%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO268+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:06:12 AM UTC 2025
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO268+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.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 14:44:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(left_convergent_lines_type, type, (
% 0.20/0.44 left_convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.44 tff(tptp_fun_M_0_type, type, (
% 0.20/0.44 tptp_fun_M_0: $i)).
% 0.20/0.44 tff(tptp_fun_L_1_type, type, (
% 0.20/0.44 tptp_fun_L_1: $i)).
% 0.20/0.44 tff(reverse_line_type, type, (
% 0.20/0.44 reverse_line: $i > $i)).
% 0.20/0.44 tff(unequally_directed_lines_type, type, (
% 0.20/0.44 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.20/0.44 tff(unequally_directed_opposite_lines_type, type, (
% 0.20/0.44 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.20/0.44 tff(1,assumption,(left_convergent_lines(L!1, M!0) | left_convergent_lines(L!1, reverse_line(M!0))), introduced(assumption)).
% 0.20/0.44 tff(2,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 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')).
% 0.20/0.44 tff(6,plain,
% 0.20/0.44 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.44 tff(7,plain,(
% 0.20/0.44 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[6])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!1, M!0) | left_convergent_lines(L!1, reverse_line(M!0))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.44 tff(11,plain,(~(left_convergent_lines(L!1, M!0) | left_convergent_lines(L!1, reverse_line(M!0)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 ((left_convergent_lines(L!1, M!0) | left_convergent_lines(L!1, reverse_line(M!0))) | (~left_convergent_lines(L!1, M!0))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (~left_convergent_lines(L!1, M!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 ((left_convergent_lines(L!1, M!0) | left_convergent_lines(L!1, reverse_line(M!0))) | (~left_convergent_lines(L!1, reverse_line(M!0)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (~left_convergent_lines(L!1, reverse_line(M!0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.20/0.44 tff(16,assumption,(left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0)))), introduced(assumption)).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[17, 8, 16])).
% 0.20/0.44 tff(19,plain,(~(left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 ((left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0)))) | (~left_convergent_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (~left_convergent_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.45 tff(22,assumption,(~unequally_directed_lines(L!1, M!0)), introduced(assumption)).
% 0.20/0.45 tff(23,assumption,(~unequally_directed_lines(L!1, reverse_line(M!0))), introduced(assumption)).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(27,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')).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.45 tff(29,plain,(
% 0.20/0.45 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[28])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[33, 30, 22, 23])).
% 0.20/0.45 tff(35,plain,(unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, M!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 (unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[35, 22])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 ((~(unequally_directed_lines(L!1, M!0) <=> unequally_directed_opposite_lines(L!1, reverse_line(M!0)))) <=> (~(unequally_directed_lines(L!1, M!0) <=> unequally_directed_opposite_lines(L!1, reverse_line(M!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))) <=> (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(39,axiom,(~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[40, 38])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.45 tff(44,plain,(
% 0.20/0.45 ~(unequally_directed_lines(L!1, M!0) <=> unequally_directed_opposite_lines(L!1, reverse_line(M!0)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[43])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (~(unequally_directed_lines(L!1, M!0) <=> unequally_directed_opposite_lines(L!1, reverse_line(M!0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 ((unequally_directed_lines(L!1, M!0) <=> unequally_directed_opposite_lines(L!1, reverse_line(M!0))) | unequally_directed_lines(L!1, M!0) | unequally_directed_opposite_lines(L!1, reverse_line(M!0))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (unequally_directed_lines(L!1, M!0) | unequally_directed_opposite_lines(L!1, reverse_line(M!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (unequally_directed_opposite_lines(L!1, reverse_line(M!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[47, 22])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(52,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')).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.45 tff(54,plain,(
% 0.20/0.45 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[53])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!1, reverse_line(M!0)) <=> unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (unequally_directed_opposite_lines(L!1, reverse_line(M!0)) <=> unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 ((~(unequally_directed_opposite_lines(L!1, reverse_line(M!0)) <=> unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))) | (~unequally_directed_opposite_lines(L!1, reverse_line(M!0))) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 ((~unequally_directed_opposite_lines(L!1, reverse_line(M!0))) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[59, 48])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (^[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))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (![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)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (^[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))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (![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)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.45 tff(68,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')).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (![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)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (![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)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.45 tff(71,plain,(
% 0.20/0.45 ![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)))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[70])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (((~![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!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!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(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 ((left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))) <=> ((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (((~![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!1, reverse_line(reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!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(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 (((~![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!1, reverse_line(reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!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(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 ((~![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!1, reverse_line(reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 ((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[79, 73])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[80, 60, 36, 15, 21])).
% 0.20/0.45 tff(82,plain,(unequally_directed_lines(L!1, M!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 ((unequally_directed_lines(L!1, M!0) <=> unequally_directed_opposite_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_opposite_lines(L!1, reverse_line(M!0)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_opposite_lines(L!1, reverse_line(M!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[83, 45])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (~unequally_directed_opposite_lines(L!1, reverse_line(M!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[84, 82])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 ((~(unequally_directed_opposite_lines(L!1, reverse_line(M!0)) <=> unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))) | unequally_directed_opposite_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 (unequally_directed_opposite_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[86, 57])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[87, 85])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[91, 30])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 (unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[92, 88])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (((~![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!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, M!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(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, M!0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 ((left_convergent_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, M!0)) | left_convergent_lines(L!1, M!0) | (~unequally_directed_lines(L!1, reverse_line(M!0)))) <=> ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, M!0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 (((~![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!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, M!0)) | left_convergent_lines(L!1, M!0) | (~unequally_directed_lines(L!1, reverse_line(M!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(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, M!0)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[95])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 (((~![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!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, M!0)) | left_convergent_lines(L!1, M!0) | (~unequally_directed_lines(L!1, reverse_line(M!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(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, M!0))),
% 0.20/0.45 inference(transitivity,[status(thm)],[96, 94])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 ((~![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!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, M!0)) | left_convergent_lines(L!1, M!0) | (~unequally_directed_lines(L!1, reverse_line(M!0))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, M!0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[99, 73, 82, 93, 15, 13])).
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------