%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO231+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:06:04 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO231+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:42:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(left_convergent_lines_type, type, (
% 0.20/0.38 left_convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_N_0_type, type, (
% 0.20/0.38 tptp_fun_N_0: $i)).
% 0.20/0.38 tff(tptp_fun_M_1_type, type, (
% 0.20/0.38 tptp_fun_M_1: $i)).
% 0.20/0.38 tff(reverse_line_type, type, (
% 0.20/0.38 reverse_line: $i > $i)).
% 0.20/0.38 tff(unequally_directed_lines_type, type, (
% 0.20/0.38 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_L_2_type, type, (
% 0.20/0.38 tptp_fun_L_2: $i)).
% 0.20/0.38 tff(unequally_directed_opposite_lines_type, type, (
% 0.20/0.38 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.20/0.38 tff(equally_directed_opposite_lines_type, type, (
% 0.20/0.38 equally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.20/0.38 tff(equally_directed_lines_type, type, (
% 0.20/0.38 equally_directed_lines: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,assumption,(left_convergent_lines(M!1, N!0) | left_convergent_lines(M!1, reverse_line(N!0))), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[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)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 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/GEO009+0.ax','ax11_basics')).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,(
% 0.20/0.38 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(M!1, N!0) | left_convergent_lines(M!1, reverse_line(N!0))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.38 tff(11,plain,(~(left_convergent_lines(M!1, N!0) | left_convergent_lines(M!1, reverse_line(N!0)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 ((left_convergent_lines(M!1, N!0) | left_convergent_lines(M!1, reverse_line(N!0))) | (~left_convergent_lines(M!1, N!0))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (~left_convergent_lines(M!1, N!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 ((left_convergent_lines(M!1, N!0) | left_convergent_lines(M!1, reverse_line(N!0))) | (~left_convergent_lines(M!1, reverse_line(N!0)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (~left_convergent_lines(M!1, reverse_line(N!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.20/0.38 tff(16,assumption,(~unequally_directed_lines(M!1, N!0)), introduced(assumption)).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (^[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))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(20,axiom,(![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a1_defns')).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.38 tff(22,plain,(
% 0.20/0.38 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!2, M!1) <=> unequally_directed_lines(L!2, reverse_line(M!1)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (unequally_directed_opposite_lines(L!2, M!1) <=> unequally_directed_lines(L!2, reverse_line(M!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (^[X: $i, Y: $i] : refl((~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y))) <=> (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (^[X: $i, Y: $i] : trans(rewrite((equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))) <=> (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))), rewrite((~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y))) <=> (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))), ((equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))) <=> (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.38 tff(31,axiom,(![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a5_defns')).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.38 tff(34,plain,(
% 0.20/0.38 ![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[33])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))) | (~(unequally_directed_opposite_lines(L!2, M!1) <=> equally_directed_opposite_lines(L!2, M!1)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (~(unequally_directed_opposite_lines(L!2, M!1) <=> equally_directed_opposite_lines(L!2, M!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 ((~![L: $i, M: $i, N: $i] : ((~(equally_directed_opposite_lines(L, M) & equally_directed_lines(L, N))) | equally_directed_opposite_lines(M, N))) <=> (~![L: $i, M: $i, N: $i] : ((~(equally_directed_opposite_lines(L, M) & equally_directed_lines(L, N))) | equally_directed_opposite_lines(M, N)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 ((~![L: $i, M: $i, N: $i] : ((equally_directed_opposite_lines(L, M) & equally_directed_lines(L, N)) => equally_directed_opposite_lines(M, N))) <=> (~![L: $i, M: $i, N: $i] : ((~(equally_directed_opposite_lines(L, M) & equally_directed_lines(L, N))) | equally_directed_opposite_lines(M, N)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(40,axiom,(~![L: $i, M: $i, N: $i] : ((equally_directed_opposite_lines(L, M) & equally_directed_lines(L, N)) => equally_directed_opposite_lines(M, N))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (~![L: $i, M: $i, N: $i] : ((~(equally_directed_opposite_lines(L, M) & equally_directed_lines(L, N))) | equally_directed_opposite_lines(M, N))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (~![L: $i, M: $i, N: $i] : ((~(equally_directed_opposite_lines(L, M) & equally_directed_lines(L, N))) | equally_directed_opposite_lines(M, N))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (~![L: $i, M: $i, N: $i] : ((~(equally_directed_opposite_lines(L, M) & equally_directed_lines(L, N))) | equally_directed_opposite_lines(M, N))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (~![L: $i, M: $i, N: $i] : ((~(equally_directed_opposite_lines(L, M) & equally_directed_lines(L, N))) | equally_directed_opposite_lines(M, N))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.20/0.38 tff(45,plain,(
% 0.20/0.38 ~((~(equally_directed_opposite_lines(L!2, M!1) & equally_directed_lines(L!2, N!0))) | equally_directed_opposite_lines(M!1, N!0))),
% 0.20/0.38 inference(skolemize,[status(sab)],[44])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 (equally_directed_opposite_lines(L!2, M!1) & equally_directed_lines(L!2, N!0)),
% 0.20/0.38 inference(or_elim,[status(thm)],[45])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (equally_directed_opposite_lines(L!2, M!1)),
% 0.20/0.38 inference(and_elim,[status(thm)],[46])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 ((unequally_directed_opposite_lines(L!2, M!1) <=> equally_directed_opposite_lines(L!2, M!1)) | (~unequally_directed_opposite_lines(L!2, M!1)) | (~equally_directed_opposite_lines(L!2, M!1))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 ((unequally_directed_opposite_lines(L!2, M!1) <=> equally_directed_opposite_lines(L!2, M!1)) | (~unequally_directed_opposite_lines(L!2, M!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (~unequally_directed_opposite_lines(L!2, M!1)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[49, 37])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 ((~(unequally_directed_opposite_lines(L!2, M!1) <=> unequally_directed_lines(L!2, reverse_line(M!1)))) | unequally_directed_opposite_lines(L!2, M!1) | (~unequally_directed_lines(L!2, reverse_line(M!1)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 ((~(unequally_directed_opposite_lines(L!2, M!1) <=> unequally_directed_lines(L!2, reverse_line(M!1)))) | (~unequally_directed_lines(L!2, reverse_line(M!1)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 (~unequally_directed_lines(L!2, reverse_line(M!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[52, 25])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 (^[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))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.38 tff(56,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(57,axiom,(![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax8_basics')).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.38 tff(59,plain,(
% 0.20/0.38 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[58])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!2, M!1) | unequally_directed_lines(L!2, reverse_line(M!1)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!2, M!1) | unequally_directed_lines(L!2, reverse_line(M!1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!2, M!1) | unequally_directed_lines(L!2, reverse_line(M!1)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!2, M!1) | unequally_directed_lines(L!2, reverse_line(M!1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 (unequally_directed_lines(L!2, M!1)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[63, 60, 53])).
% 0.20/0.38 tff(65,plain,
% 0.20/0.38 (^[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))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(66,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.38 tff(67,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(68,plain,
% 0.20/0.38 (^[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)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.38 tff(70,axiom,(![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a4_defns')).
% 0.20/0.38 tff(71,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.38 tff(72,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.38 tff(73,plain,(
% 0.20/0.38 ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[72])).
% 0.20/0.38 tff(74,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.20/0.38 tff(75,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(L!2, N!0) <=> equally_directed_lines(L!2, N!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(76,plain,
% 0.20/0.38 (~(unequally_directed_lines(L!2, N!0) <=> equally_directed_lines(L!2, N!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.38 tff(77,plain,
% 0.20/0.38 (equally_directed_lines(L!2, N!0)),
% 0.20/0.38 inference(and_elim,[status(thm)],[46])).
% 0.20/0.38 tff(78,plain,
% 0.20/0.38 ((unequally_directed_lines(L!2, N!0) <=> equally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, N!0)) | (~equally_directed_lines(L!2, N!0))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(79,plain,
% 0.20/0.38 ((unequally_directed_lines(L!2, N!0) <=> equally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, N!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.38 tff(80,plain,
% 0.20/0.38 (~unequally_directed_lines(L!2, N!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[79, 76])).
% 0.20/0.38 tff(81,plain,
% 0.20/0.38 (^[L: $i, M: $i, N: $i] : refl((unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(82,plain,
% 0.20/0.38 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.38 tff(83,plain,
% 0.20/0.38 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(84,plain,
% 0.20/0.38 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(L, N) | unequally_directed_lines(M, N)) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))))), rewrite((unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(85,plain,
% 0.20/0.38 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.38 tff(86,axiom,(![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax6_basics')).
% 0.20/0.38 tff(87,plain,
% 0.20/0.38 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.38 tff(88,plain,
% 0.20/0.38 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.38 tff(89,plain,(
% 0.20/0.38 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[88])).
% 0.20/0.38 tff(90,plain,
% 0.20/0.38 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.20/0.38 tff(91,plain,
% 0.20/0.38 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, M!1)) | unequally_directed_lines(M!1, N!0))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, M!1)) | unequally_directed_lines(M!1, N!0))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(92,plain,
% 0.20/0.38 ((unequally_directed_lines(M!1, N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, M!1))) <=> (unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, M!1)) | unequally_directed_lines(M!1, N!0))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(93,plain,
% 0.20/0.38 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, M!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, M!1)) | unequally_directed_lines(M!1, N!0)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.38 tff(94,plain,
% 0.20/0.38 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, M!1)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, M!1)) | unequally_directed_lines(M!1, N!0))),
% 0.20/0.38 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.38 tff(95,plain,
% 0.20/0.38 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(M!1, N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, M!1)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(96,plain,
% 0.20/0.38 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, M!1)) | unequally_directed_lines(M!1, N!0)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.38 tff(97,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[96, 90, 80, 64, 16])).
% 0.20/0.38 tff(98,plain,(unequally_directed_lines(M!1, N!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(99,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(M!1, N!0) <=> unequally_directed_lines(M!1, reverse_line(N!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(100,plain,
% 0.20/0.38 (unequally_directed_opposite_lines(M!1, N!0) <=> unequally_directed_lines(M!1, reverse_line(N!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[99, 23])).
% 0.20/0.38 tff(101,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))) | (~(unequally_directed_opposite_lines(M!1, N!0) <=> equally_directed_opposite_lines(M!1, N!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 (~(unequally_directed_opposite_lines(M!1, N!0) <=> equally_directed_opposite_lines(M!1, N!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[101, 35])).
% 0.20/0.39 tff(103,plain,
% 0.20/0.39 (~equally_directed_opposite_lines(M!1, N!0)),
% 0.20/0.39 inference(or_elim,[status(thm)],[45])).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 ((unequally_directed_opposite_lines(M!1, N!0) <=> equally_directed_opposite_lines(M!1, N!0)) | unequally_directed_opposite_lines(M!1, N!0) | equally_directed_opposite_lines(M!1, N!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 ((unequally_directed_opposite_lines(M!1, N!0) <=> equally_directed_opposite_lines(M!1, N!0)) | unequally_directed_opposite_lines(M!1, N!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.20/0.39 tff(106,plain,
% 0.20/0.39 (unequally_directed_opposite_lines(M!1, N!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[105, 102])).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 ((~(unequally_directed_opposite_lines(M!1, N!0) <=> unequally_directed_lines(M!1, reverse_line(N!0)))) | (~unequally_directed_opposite_lines(M!1, N!0)) | unequally_directed_lines(M!1, reverse_line(N!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(108,plain,
% 0.20/0.39 ((~(unequally_directed_opposite_lines(M!1, N!0) <=> unequally_directed_lines(M!1, reverse_line(N!0)))) | unequally_directed_lines(M!1, reverse_line(N!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.39 tff(109,plain,
% 0.20/0.39 (unequally_directed_lines(M!1, reverse_line(N!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[108, 100])).
% 0.20/0.39 tff(110,plain,
% 0.20/0.39 (^[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)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(111,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.39 tff(112,plain,
% 0.20/0.39 (^[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)) | (~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))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(113,plain,
% 0.20/0.39 (![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)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.39 tff(114,plain,
% 0.20/0.39 (![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)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(115,plain,
% 0.20/0.39 (^[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))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(116,plain,
% 0.20/0.39 (![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)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[115])).
% 0.20/0.39 tff(117,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/GEO009+0.ax','ax9_basics')).
% 0.20/0.39 tff(118,plain,
% 0.20/0.39 (![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)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.39 tff(119,plain,
% 0.20/0.39 (![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)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.20/0.39 tff(120,plain,(
% 0.20/0.39 ![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)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[119])).
% 0.20/0.39 tff(121,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.20/0.39 tff(122,plain,
% 0.20/0.39 (![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))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.20/0.39 tff(123,plain,
% 0.20/0.39 (((~![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!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0))) <=> ((~![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!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(124,plain,
% 0.20/0.39 ((left_convergent_lines(M!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, N!0) | (~unequally_directed_lines(M!1, reverse_line(N!0)))) <=> ((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(125,plain,
% 0.20/0.39 (((~![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!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, N!0) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) <=> ((~![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!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[124])).
% 0.20/0.39 tff(126,plain,
% 0.20/0.39 (((~![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!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, N!0) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) <=> ((~![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!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0))),
% 0.20/0.39 inference(transitivity,[status(thm)],[125, 123])).
% 0.20/0.39 tff(127,plain,
% 0.20/0.39 ((~![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!1, reverse_line(N!0)) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, N!0) | (~unequally_directed_lines(M!1, reverse_line(N!0))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(128,plain,
% 0.20/0.39 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.39 tff(129,plain,
% 0.20/0.39 ((~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[128, 122, 109])).
% 0.20/0.39 tff(130,plain,
% 0.20/0.39 (left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[129, 98])).
% 0.20/0.39 tff(131,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[130, 15, 13])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------