%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO261+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 05:06:10 AM UTC 2025
% Result : Theorem 0.41s 0.61s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : GEO261+3 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.12 % 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 14:43:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.41/0.61 % SZS status Theorem
% 0.41/0.61 % SZS output start Proof
% 0.41/0.61 tff(unequally_directed_lines_type, type, (
% 0.41/0.61 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.41/0.61 tff(reverse_line_type, type, (
% 0.41/0.61 reverse_line: $i > $i)).
% 0.41/0.61 tff(line_connecting_type, type, (
% 0.41/0.61 line_connecting: ( $i * $i ) > $i)).
% 0.41/0.61 tff(tptp_fun_A_2_type, type, (
% 0.41/0.61 tptp_fun_A_2: $i)).
% 0.41/0.61 tff(tptp_fun_B_1_type, type, (
% 0.41/0.61 tptp_fun_B_1: $i)).
% 0.41/0.61 tff(tptp_fun_M_3_type, type, (
% 0.41/0.61 tptp_fun_M_3: $i)).
% 0.41/0.61 tff(left_convergent_lines_type, type, (
% 0.41/0.61 left_convergent_lines: ( $i * $i ) > $o)).
% 0.41/0.61 tff(tptp_fun_L_4_type, type, (
% 0.41/0.61 tptp_fun_L_4: $i)).
% 0.41/0.61 tff(unequally_directed_opposite_lines_type, type, (
% 0.41/0.61 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.41/0.61 tff(convergent_lines_type, type, (
% 0.41/0.61 convergent_lines: ( $i * $i ) > $o)).
% 0.41/0.61 tff(incident_point_and_line_type, type, (
% 0.41/0.61 incident_point_and_line: ( $i * $i ) > $o)).
% 0.41/0.61 tff(between_on_line_type, type, (
% 0.41/0.61 between_on_line: ( $i * $i * $i * $i ) > $o)).
% 0.41/0.61 tff(tptp_fun_C_0_type, type, (
% 0.41/0.61 tptp_fun_C_0: $i)).
% 0.41/0.61 tff(divides_points_type, type, (
% 0.41/0.61 divides_points: ( $i * $i * $i ) > $o)).
% 0.41/0.61 tff(1,assumption,(~((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))), introduced(assumption)).
% 0.41/0.61 tff(2,plain,
% 0.41/0.61 (((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))) | unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(3,plain,
% 0.41/0.61 (unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.41/0.61 tff(4,plain,
% 0.41/0.61 (((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))) | unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(5,plain,
% 0.41/0.61 (unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.41/0.61 tff(6,assumption,(left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))), introduced(assumption)).
% 0.41/0.61 tff(7,plain,
% 0.41/0.61 (^[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)))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(8,plain,
% 0.41/0.61 (![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))))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[7])).
% 0.41/0.61 tff(9,plain,
% 0.41/0.61 (![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))))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(10,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax11_basics')).
% 0.41/0.61 tff(11,plain,
% 0.41/0.61 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.41/0.61 tff(12,plain,(
% 0.41/0.61 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.41/0.61 inference(skolemize,[status(sab)],[11])).
% 0.41/0.61 tff(13,plain,
% 0.41/0.61 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.41/0.61 tff(14,plain,
% 0.41/0.61 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(15,plain,
% 0.41/0.61 ($false),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[14, 13, 6])).
% 0.41/0.61 tff(16,plain,(~(left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.61 tff(17,plain,
% 0.41/0.61 ((left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | (~left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(18,plain,
% 0.41/0.61 (~left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.41/0.61 tff(19,assumption,(left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))), introduced(assumption)).
% 0.41/0.61 tff(20,plain,
% 0.41/0.61 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(21,plain,
% 0.41/0.61 ($false),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[20, 13, 19])).
% 0.41/0.61 tff(22,plain,(~(left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.61 tff(23,plain,
% 0.41/0.61 ((left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(24,plain,
% 0.41/0.61 (~left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.41/0.61 tff(25,plain,
% 0.41/0.61 (^[L: $i, M: $i] : refl((left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(26,plain,
% 0.41/0.61 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[25])).
% 0.41/0.61 tff(27,plain,
% 0.41/0.61 (^[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)) | (~unequally_directed_lines(L, M)) | left_convergent_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)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(28,plain,
% 0.41/0.61 (![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)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[27])).
% 0.41/0.61 tff(29,plain,
% 0.41/0.61 (![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)))))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(30,plain,
% 0.41/0.61 (^[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))))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(31,plain,
% 0.41/0.61 (![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)))))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[30])).
% 0.41/0.61 tff(32,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/sandbox2/benchmark/Axioms/GEO009+0.ax','ax9_basics')).
% 0.41/0.61 tff(33,plain,
% 0.41/0.61 (![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)))))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.41/0.61 tff(34,plain,
% 0.41/0.61 (![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)))))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.41/0.61 tff(35,plain,(
% 0.41/0.61 ![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)))))),
% 0.41/0.61 inference(skolemize,[status(sab)],[34])).
% 0.41/0.61 tff(36,plain,
% 0.41/0.61 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.41/0.61 tff(37,plain,
% 0.41/0.61 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.41/0.61 tff(38,plain,
% 0.41/0.61 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(39,plain,
% 0.41/0.61 ((left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))) <=> ((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(40,plain,
% 0.41/0.61 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))),
% 0.41/0.61 inference(monotonicity,[status(thm)],[39])).
% 0.41/0.61 tff(41,plain,
% 0.41/0.61 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))),
% 0.41/0.61 inference(transitivity,[status(thm)],[40, 38])).
% 0.41/0.61 tff(42,plain,
% 0.41/0.61 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(43,plain,
% 0.41/0.61 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.41/0.61 tff(44,plain,
% 0.41/0.61 ($false),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[43, 37, 24, 18, 5, 3])).
% 0.41/0.61 tff(45,plain,((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.61 tff(46,assumption,(~((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))), introduced(assumption)).
% 0.41/0.61 tff(47,plain,
% 0.41/0.61 (((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))) | unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(48,plain,
% 0.41/0.61 (unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.41/0.61 tff(49,plain,
% 0.41/0.61 (((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))) | unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(50,plain,
% 0.41/0.61 (unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.41/0.61 tff(51,assumption,(left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))), introduced(assumption)).
% 0.41/0.61 tff(52,plain,
% 0.41/0.61 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(53,plain,
% 0.41/0.61 ($false),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[52, 13, 51])).
% 0.41/0.61 tff(54,plain,(~(left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.61 tff(55,plain,
% 0.41/0.61 ((left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | (~left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(56,plain,
% 0.41/0.61 (~left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.41/0.61 tff(57,plain,
% 0.41/0.61 ((left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | (~left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(58,plain,
% 0.41/0.61 (~left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.41/0.61 tff(59,plain,
% 0.41/0.61 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(60,plain,
% 0.41/0.61 ((left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))) <=> ((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(61,plain,
% 0.41/0.61 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))),
% 0.41/0.61 inference(monotonicity,[status(thm)],[60])).
% 0.41/0.61 tff(62,plain,
% 0.41/0.61 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))),
% 0.41/0.61 inference(transitivity,[status(thm)],[61, 59])).
% 0.41/0.61 tff(63,plain,
% 0.41/0.61 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(64,plain,
% 0.41/0.61 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | left_convergent_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.41/0.61 tff(65,plain,
% 0.41/0.61 ($false),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[64, 37, 58, 56, 50, 48])).
% 0.41/0.61 tff(66,plain,((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.61 tff(67,plain,
% 0.41/0.61 (^[X: $i, Y: $i] : refl((unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(68,plain,
% 0.41/0.61 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[67])).
% 0.41/0.61 tff(69,plain,
% 0.41/0.61 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(70,axiom,(![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a1_defns')).
% 0.41/0.61 tff(71,plain,
% 0.41/0.61 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.41/0.61 tff(72,plain,(
% 0.41/0.61 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.41/0.61 inference(skolemize,[status(sab)],[71])).
% 0.41/0.61 tff(73,plain,
% 0.41/0.61 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.41/0.61 tff(74,plain,
% 0.41/0.61 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!4, M!3) <=> unequally_directed_lines(L!4, reverse_line(M!3)))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(75,plain,
% 0.41/0.61 (unequally_directed_opposite_lines(L!4, M!3) <=> unequally_directed_lines(L!4, reverse_line(M!3))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.41/0.61 tff(76,plain,
% 0.41/0.61 (^[L: $i, M: $i] : refl((~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(77,plain,
% 0.41/0.61 (![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M))) <=> ![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[76])).
% 0.41/0.61 tff(78,plain,
% 0.41/0.61 (^[L: $i, M: $i] : trans(trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))))), ((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> (convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))))))), rewrite((convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))), ((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M))))), rewrite((~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))), ((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))))),
% 0.41/0.61 inference(bind,[status(th)],[])).
% 0.41/0.61 tff(79,plain,
% 0.41/0.61 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> ![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))),
% 0.41/0.61 inference(quant_intro,[status(thm)],[78])).
% 0.41/0.61 tff(80,plain,
% 0.41/0.61 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> ![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(81,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a7_defns')).
% 0.41/0.61 tff(82,plain,
% 0.41/0.61 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.41/0.61 tff(83,plain,(
% 0.41/0.61 ![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)))),
% 0.41/0.61 inference(skolemize,[status(sab)],[82])).
% 0.41/0.61 tff(84,plain,
% 0.41/0.61 (![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.41/0.61 tff(85,plain,
% 0.41/0.61 (![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.41/0.61 tff(86,plain,
% 0.41/0.61 ((~![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))) <=> convergent_lines(L, M)))) | (~(((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3))) <=> convergent_lines(L!4, M!3)))),
% 0.41/0.61 inference(quant_inst,[status(thm)],[])).
% 0.41/0.61 tff(87,plain,
% 0.41/0.61 (~(((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3))) <=> convergent_lines(L!4, M!3))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.41/0.61 tff(88,plain,
% 0.41/0.61 ((~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_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) & incident_point_and_line(B, M))) | divides_points(M, A, C)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(89,plain,
% 0.41/0.61 ((~![L: $i, M: $i, A: $i, B: $i, C: $i] : (((between_on_line(L, A, B, C) & convergent_lines(L, M)) & incident_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) & incident_point_and_line(B, M))) | divides_points(M, A, C)))),
% 0.41/0.61 inference(rewrite,[status(thm)],[])).
% 0.41/0.61 tff(90,axiom,(~![L: $i, M: $i, A: $i, B: $i, C: $i] : (((between_on_line(L, A, B, C) & convergent_lines(L, M)) & incident_point_and_line(B, M)) => divides_points(M, A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.41/0.61 tff(91,plain,
% 0.41/0.61 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.41/0.61 tff(92,plain,
% 0.41/0.61 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[91, 88])).
% 0.41/0.61 tff(93,plain,
% 0.41/0.61 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.41/0.61 tff(94,plain,
% 0.41/0.61 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C))),
% 0.41/0.61 inference(modus_ponens,[status(thm)],[93, 88])).
% 0.41/0.61 tff(95,plain,(
% 0.41/0.61 ~((~(between_on_line(L!4, A!2, B!1, C!0) & convergent_lines(L!4, M!3) & incident_point_and_line(B!1, M!3))) | divides_points(M!3, A!2, C!0))),
% 0.41/0.61 inference(skolemize,[status(sab)],[94])).
% 0.41/0.61 tff(96,plain,
% 0.41/0.61 (between_on_line(L!4, A!2, B!1, C!0) & convergent_lines(L!4, M!3) & incident_point_and_line(B!1, M!3)),
% 0.41/0.61 inference(or_elim,[status(thm)],[95])).
% 0.41/0.61 tff(97,plain,
% 0.41/0.61 (convergent_lines(L!4, M!3)),
% 0.41/0.61 inference(and_elim,[status(thm)],[96])).
% 0.41/0.61 tff(98,plain,
% 0.41/0.61 ((((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3))) <=> convergent_lines(L!4, M!3)) | (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3)))) | (~convergent_lines(L!4, M!3))),
% 0.41/0.61 inference(tautology,[status(thm)],[])).
% 0.41/0.61 tff(99,plain,
% 0.41/0.61 ((((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3))) <=> convergent_lines(L!4, M!3)) | (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3))))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.41/0.61 tff(100,plain,
% 0.41/0.61 (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3)))),
% 0.41/0.61 inference(unit_resolution,[status(thm)],[99, 87])).
% 0.41/0.61 tff(101,plain,
% 0.41/0.61 (((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3))) | unequally_directed_opposite_lines(L!4, M!3)),
% 0.41/0.62 inference(tautology,[status(thm)],[])).
% 0.41/0.62 tff(102,plain,
% 0.41/0.62 (unequally_directed_opposite_lines(L!4, M!3)),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.41/0.62 tff(103,plain,
% 0.41/0.62 ((~(unequally_directed_opposite_lines(L!4, M!3) <=> unequally_directed_lines(L!4, reverse_line(M!3)))) | (~unequally_directed_opposite_lines(L!4, M!3)) | unequally_directed_lines(L!4, reverse_line(M!3))),
% 0.41/0.62 inference(tautology,[status(thm)],[])).
% 0.41/0.62 tff(104,plain,
% 0.41/0.62 ((~(unequally_directed_opposite_lines(L!4, M!3) <=> unequally_directed_lines(L!4, reverse_line(M!3)))) | unequally_directed_lines(L!4, reverse_line(M!3))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.41/0.62 tff(105,plain,
% 0.41/0.62 (unequally_directed_lines(L!4, reverse_line(M!3))),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[104, 75])).
% 0.41/0.62 tff(106,plain,
% 0.41/0.62 (((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3))) | unequally_directed_lines(L!4, M!3)),
% 0.41/0.62 inference(tautology,[status(thm)],[])).
% 0.41/0.62 tff(107,plain,
% 0.41/0.62 (unequally_directed_lines(L!4, M!3)),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[106, 100])).
% 0.41/0.62 tff(108,plain,
% 0.41/0.62 (^[L: $i, M: $i, N: $i] : refl(((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 0.41/0.62 inference(bind,[status(th)],[])).
% 0.41/0.62 tff(109,plain,
% 0.41/0.62 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.41/0.62 inference(quant_intro,[status(thm)],[108])).
% 0.41/0.62 tff(110,plain,
% 0.41/0.62 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) <=> (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N)))))), rewrite((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) <=> (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))), 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)))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite(((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.41/0.62 inference(bind,[status(th)],[])).
% 0.41/0.62 tff(111,plain,
% 0.41/0.62 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.41/0.62 inference(quant_intro,[status(thm)],[110])).
% 0.41/0.62 tff(112,plain,
% 0.41/0.62 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(113,plain,
% 0.41/0.62 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite(((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))), (((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))))), rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(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, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))))),
% 0.41/0.62 inference(bind,[status(th)],[])).
% 0.41/0.62 tff(114,plain,
% 0.41/0.62 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.41/0.62 inference(quant_intro,[status(thm)],[113])).
% 0.41/0.62 tff(115,axiom,(![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax7_basics')).
% 0.41/0.62 tff(116,plain,
% 0.41/0.62 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.41/0.62 tff(117,plain,
% 0.41/0.62 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.41/0.62 tff(118,plain,(
% 0.41/0.62 ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.41/0.62 inference(skolemize,[status(sab)],[117])).
% 0.41/0.62 tff(119,plain,
% 0.41/0.62 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.41/0.62 tff(120,plain,
% 0.41/0.62 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[119, 109])).
% 0.41/0.62 tff(121,plain,
% 0.41/0.62 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | (~((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | (~((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(122,plain,
% 0.41/0.62 (((~unequally_directed_lines(L!4, M!3)) | (~((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~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))) | (~((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))))),
% 0.41/0.62 inference(rewrite,[status(thm)],[])).
% 0.41/0.62 tff(123,plain,
% 0.41/0.62 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!4, M!3)) | (~((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~unequally_directed_lines(L!4, reverse_line(M!3))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | (~((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))))))),
% 0.41/0.62 inference(monotonicity,[status(thm)],[122])).
% 0.41/0.62 tff(124,plain,
% 0.41/0.62 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!4, M!3)) | (~((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~unequally_directed_lines(L!4, reverse_line(M!3))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | (~((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))))),
% 0.41/0.62 inference(transitivity,[status(thm)],[123, 121])).
% 0.41/0.62 tff(125,plain,
% 0.41/0.62 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!4, M!3)) | (~((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~unequally_directed_lines(L!4, reverse_line(M!3))))),
% 0.41/0.62 inference(quant_inst,[status(thm)],[])).
% 0.41/0.62 tff(126,plain,
% 0.41/0.62 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | (~((~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(L!4, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2)))))))))) | (~((~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))) | (~unequally_directed_lines(M!3, reverse_line(reverse_line(reverse_line(reverse_line(reverse_line(line_connecting(B!1, A!2))))))))))),
% 0.41/0.62 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.41/0.62 tff(127,plain,
% 0.41/0.62 ($false),
% 0.41/0.62 inference(unit_resolution,[status(thm)],[126, 120, 107, 105, 66, 45])).
% 0.41/0.62 % SZS output end Proof
% 0.41/0.62 % E exiting
%------------------------------------------------------------------------------