%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO269+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 05:06:12 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO269+3 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 14:43:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(unequally_directed_lines_type, type, (
% 0.20/0.37 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.20/0.37 tff(tptp_fun_L_0_type, type, (
% 0.20/0.37 tptp_fun_L_0: $i)).
% 0.20/0.37 tff(reverse_line_type, type, (
% 0.20/0.37 reverse_line: $i > $i)).
% 0.20/0.37 tff(left_convergent_lines_type, type, (
% 0.20/0.37 left_convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.37 tff(unequally_directed_opposite_lines_type, type, (
% 0.20/0.37 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.20/0.37 tff(equally_directed_opposite_lines_type, type, (
% 0.20/0.37 equally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.20/0.37 tff(1,assumption,(left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))), introduced(assumption)).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (^[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)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (![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))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (![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))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(5,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')).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.37 tff(7,plain,(
% 0.20/0.37 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.37 inference(skolemize,[status(sab)],[6])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.37 tff(11,plain,(~(left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 ((left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))) | (~left_convergent_lines(L!0, reverse_line(L!0)))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (~left_convergent_lines(L!0, reverse_line(L!0))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 ((left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))) | (~left_convergent_lines(L!0, reverse_line(reverse_line(L!0))))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (~left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (^[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))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (![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)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (![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)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(19,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')).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.37 tff(21,plain,(
% 0.20/0.37 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[20])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 (unequally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 (^[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))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 (![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)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 (![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)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 (^[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)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 (![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)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.37 tff(30,axiom,(![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a5_defns')).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.37 tff(33,plain,(
% 0.20/0.37 ![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[32])).
% 0.20/0.37 tff(34,plain,
% 0.20/0.37 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 ((~![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))) | (~(unequally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> equally_directed_opposite_lines(L!0, reverse_line(L!0))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(36,plain,
% 0.20/0.37 (~(unequally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> equally_directed_opposite_lines(L!0, reverse_line(L!0)))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.37 tff(37,plain,
% 0.20/0.37 ((~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))) <=> (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(38,axiom,(~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.20/0.37 tff(39,plain,
% 0.20/0.37 (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.37 tff(40,plain,
% 0.20/0.37 (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[39, 37])).
% 0.20/0.37 tff(41,plain,
% 0.20/0.37 (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.20/0.37 tff(42,plain,
% 0.20/0.37 (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.37 tff(43,plain,(
% 0.20/0.37 ~equally_directed_opposite_lines(L!0, reverse_line(L!0))),
% 0.20/0.37 inference(skolemize,[status(sab)],[42])).
% 0.20/0.37 tff(44,plain,
% 0.20/0.37 ((unequally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> equally_directed_opposite_lines(L!0, reverse_line(L!0))) | unequally_directed_opposite_lines(L!0, reverse_line(L!0)) | equally_directed_opposite_lines(L!0, reverse_line(L!0))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(45,plain,
% 0.20/0.37 ((unequally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> equally_directed_opposite_lines(L!0, reverse_line(L!0))) | unequally_directed_opposite_lines(L!0, reverse_line(L!0))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.37 tff(46,plain,
% 0.20/0.37 (unequally_directed_opposite_lines(L!0, reverse_line(L!0))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[45, 36])).
% 0.20/0.37 tff(47,plain,
% 0.20/0.37 ((~(unequally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))))) | (~unequally_directed_opposite_lines(L!0, reverse_line(L!0))) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(48,plain,
% 0.20/0.37 ((~(unequally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))))) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.37 tff(49,plain,
% 0.20/0.37 (unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[48, 24])).
% 0.20/0.37 tff(50,plain,
% 0.20/0.37 (^[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)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(51,plain,
% 0.20/0.37 (![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))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.37 tff(52,plain,
% 0.20/0.37 (^[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))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(53,plain,
% 0.20/0.37 (![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))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.37 tff(54,plain,
% 0.20/0.37 (![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)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(55,plain,
% 0.20/0.37 (^[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))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(56,plain,
% 0.20/0.37 (![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)))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.37 tff(57,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')).
% 0.20/0.37 tff(58,plain,
% 0.20/0.37 (![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)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.37 tff(59,plain,
% 0.20/0.37 (![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)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.37 tff(60,plain,(
% 0.20/0.37 ![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)))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[59])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 (((~![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!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!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!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 ((left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))))) <=> ((~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(65,plain,
% 0.20/0.38 (((~![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!0, reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!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!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.38 tff(66,plain,
% 0.20/0.38 (((~![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!0, reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!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!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.38 tff(67,plain,
% 0.20/0.38 ((~![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!0, reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(68,plain,
% 0.20/0.38 ((~![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!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 ((~unequally_directed_lines(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[68, 62, 49])).
% 0.20/0.38 tff(70,plain,
% 0.20/0.38 (~unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[69, 15, 13])).
% 0.20/0.38 tff(71,assumption,(~unequally_directed_lines(L!0, L!0)), introduced(assumption)).
% 0.20/0.38 tff(72,assumption,(~unequally_directed_lines(L!0, reverse_line(L!0))), introduced(assumption)).
% 0.20/0.38 tff(73,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(74,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)],[73])).
% 0.20/0.38 tff(75,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(76,axiom,(![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax8_basics')).
% 0.20/0.38 tff(77,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)],[76, 75])).
% 0.20/0.38 tff(78,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)],[77])).
% 0.20/0.38 tff(79,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)],[78, 74])).
% 0.20/0.38 tff(80,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!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(81,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!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(82,plain,
% 0.20/0.38 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.38 tff(83,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[82, 79, 72, 71])).
% 0.20/0.38 tff(84,plain,(unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, L!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(85,plain,
% 0.20/0.38 (unequally_directed_lines(L!0, L!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[84, 70])).
% 0.20/0.38 tff(86,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(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))) <=> ![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)],[86])).
% 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))) <=> ![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(89,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(90,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)],[89])).
% 0.20/0.38 tff(91,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/sandbox2/benchmark/Axioms/GEO009+0.ax','ax6_basics')).
% 0.20/0.38 tff(92,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)],[91, 90])).
% 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)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[92, 88])).
% 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)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[93])).
% 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)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[94, 87])).
% 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!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!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!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(97,plain,
% 0.20/0.38 ((unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0))) <=> (unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(98,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!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!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!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.38 tff(99,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!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!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!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[98, 96])).
% 0.20/0.38 tff(100,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!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(101,plain,
% 0.20/0.38 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.38 tff(102,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[101, 95, 70, 85])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------