%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO245+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:06:07 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO245+3 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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 14:43:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(left_apart_point_type, type, (
% 0.12/0.38 left_apart_point: ( $i * $i ) > $o)).
% 0.12/0.38 tff(line_connecting_type, type, (
% 0.12/0.38 line_connecting: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_A_2_type, type, (
% 0.12/0.38 tptp_fun_A_2: $i)).
% 0.12/0.38 tff(tptp_fun_B_1_type, type, (
% 0.12/0.38 tptp_fun_B_1: $i)).
% 0.12/0.38 tff(right_apart_point_type, type, (
% 0.12/0.38 right_apart_point: ( $i * $i ) > $o)).
% 0.12/0.38 tff(apart_point_and_line_type, type, (
% 0.12/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.38 tff(distinct_points_type, type, (
% 0.12/0.38 distinct_points: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_C_0_type, type, (
% 0.12/0.38 tptp_fun_C_0: $i)).
% 0.12/0.38 tff(reverse_line_type, type, (
% 0.12/0.38 reverse_line: $i > $i)).
% 0.12/0.38 tff(distinct_lines_type, type, (
% 0.12/0.38 distinct_lines: ( $i * $i ) > $o)).
% 0.12/0.38 tff(unequally_directed_lines_type, type, (
% 0.12/0.38 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.12/0.38 tff(equally_directed_lines_type, type, (
% 0.12/0.38 equally_directed_lines: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[A: $i, L: $i] : refl((apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))) <=> (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a6_defns')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,(
% 0.12/0.38 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))) | (apart_point_and_line(A!2, line_connecting(B!1, A!2)) <=> (left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (apart_point_and_line(A!2, line_connecting(B!1, A!2)) <=> (left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,assumption,(distinct_points(A!2, A!2)), introduced(assumption)).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (^[A: $i] : refl((~distinct_points(A, A)) <=> (~distinct_points(A, A)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![A: $i] : (~distinct_points(A, A)) <=> ![A: $i] : (~distinct_points(A, A))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![A: $i] : (~distinct_points(A, A)) <=> ![A: $i] : (~distinct_points(A, A))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,axiom,(![A: $i] : (~distinct_points(A, A))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax1_basics')).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![A: $i] : (~distinct_points(A, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.38 tff(16,plain,(
% 0.12/0.38 ![A: $i] : (~distinct_points(A, A))),
% 0.12/0.38 inference(skolemize,[status(sab)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![A: $i] : (~distinct_points(A, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 ((~![A: $i] : (~distinct_points(A, A))) | (~distinct_points(A!2, A!2))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.12/0.38 tff(20,plain,(~distinct_points(A!2, A!2)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(21,assumption,(~distinct_points(A!2, A!2)), introduced(assumption)).
% 0.12/0.38 tff(22,assumption,(~distinct_points(B!1, A!2)), introduced(assumption)).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 ((~(right_apart_point(B!1, line_connecting(A!2, C!0)) | (~distinct_points(A!2, B!1)) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))) <=> (~(right_apart_point(B!1, line_connecting(A!2, C!0)) | (~distinct_points(A!2, B!1)) | (~left_apart_point(C!0, line_connecting(A!2, B!1)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))) <=> (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (left_apart_point(C, line_connecting(A, B)) => right_apart_point(B, line_connecting(A, C))))) <=> (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(26,axiom,(~![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (left_apart_point(C, line_connecting(A, B)) => right_apart_point(B, line_connecting(A, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (~![A: $i, B: $i, C: $i] : (right_apart_point(B, line_connecting(A, C)) | (~distinct_points(A, B)) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.12/0.38 tff(31,plain,(
% 0.12/0.38 ~(right_apart_point(B!1, line_connecting(A!2, C!0)) | (~distinct_points(A!2, B!1)) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[30])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (~(right_apart_point(B!1, line_connecting(A!2, C!0)) | (~distinct_points(A!2, B!1)) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[31, 23])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (distinct_points(A!2, B!1)),
% 0.12/0.38 inference(or_elim,[status(thm)],[32])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (^[A: $i, B: $i, C: $i] : refl((distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((distinct_points(A, C) | distinct_points(B, C)) <=> (distinct_points(A, C) | distinct_points(B, C))), ((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))))), rewrite((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))), ((distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C))) <=> ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.39 tff(39,axiom,(![A: $i, B: $i, C: $i] : (distinct_points(A, B) => (distinct_points(A, C) | distinct_points(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax2_basics')).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.12/0.39 tff(42,plain,(
% 0.12/0.39 ![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[41])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | ((~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 ((distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1))) <=> ((~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | ((~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[45])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2))),
% 0.12/0.39 inference(transitivity,[status(thm)],[46, 44])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (distinct_points(A!2, A!2) | distinct_points(B!1, A!2) | (~distinct_points(A!2, B!1)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : (distinct_points(A, C) | distinct_points(B, C) | (~distinct_points(A, B)))) | (~distinct_points(A!2, B!1)) | distinct_points(B!1, A!2) | distinct_points(A!2, A!2)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[49, 43, 33, 22, 21])).
% 0.12/0.39 tff(51,plain,(distinct_points(A!2, A!2) | distinct_points(B!1, A!2)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (distinct_points(B!1, A!2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[51, 20])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.12/0.39 tff(60,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/sandbox2/benchmark/Axioms/GEO009+0.ax','ax5_cons_objs')).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.12/0.39 tff(63,plain,(
% 0.12/0.39 ![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)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[62])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (((~![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(B!1, A!2)) | (~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2)))))) <=> ((~![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(B!1, A!2)) | (~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 ((~![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(B!1, A!2)) | (~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 ((~![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(B!1, A!2)) | (~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 ((~distinct_points(B!1, A!2)) | (~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[69, 52])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 ((apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2))) | (~apart_point_and_line(A!2, line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (~apart_point_and_line(A!2, line_connecting(B!1, A!2))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 ((~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) <=> (left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))))) | apart_point_and_line(A!2, line_connecting(B!1, A!2)) | (~(left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 ((~(apart_point_and_line(A!2, line_connecting(B!1, A!2)) <=> (left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))))) | (~(left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (~(left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[74, 9])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 ((left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))) | (~left_apart_point(A!2, line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (~left_apart_point(A!2, line_connecting(B!1, A!2))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))) | (apart_point_and_line(B!1, line_connecting(B!1, A!2)) <=> (left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 (apart_point_and_line(B!1, line_connecting(B!1, A!2)) <=> (left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[78, 7])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 ((apart_point_and_line(A!2, line_connecting(B!1, A!2)) | apart_point_and_line(B!1, line_connecting(B!1, A!2))) | (~apart_point_and_line(B!1, line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 (~apart_point_and_line(B!1, line_connecting(B!1, A!2))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[80, 70])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 ((~(apart_point_and_line(B!1, line_connecting(B!1, A!2)) <=> (left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))))) | apart_point_and_line(B!1, line_connecting(B!1, A!2)) | (~(left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 ((~(apart_point_and_line(B!1, line_connecting(B!1, A!2)) <=> (left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))))) | (~(left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (~(left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[83, 79])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 ((left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))) | (~left_apart_point(B!1, line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 (~left_apart_point(B!1, line_connecting(B!1, A!2))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 (^[X: $i, Y: $i] : refl((right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[87])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(90,axiom,(![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a2_defns')).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.12/0.39 tff(92,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[91])).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.12/0.39 tff(94,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(B!1, line_connecting(B!1, A!2)) <=> left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(95,plain,
% 0.12/0.39 (right_apart_point(B!1, line_connecting(B!1, A!2)) <=> left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.12/0.39 tff(96,plain,
% 0.12/0.39 ((left_apart_point(B!1, line_connecting(B!1, A!2)) | right_apart_point(B!1, line_connecting(B!1, A!2))) | (~right_apart_point(B!1, line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 (~right_apart_point(B!1, line_connecting(B!1, A!2))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[96, 84])).
% 0.12/0.39 tff(98,plain,
% 0.12/0.39 ((~(right_apart_point(B!1, line_connecting(B!1, A!2)) <=> left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))))) | right_apart_point(B!1, line_connecting(B!1, A!2)) | (~left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 ((~(right_apart_point(B!1, line_connecting(B!1, A!2)) <=> left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))))) | (~left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 (~left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(A!2, line_connecting(B!1, A!2)) <=> left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(102,plain,
% 0.12/0.39 (right_apart_point(A!2, line_connecting(B!1, A!2)) <=> left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[101, 93])).
% 0.12/0.39 tff(103,plain,
% 0.12/0.39 ((left_apart_point(A!2, line_connecting(B!1, A!2)) | right_apart_point(A!2, line_connecting(B!1, A!2))) | (~right_apart_point(A!2, line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(104,plain,
% 0.12/0.39 (~right_apart_point(A!2, line_connecting(B!1, A!2))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[103, 75])).
% 0.12/0.39 tff(105,plain,
% 0.12/0.39 ((~(right_apart_point(A!2, line_connecting(B!1, A!2)) <=> left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))))) | right_apart_point(A!2, line_connecting(B!1, A!2)) | (~left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(106,plain,
% 0.12/0.39 ((~(right_apart_point(A!2, line_connecting(B!1, A!2)) <=> left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))))) | (~left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.12/0.39 tff(107,plain,
% 0.12/0.39 (~left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[106, 102])).
% 0.12/0.39 tff(108,assumption,(left_apart_point(C!0, line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))), introduced(assumption)).
% 0.12/0.39 tff(109,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(110,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[109])).
% 0.12/0.39 tff(111,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(112,axiom,(![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax10_basics')).
% 0.12/0.39 tff(113,plain,
% 0.12/0.39 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.12/0.39 tff(114,plain,(
% 0.12/0.39 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[113])).
% 0.12/0.39 tff(115,plain,
% 0.12/0.39 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.12/0.39 tff(116,plain,
% 0.12/0.39 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(C!0, line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(117,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[116, 115, 108])).
% 0.12/0.39 tff(118,plain,(~(left_apart_point(C!0, line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(119,plain,
% 0.12/0.39 ((left_apart_point(C!0, line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))) | (~left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(120,plain,
% 0.12/0.39 (~left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.12/0.39 tff(121,plain,
% 0.12/0.39 (^[X: $i, Y: $i] : refl((~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(122,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[121])).
% 0.12/0.40 tff(123,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(124,plain,
% 0.12/0.40 (^[X: $i, Y: $i] : trans(rewrite((equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))), rewrite((~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))), ((equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(125,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[124])).
% 0.12/0.40 tff(126,axiom,(![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a4_defns')).
% 0.12/0.40 tff(127,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.12/0.40 tff(128,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.12/0.40 tff(129,plain,(
% 0.12/0.40 ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[128])).
% 0.12/0.40 tff(130,plain,
% 0.12/0.40 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.12/0.40 tff(131,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) <=> equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(132,plain,
% 0.12/0.40 (~(unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) <=> equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.12/0.40 tff(133,plain,
% 0.12/0.40 (^[A: $i, B: $i] : refl(((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(134,plain,
% 0.12/0.40 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[133])).
% 0.12/0.40 tff(135,plain,
% 0.12/0.40 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(136,plain,
% 0.12/0.40 (^[A: $i, B: $i] : rewrite((distinct_points(A, B) => equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(137,plain,
% 0.12/0.40 (![A: $i, B: $i] : (distinct_points(A, B) => equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A)))) <=> ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[136])).
% 0.12/0.40 tff(138,axiom,(![A: $i, B: $i] : (distinct_points(A, B) => equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax9_cons_objs')).
% 0.12/0.40 tff(139,plain,
% 0.12/0.40 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.12/0.40 tff(140,plain,
% 0.12/0.40 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.12/0.40 tff(141,plain,(
% 0.12/0.40 ![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[140])).
% 0.12/0.40 tff(142,plain,
% 0.12/0.40 (![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.12/0.40 tff(143,plain,
% 0.12/0.40 (((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(A!2, B!1)) | equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))) <=> ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(A!2, B!1)) | equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(144,plain,
% 0.12/0.40 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | ((~distinct_points(A!2, B!1)) | equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(145,plain,
% 0.12/0.40 ((~![A: $i, B: $i] : ((~distinct_points(A, B)) | equally_directed_lines(line_connecting(A, B), reverse_line(line_connecting(B, A))))) | (~distinct_points(A!2, B!1)) | equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.12/0.40 tff(146,plain,
% 0.12/0.40 (equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[145, 142, 33])).
% 0.12/0.40 tff(147,plain,
% 0.12/0.40 ((unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) <=> equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))) | (~equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(148,plain,
% 0.12/0.40 ((unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))) <=> equally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))) | (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.12/0.40 tff(149,plain,
% 0.12/0.40 (~unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[148, 132])).
% 0.12/0.40 tff(150,plain,
% 0.12/0.40 (^[L: $i, M: $i] : refl((unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(151,plain,
% 0.12/0.40 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[150])).
% 0.12/0.40 tff(152,plain,
% 0.12/0.40 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(153,axiom,(![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax8_basics')).
% 0.12/0.40 tff(154,plain,
% 0.12/0.40 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.12/0.40 tff(155,plain,(
% 0.12/0.40 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[154])).
% 0.12/0.40 tff(156,plain,
% 0.12/0.40 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.12/0.40 tff(157,plain,
% 0.12/0.40 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(158,plain,
% 0.12/0.40 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(159,plain,
% 0.12/0.40 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | unequally_directed_lines(line_connecting(A!2, B!1), reverse_line(line_connecting(B!1, A!2)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.12/0.40 tff(160,plain,
% 0.12/0.40 (unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[159, 156, 149])).
% 0.12/0.40 tff(161,plain,
% 0.12/0.40 (left_apart_point(C!0, line_connecting(A!2, B!1))),
% 0.12/0.40 inference(or_elim,[status(thm)],[32])).
% 0.12/0.40 tff(162,plain,
% 0.12/0.40 (^[A: $i, L: $i, M: $i] : refl(((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~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, L))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(163,plain,
% 0.12/0.40 (![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L))) <=> ![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[162])).
% 0.12/0.40 tff(164,plain,
% 0.12/0.40 (^[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))))), ((distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(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, L)) | (~unequally_directed_lines(L, M)))))), rewrite((distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | ((~left_apart_point(A, L)) | (~unequally_directed_lines(L, M)))) <=> ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))), ((distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))) <=> ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(165,plain,
% 0.12/0.40 (![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))) <=> ![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[164])).
% 0.12/0.40 tff(166,plain,
% 0.12/0.40 (![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))) <=> ![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(167,plain,
% 0.12/0.40 (^[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)))) <=> (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(168,plain,
% 0.12/0.40 (![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] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[167])).
% 0.12/0.40 tff(169,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/sandbox2/benchmark/Axioms/GEO009+0.ax','ax2_subs')).
% 0.12/0.40 tff(170,plain,
% 0.12/0.40 (![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.12/0.40 tff(171,plain,
% 0.12/0.40 (![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.12/0.40 tff(172,plain,(
% 0.12/0.40 ![A: $i, L: $i, M: $i] : (distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~(left_apart_point(A, L) & unequally_directed_lines(L, M))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[171])).
% 0.12/0.40 tff(173,plain,
% 0.12/0.40 (![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.12/0.40 tff(174,plain,
% 0.12/0.40 (![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[173, 163])).
% 0.12/0.40 tff(175,plain,
% 0.12/0.40 (((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~left_apart_point(C!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))) <=> ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | (~left_apart_point(C!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(176,plain,
% 0.12/0.40 (((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~left_apart_point(C!0, line_connecting(A!2, B!1)))) <=> ((~left_apart_point(C!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(177,plain,
% 0.12/0.40 (((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))) <=> ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~left_apart_point(C!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[176])).
% 0.12/0.40 tff(178,plain,
% 0.12/0.40 (((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))) <=> ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | (~left_apart_point(C!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[177, 175])).
% 0.12/0.40 tff(179,plain,
% 0.12/0.40 ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | ((~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2))) | (~left_apart_point(C!0, line_connecting(A!2, B!1))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(180,plain,
% 0.12/0.40 ((~![A: $i, L: $i, M: $i] : ((~unequally_directed_lines(L, M)) | distinct_lines(L, M) | left_apart_point(A, reverse_line(M)) | (~left_apart_point(A, L)))) | (~left_apart_point(C!0, line_connecting(A!2, B!1))) | (~unequally_directed_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))) | distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.12/0.41 tff(181,plain,
% 0.12/0.41 (distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)) | left_apart_point(C!0, reverse_line(line_connecting(B!1, A!2)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[180, 174, 161, 160])).
% 0.12/0.41 tff(182,plain,
% 0.12/0.41 (distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[181, 120])).
% 0.12/0.41 tff(183,plain,
% 0.12/0.41 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(B!1, line_connecting(A!2, B!1)) <=> left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(184,plain,
% 0.12/0.41 (right_apart_point(B!1, line_connecting(A!2, B!1)) <=> left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[183, 93])).
% 0.12/0.41 tff(185,plain,
% 0.12/0.41 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))) | (apart_point_and_line(B!1, line_connecting(A!2, B!1)) <=> (left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(186,plain,
% 0.12/0.41 (apart_point_and_line(B!1, line_connecting(A!2, B!1)) <=> (left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[185, 7])).
% 0.12/0.41 tff(187,plain,
% 0.12/0.41 (((~![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!2, B!1)) | (~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!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!2, B!1)) | (~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(188,plain,
% 0.12/0.41 ((~![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!2, B!1)) | (~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1)))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(189,plain,
% 0.12/0.41 ((~![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!2, B!1)) | (~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.12/0.41 tff(190,plain,
% 0.12/0.41 (~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[189, 65, 33])).
% 0.12/0.41 tff(191,plain,
% 0.12/0.41 ((apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1))) | (~apart_point_and_line(B!1, line_connecting(A!2, B!1)))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(192,plain,
% 0.12/0.41 (~apart_point_and_line(B!1, line_connecting(A!2, B!1))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.12/0.41 tff(193,plain,
% 0.12/0.41 ((~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) <=> (left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))))) | apart_point_and_line(B!1, line_connecting(A!2, B!1)) | (~(left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(194,plain,
% 0.12/0.41 ((~(apart_point_and_line(B!1, line_connecting(A!2, B!1)) <=> (left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))))) | (~(left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.19/0.41 tff(195,plain,
% 0.19/0.41 (~(left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[194, 186])).
% 0.19/0.41 tff(196,plain,
% 0.19/0.41 ((left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))) | (~right_apart_point(B!1, line_connecting(A!2, B!1)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(197,plain,
% 0.19/0.41 (~right_apart_point(B!1, line_connecting(A!2, B!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.19/0.41 tff(198,plain,
% 0.19/0.41 ((~(right_apart_point(B!1, line_connecting(A!2, B!1)) <=> left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))))) | right_apart_point(B!1, line_connecting(A!2, B!1)) | (~left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(199,plain,
% 0.19/0.41 ((~(right_apart_point(B!1, line_connecting(A!2, B!1)) <=> left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))))) | (~left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.19/0.41 tff(200,plain,
% 0.19/0.41 (~left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[199, 184])).
% 0.19/0.41 tff(201,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(A!2, line_connecting(A!2, B!1)) <=> left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(202,plain,
% 0.19/0.41 (right_apart_point(A!2, line_connecting(A!2, B!1)) <=> left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[201, 93])).
% 0.19/0.41 tff(203,plain,
% 0.19/0.41 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))) | (apart_point_and_line(A!2, line_connecting(A!2, B!1)) <=> (left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(204,plain,
% 0.19/0.41 (apart_point_and_line(A!2, line_connecting(A!2, B!1)) <=> (left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[203, 7])).
% 0.19/0.41 tff(205,plain,
% 0.19/0.41 ((apart_point_and_line(B!1, line_connecting(A!2, B!1)) | apart_point_and_line(A!2, line_connecting(A!2, B!1))) | (~apart_point_and_line(A!2, line_connecting(A!2, B!1)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(206,plain,
% 0.19/0.41 (~apart_point_and_line(A!2, line_connecting(A!2, B!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[205, 190])).
% 0.19/0.41 tff(207,plain,
% 0.19/0.41 ((~(apart_point_and_line(A!2, line_connecting(A!2, B!1)) <=> (left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))))) | apart_point_and_line(A!2, line_connecting(A!2, B!1)) | (~(left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(208,plain,
% 0.19/0.41 ((~(apart_point_and_line(A!2, line_connecting(A!2, B!1)) <=> (left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))))) | (~(left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.19/0.41 tff(209,plain,
% 0.19/0.41 (~(left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[208, 204])).
% 0.19/0.41 tff(210,plain,
% 0.19/0.41 ((left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))) | (~right_apart_point(A!2, line_connecting(A!2, B!1)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(211,plain,
% 0.19/0.41 (~right_apart_point(A!2, line_connecting(A!2, B!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.19/0.41 tff(212,plain,
% 0.19/0.41 ((~(right_apart_point(A!2, line_connecting(A!2, B!1)) <=> left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))))) | right_apart_point(A!2, line_connecting(A!2, B!1)) | (~left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(213,plain,
% 0.19/0.41 ((~(right_apart_point(A!2, line_connecting(A!2, B!1)) <=> left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))))) | (~left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.19/0.41 tff(214,plain,
% 0.19/0.41 (~left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[213, 202])).
% 0.19/0.41 tff(215,plain,
% 0.19/0.41 ((left_apart_point(B!1, line_connecting(A!2, B!1)) | right_apart_point(B!1, line_connecting(A!2, B!1))) | (~left_apart_point(B!1, line_connecting(A!2, B!1)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(216,plain,
% 0.19/0.41 (~left_apart_point(B!1, line_connecting(A!2, B!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[215, 195])).
% 0.19/0.41 tff(217,plain,
% 0.19/0.41 ((left_apart_point(A!2, line_connecting(A!2, B!1)) | right_apart_point(A!2, line_connecting(A!2, B!1))) | (~left_apart_point(A!2, line_connecting(A!2, B!1)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(218,plain,
% 0.19/0.41 (~left_apart_point(A!2, line_connecting(A!2, B!1))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[217, 209])).
% 0.19/0.41 tff(219,plain,
% 0.19/0.41 (^[A: $i, B: $i, L: $i, M: $i] : refl((left_apart_point(B, M) | left_apart_point(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(220,plain,
% 0.19/0.41 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[219])).
% 0.19/0.41 tff(221,plain,
% 0.19/0.41 (^[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, M) | left_apart_point(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(222,plain,
% 0.19/0.41 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[221])).
% 0.19/0.41 tff(223,plain,
% 0.19/0.41 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(224,plain,
% 0.19/0.41 (^[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, M) | left_apart_point(B, reverse_line(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(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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, M) | left_apart_point(B, reverse_line(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))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(225,plain,
% 0.19/0.41 (![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, M) | left_apart_point(B, reverse_line(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))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[224])).
% 0.19/0.41 tff(226,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/sandbox2/benchmark/Axioms/GEO009+0.ax','ax1_uniq_cons')).
% 0.19/0.41 tff(227,plain,
% 0.19/0.41 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.19/0.42 tff(228,plain,
% 0.19/0.42 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[227, 223])).
% 0.19/0.42 tff(229,plain,(
% 0.19/0.42 ![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[228])).
% 0.19/0.42 tff(230,plain,
% 0.19/0.42 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[229, 222])).
% 0.19/0.42 tff(231,plain,
% 0.19/0.42 (![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[230, 220])).
% 0.19/0.42 tff(232,plain,
% 0.19/0.42 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(233,plain,
% 0.19/0.42 ((left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | (~distinct_points(A!2, B!1)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))) <=> ((~distinct_points(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(234,plain,
% 0.19/0.42 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | (~distinct_points(A!2, B!1)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[233])).
% 0.19/0.42 tff(235,plain,
% 0.19/0.42 (((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | (~distinct_points(A!2, B!1)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))) <=> ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[234, 232])).
% 0.19/0.43 tff(236,plain,
% 0.19/0.43 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(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!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | (~distinct_points(A!2, B!1)) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(237,plain,
% 0.19/0.43 ((~![A: $i, B: $i, L: $i, M: $i] : (left_apart_point(B, M) | left_apart_point(B, reverse_line(M)) | left_apart_point(A, reverse_line(M)) | left_apart_point(B, reverse_line(L)) | left_apart_point(A, reverse_line(L)) | left_apart_point(A, M) | left_apart_point(B, L) | left_apart_point(A, L) | (~distinct_points(A, B)) | (~distinct_lines(L, M)))) | (~distinct_points(A!2, B!1)) | left_apart_point(A!2, line_connecting(A!2, B!1)) | left_apart_point(B!1, line_connecting(A!2, B!1)) | left_apart_point(A!2, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(B!1, reverse_line(line_connecting(A!2, B!1))) | left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2))) | (~distinct_lines(line_connecting(A!2, B!1), line_connecting(B!1, A!2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.19/0.43 tff(238,plain,
% 0.19/0.43 (left_apart_point(A!2, reverse_line(line_connecting(B!1, A!2))) | left_apart_point(A!2, line_connecting(B!1, A!2)) | left_apart_point(B!1, line_connecting(B!1, A!2)) | left_apart_point(B!1, reverse_line(line_connecting(B!1, A!2)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[237, 231, 33, 218, 216, 214, 200, 182])).
% 0.19/0.43 tff(239,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[238, 107, 100, 86, 77])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------