).
% 0.19/0.38 tff(tptp_fun_A_3_type, type, (
% 0.19/0.38 tptp_fun_A_3: $i)).
% 0.19/0.38 tff(tptp_fun_C_1_type, type, (
% 0.19/0.38 tptp_fun_C_1: $i)).
% 0.19/0.38 tff(divides_points_type, type, (
% 0.19/0.38 divides_points: ( $i * $i * $i ) > $o)).
% 0.19/0.38 tff(apart_point_and_line_type, type, (
% 0.19/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,assumption,(left_apart_point(C!1, reverse_line(L!0))), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (^[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)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![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))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (^[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)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![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))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 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')).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![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))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.38 tff(9,plain,(
% 0.19/0.38 ![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))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[8])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (![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))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (![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))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (((~![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))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 ((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)))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (((~![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))))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[13])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (((~![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))))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[14, 12])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 ((~![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))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 ((~![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)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (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))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[17, 11])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 ((~(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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 ((~![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((~![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 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')).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (~![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (~![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (~![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (~![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 20])).
% 0.19/0.39 tff(27,plain,(
% 0.19/0.39 ~(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)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (~(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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (~divides_points(L!0, B!2, C!1)),
% 0.19/0.39 inference(or_elim,[status(thm)],[28])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((~(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)))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ((~(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)))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (~((~((~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))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[31, 18])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (((~((~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))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ((~((~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)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (~left_apart_point(B!2, L!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[36, 1])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))) | left_apart_point(B!2, L!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (((~![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))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 ((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)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~![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))))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (((~![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))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[42, 40])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~![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))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 ((~![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)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (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))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[45, 11])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (~divides_points(L!0, A!3, C!1)),
% 0.19/0.39 inference(or_elim,[status(thm)],[28])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 ((~(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)))))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((~(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)))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (~((~((~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))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (((~((~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))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 ((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((~((~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)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((~left_apart_point(A!3, L!0)) | (~left_apart_point(C!1, reverse_line(L!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (~left_apart_point(A!3, L!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[54, 1])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))) | left_apart_point(A!3, L!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (((~![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))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 ((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)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (((~![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))))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (((~![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))))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 ((~![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))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((~![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)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (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))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[63, 11])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (divides_points(L!0, A!3, B!2)),
% 0.19/0.40 inference(or_elim,[status(thm)],[28])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ((~(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))))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ((~(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))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 ((~((~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)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 64])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((~((~((~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)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 ((~((~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)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[70, 57, 39])).
% 0.19/0.40 tff(72,plain,(~left_apart_point(C!1, reverse_line(L!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(76,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')).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.40 tff(78,plain,(
% 0.19/0.40 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[77])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 ((~![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))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (apart_point_and_line(C!1, L!0) <=> (left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (apart_point_and_line(C!1, L!0)),
% 0.19/0.40 inference(or_elim,[status(thm)],[28])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ((~(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)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ((~(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)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[84, 81])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 ((~(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))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (left_apart_point(C!1, L!0) | left_apart_point(C!1, reverse_line(L!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (left_apart_point(C!1, L!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[87, 72])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (((~((~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))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 ((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[89, 32])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 ((~((~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)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((~left_apart_point(C!1, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (~left_apart_point(B!2, reverse_line(L!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[92, 88])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (((~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))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 ((~left_apart_point(A!3, L!0)) | (~left_apart_point(B!2, reverse_line(L!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (((~((~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))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[96, 50])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~((~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)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ((~left_apart_point(C!1, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (~left_apart_point(A!3, reverse_line(L!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[99, 88])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (((~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))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 ((~left_apart_point(B!2, L!0)) | (~left_apart_point(A!3, reverse_line(L!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[70, 102, 95])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------