%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO261+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:06:10 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO261+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 14:43:56 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(left_convergent_lines_type, type, (
% 0.13/0.39 left_convergent_lines: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_M_3_type, type, (
% 0.13/0.39 tptp_fun_M_3: $i)).
% 0.13/0.39 tff(tptp_fun_L_4_type, type, (
% 0.13/0.39 tptp_fun_L_4: $i)).
% 0.13/0.39 tff(reverse_line_type, type, (
% 0.13/0.39 reverse_line: $i > $i)).
% 0.13/0.39 tff(unequally_directed_lines_type, type, (
% 0.13/0.39 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.13/0.39 tff(convergent_lines_type, type, (
% 0.13/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.13/0.39 tff(apart_point_and_line_type, type, (
% 0.13/0.39 apart_point_and_line: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_B_1_type, type, (
% 0.13/0.39 tptp_fun_B_1: $i)).
% 0.13/0.39 tff(between_on_line_type, type, (
% 0.13/0.39 between_on_line: ( $i * $i * $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_C_0_type, type, (
% 0.13/0.39 tptp_fun_C_0: $i)).
% 0.13/0.39 tff(tptp_fun_A_2_type, type, (
% 0.13/0.39 tptp_fun_A_2: $i)).
% 0.13/0.39 tff(divides_points_type, type, (
% 0.13/0.39 divides_points: ( $i * $i * $i ) > $o)).
% 0.13/0.39 tff(1,assumption,(left_convergent_lines(L!4, M!3) | left_convergent_lines(L!4, reverse_line(M!3))), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (^[L: $i, M: $i] : refl((~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag11')).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.39 tff(7,plain,(
% 0.13/0.39 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[6])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!4, M!3) | left_convergent_lines(L!4, reverse_line(M!3))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.13/0.39 tff(11,plain,(~(left_convergent_lines(L!4, M!3) | left_convergent_lines(L!4, reverse_line(M!3)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 ((left_convergent_lines(L!4, M!3) | left_convergent_lines(L!4, reverse_line(M!3))) | (~left_convergent_lines(L!4, M!3))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (~left_convergent_lines(L!4, M!3)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 ((left_convergent_lines(L!4, M!3) | left_convergent_lines(L!4, reverse_line(M!3))) | (~left_convergent_lines(L!4, reverse_line(M!3)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (~left_convergent_lines(L!4, reverse_line(M!3))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (^[L: $i, M: $i] : refl((~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M))) <=> ![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (^[L: $i, M: $i] : trans(trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))), ((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M))))), rewrite((~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))), ((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (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)))) <=> convergent_lines(L, M)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(21,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','con_def')).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.13/0.39 tff(23,plain,(
% 0.13/0.39 ![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[22])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))) | (~(((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3)))) <=> convergent_lines(L!4, M!3)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~(((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3)))) <=> convergent_lines(L!4, M!3))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 ((~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & (~apart_point_and_line(B, M)))) | divides_points(M, A, C))) <=> (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & (~apart_point_and_line(B, M)))) | divides_points(M, A, C)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((~![L: $i, M: $i, A: $i, B: $i, C: $i] : (((between_on_line(L, A, B, C) & convergent_lines(L, M)) & (~apart_point_and_line(B, M))) => divides_points(M, A, C))) <=> (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & (~apart_point_and_line(B, M)))) | divides_points(M, A, C)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(30,axiom,(~![L: $i, M: $i, A: $i, B: $i, C: $i] : (((between_on_line(L, A, B, C) & convergent_lines(L, M)) & (~apart_point_and_line(B, M))) => divides_points(M, A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & (~apart_point_and_line(B, M)))) | divides_points(M, A, C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & (~apart_point_and_line(B, M)))) | divides_points(M, A, C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & (~apart_point_and_line(B, M)))) | divides_points(M, A, C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & (~apart_point_and_line(B, M)))) | divides_points(M, A, C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.13/0.39 tff(35,plain,(
% 0.13/0.39 ~((~(between_on_line(L!4, A!2, B!1, C!0) & convergent_lines(L!4, M!3) & (~apart_point_and_line(B!1, M!3)))) | divides_points(M!3, A!2, C!0))),
% 0.13/0.39 inference(skolemize,[status(sab)],[34])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (between_on_line(L!4, A!2, B!1, C!0) & convergent_lines(L!4, M!3) & (~apart_point_and_line(B!1, M!3))),
% 0.13/0.39 inference(or_elim,[status(thm)],[35])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (convergent_lines(L!4, M!3)),
% 0.13/0.39 inference(and_elim,[status(thm)],[36])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 ((((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3)))) <=> convergent_lines(L!4, M!3)) | (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))))) | (~convergent_lines(L!4, M!3))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 ((((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3)))) <=> convergent_lines(L!4, M!3)) | (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3)))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[39, 27])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3)))) | unequally_directed_lines(L!4, reverse_line(M!3))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (unequally_directed_lines(L!4, reverse_line(M!3))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3)))) | unequally_directed_lines(L!4, M!3)),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (unequally_directed_lines(L!4, M!3)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (^[L: $i, M: $i] : refl((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (^[L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (^[L: $i, M: $i] : rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.13/0.39 tff(52,axiom,(![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag9')).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.13/0.39 tff(55,plain,(
% 0.13/0.39 ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[54])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 ((left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3) | (~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3)))) <=> ((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3) | (~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3)))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[59])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3) | (~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3))),
% 0.13/0.39 inference(transitivity,[status(thm)],[60, 58])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3) | (~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 (left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[63, 57, 44, 42])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[64, 15, 13])).
% 0.13/0.40 % SZS output end Proof
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------