%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO231+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.18s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO231+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.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 14:42:54 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 % SZS output start Proof
% 0.18/0.41 tff(unequally_directed_lines_type, type, (
% 0.18/0.41 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.18/0.41 tff(tptp_fun_N_0_type, type, (
% 0.18/0.41 tptp_fun_N_0: $i)).
% 0.18/0.41 tff(tptp_fun_M_1_type, type, (
% 0.18/0.41 tptp_fun_M_1: $i)).
% 0.18/0.41 tff(tptp_fun_L_2_type, type, (
% 0.18/0.41 tptp_fun_L_2: $i)).
% 0.18/0.41 tff(reverse_line_type, type, (
% 0.18/0.41 reverse_line: $i > $i)).
% 0.18/0.41 tff(left_convergent_lines_type, type, (
% 0.18/0.41 left_convergent_lines: ( $i * $i ) > $o)).
% 0.18/0.41 tff(1,assumption,(~unequally_directed_lines(M!1, L!2)), introduced(assumption)).
% 0.18/0.41 tff(2,assumption,(unequally_directed_lines(M!1, M!1)), introduced(assumption)).
% 0.18/0.41 tff(3,plain,
% 0.18/0.41 (^[L: $i] : refl((~unequally_directed_lines(L, L)) <=> (~unequally_directed_lines(L, L)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(4,plain,
% 0.18/0.41 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.41 tff(5,plain,
% 0.18/0.41 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(6,axiom,(![L: $i] : (~unequally_directed_lines(L, L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag5')).
% 0.18/0.41 tff(7,plain,
% 0.18/0.41 (![L: $i] : (~unequally_directed_lines(L, L))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.41 tff(8,plain,(
% 0.18/0.41 ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.18/0.41 inference(skolemize,[status(sab)],[7])).
% 0.18/0.41 tff(9,plain,
% 0.18/0.41 (![L: $i] : (~unequally_directed_lines(L, L))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.41 tff(10,plain,
% 0.18/0.41 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(M!1, M!1))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(11,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.18/0.41 tff(12,plain,(~unequally_directed_lines(M!1, M!1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(13,assumption,(~unequally_directed_lines(reverse_line(N!0), M!1)), introduced(assumption)).
% 0.18/0.41 tff(14,assumption,(~unequally_directed_lines(M!1, M!1)), introduced(assumption)).
% 0.18/0.41 tff(15,plain,
% 0.18/0.41 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))) <=> (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(16,plain,
% 0.18/0.41 ((~![L: $i, M: $i, N: $i] : (((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N))) => (~unequally_directed_lines(M, reverse_line(N))))) <=> (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(17,axiom,(~![L: $i, M: $i, N: $i] : (((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N))) => (~unequally_directed_lines(M, reverse_line(N))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.18/0.41 tff(18,plain,
% 0.18/0.41 (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.18/0.41 tff(19,plain,
% 0.18/0.41 (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.18/0.41 tff(20,plain,
% 0.18/0.41 (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.41 tff(21,plain,
% 0.18/0.41 (~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(M, reverse_line(N))) | (~((~unequally_directed_lines(L, reverse_line(M))) & (~unequally_directed_lines(L, N)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.18/0.41 tff(22,plain,(
% 0.18/0.41 ~((~unequally_directed_lines(M!1, reverse_line(N!0))) | (~((~unequally_directed_lines(L!2, reverse_line(M!1))) & (~unequally_directed_lines(L!2, N!0)))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[21])).
% 0.18/0.41 tff(23,plain,
% 0.18/0.41 (unequally_directed_lines(M!1, reverse_line(N!0))),
% 0.18/0.41 inference(or_elim,[status(thm)],[22])).
% 0.18/0.41 tff(24,plain,
% 0.18/0.41 (^[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))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(25,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.18/0.41 tff(26,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(27,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(28,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.41 tff(29,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/GEO007+0.ax','oag6')).
% 0.18/0.41 tff(30,plain,
% 0.18/0.41 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.18/0.41 tff(31,plain,
% 0.18/0.41 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.18/0.41 tff(32,plain,(
% 0.18/0.41 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[31])).
% 0.18/0.41 tff(33,plain,
% 0.18/0.41 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.18/0.41 tff(34,plain,
% 0.18/0.41 (((~![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, reverse_line(N!0))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), 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(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), M!1))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(35,plain,
% 0.18/0.41 ((unequally_directed_lines(reverse_line(N!0), M!1) | unequally_directed_lines(M!1, M!1) | (~unequally_directed_lines(M!1, reverse_line(N!0)))) <=> ((~unequally_directed_lines(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), M!1))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(36,plain,
% 0.18/0.41 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(N!0), M!1) | unequally_directed_lines(M!1, M!1) | (~unequally_directed_lines(M!1, reverse_line(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(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), M!1)))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[35])).
% 0.18/0.41 tff(37,plain,
% 0.18/0.41 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(N!0), M!1) | unequally_directed_lines(M!1, M!1) | (~unequally_directed_lines(M!1, reverse_line(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(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), M!1))),
% 0.18/0.41 inference(transitivity,[status(thm)],[36, 34])).
% 0.18/0.41 tff(38,plain,
% 0.18/0.41 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(N!0), M!1) | unequally_directed_lines(M!1, M!1) | (~unequally_directed_lines(M!1, reverse_line(N!0))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(39,plain,
% 0.18/0.41 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), M!1)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.18/0.41 tff(40,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[39, 33, 23, 14, 13])).
% 0.18/0.41 tff(41,plain,(unequally_directed_lines(M!1, M!1) | unequally_directed_lines(reverse_line(N!0), M!1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(42,plain,
% 0.18/0.41 (unequally_directed_lines(reverse_line(N!0), M!1)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[41, 12])).
% 0.18/0.41 tff(43,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(44,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.18/0.41 tff(45,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(46,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag11')).
% 0.18/0.41 tff(47,plain,
% 0.18/0.41 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.41 tff(48,plain,(
% 0.18/0.41 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[47])).
% 0.18/0.41 tff(49,plain,
% 0.18/0.41 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.18/0.41 tff(50,plain,
% 0.18/0.41 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(N!0), M!1) | left_convergent_lines(reverse_line(N!0), reverse_line(M!1))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(51,plain,
% 0.18/0.41 (~(left_convergent_lines(reverse_line(N!0), M!1) | left_convergent_lines(reverse_line(N!0), reverse_line(M!1)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.18/0.41 tff(52,plain,
% 0.18/0.41 ((left_convergent_lines(reverse_line(N!0), M!1) | left_convergent_lines(reverse_line(N!0), reverse_line(M!1))) | (~left_convergent_lines(reverse_line(N!0), reverse_line(M!1)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(53,plain,
% 0.18/0.41 (~left_convergent_lines(reverse_line(N!0), reverse_line(M!1))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.18/0.41 tff(54,plain,
% 0.18/0.41 ((left_convergent_lines(reverse_line(N!0), M!1) | left_convergent_lines(reverse_line(N!0), reverse_line(M!1))) | (~left_convergent_lines(reverse_line(N!0), M!1))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(55,plain,
% 0.18/0.41 (~left_convergent_lines(reverse_line(N!0), M!1)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.18/0.41 tff(56,plain,
% 0.18/0.41 (^[L: $i, M: $i] : refl((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(57,plain,
% 0.18/0.41 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.18/0.41 tff(58,plain,
% 0.18/0.41 (^[L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, 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, reverse_line(M))) | (~unequally_directed_lines(L, M)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(59,plain,
% 0.18/0.41 (![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, reverse_line(M))) | (~unequally_directed_lines(L, M)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.18/0.41 tff(60,plain,
% 0.18/0.41 (![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)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(61,plain,
% 0.18/0.41 (^[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))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(62,plain,
% 0.18/0.41 (![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)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.41 tff(63,axiom,(![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag9')).
% 0.18/0.41 tff(64,plain,
% 0.18/0.41 (![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)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.18/0.41 tff(65,plain,
% 0.18/0.41 (![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)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.18/0.41 tff(66,plain,(
% 0.18/0.41 ![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)))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[65])).
% 0.18/0.41 tff(67,plain,
% 0.18/0.41 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.18/0.41 tff(68,plain,
% 0.18/0.41 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.18/0.41 tff(69,plain,
% 0.18/0.41 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | left_convergent_lines(reverse_line(N!0), reverse_line(M!1)) | left_convergent_lines(reverse_line(N!0), M!1) | (~unequally_directed_lines(reverse_line(N!0), M!1)))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | left_convergent_lines(reverse_line(N!0), reverse_line(M!1)) | left_convergent_lines(reverse_line(N!0), M!1) | (~unequally_directed_lines(reverse_line(N!0), M!1)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(70,plain,
% 0.18/0.41 ((left_convergent_lines(reverse_line(N!0), reverse_line(M!1)) | left_convergent_lines(reverse_line(N!0), M!1) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~unequally_directed_lines(reverse_line(N!0), M!1))) <=> ((~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | left_convergent_lines(reverse_line(N!0), reverse_line(M!1)) | left_convergent_lines(reverse_line(N!0), M!1) | (~unequally_directed_lines(reverse_line(N!0), M!1)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(71,plain,
% 0.18/0.41 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (left_convergent_lines(reverse_line(N!0), reverse_line(M!1)) | left_convergent_lines(reverse_line(N!0), M!1) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~unequally_directed_lines(reverse_line(N!0), M!1)))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | left_convergent_lines(reverse_line(N!0), reverse_line(M!1)) | left_convergent_lines(reverse_line(N!0), M!1) | (~unequally_directed_lines(reverse_line(N!0), M!1))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[70])).
% 0.18/0.41 tff(72,plain,
% 0.18/0.41 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (left_convergent_lines(reverse_line(N!0), reverse_line(M!1)) | left_convergent_lines(reverse_line(N!0), M!1) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~unequally_directed_lines(reverse_line(N!0), M!1)))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | left_convergent_lines(reverse_line(N!0), reverse_line(M!1)) | left_convergent_lines(reverse_line(N!0), M!1) | (~unequally_directed_lines(reverse_line(N!0), M!1)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[71, 69])).
% 0.18/0.41 tff(73,plain,
% 0.18/0.41 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (left_convergent_lines(reverse_line(N!0), reverse_line(M!1)) | left_convergent_lines(reverse_line(N!0), M!1) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~unequally_directed_lines(reverse_line(N!0), M!1)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(74,plain,
% 0.18/0.41 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | left_convergent_lines(reverse_line(N!0), reverse_line(M!1)) | left_convergent_lines(reverse_line(N!0), M!1) | (~unequally_directed_lines(reverse_line(N!0), M!1))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.41 tff(75,plain,
% 0.18/0.41 ((~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))) | (~unequally_directed_lines(reverse_line(N!0), M!1))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[74, 68, 55, 53])).
% 0.18/0.41 tff(76,plain,
% 0.18/0.41 (~unequally_directed_lines(reverse_line(N!0), reverse_line(M!1))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[75, 42])).
% 0.18/0.41 tff(77,plain,
% 0.18/0.41 ((~unequally_directed_lines(L!2, reverse_line(M!1))) & (~unequally_directed_lines(L!2, N!0))),
% 0.18/0.41 inference(or_elim,[status(thm)],[22])).
% 0.18/0.41 tff(78,plain,
% 0.18/0.41 (~unequally_directed_lines(L!2, reverse_line(M!1))),
% 0.18/0.41 inference(and_elim,[status(thm)],[77])).
% 0.18/0.41 tff(79,plain,
% 0.18/0.41 (((~![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, reverse_line(M!1)) | unequally_directed_lines(reverse_line(N!0), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(N!0), L!2)))) <=> ((~![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, reverse_line(M!1)) | unequally_directed_lines(reverse_line(N!0), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(N!0), L!2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 ((~![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, reverse_line(M!1)) | unequally_directed_lines(reverse_line(N!0), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(N!0), L!2)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 ((~![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, reverse_line(M!1)) | unequally_directed_lines(reverse_line(N!0), reverse_line(M!1)) | (~unequally_directed_lines(reverse_line(N!0), L!2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (~unequally_directed_lines(reverse_line(N!0), L!2)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[81, 33, 78, 76])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (((~![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, reverse_line(N!0))) | unequally_directed_lines(M!1, L!2) | unequally_directed_lines(reverse_line(N!0), L!2))) <=> ((~![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, reverse_line(N!0))) | unequally_directed_lines(M!1, L!2) | unequally_directed_lines(reverse_line(N!0), L!2))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 ((unequally_directed_lines(reverse_line(N!0), L!2) | unequally_directed_lines(M!1, L!2) | (~unequally_directed_lines(M!1, reverse_line(N!0)))) <=> ((~unequally_directed_lines(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, L!2) | unequally_directed_lines(reverse_line(N!0), L!2))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(N!0), L!2) | unequally_directed_lines(M!1, L!2) | (~unequally_directed_lines(M!1, reverse_line(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(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, L!2) | unequally_directed_lines(reverse_line(N!0), L!2)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[84])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(N!0), L!2) | unequally_directed_lines(M!1, L!2) | (~unequally_directed_lines(M!1, reverse_line(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(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, L!2) | unequally_directed_lines(reverse_line(N!0), L!2))),
% 0.19/0.42 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(reverse_line(N!0), L!2) | unequally_directed_lines(M!1, L!2) | (~unequally_directed_lines(M!1, reverse_line(N!0))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | unequally_directed_lines(M!1, L!2) | unequally_directed_lines(reverse_line(N!0), L!2)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[88, 33, 23, 82, 1])).
% 0.19/0.42 tff(90,plain,(unequally_directed_lines(M!1, L!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(91,assumption,(~unequally_directed_lines(M!1, N!0)), introduced(assumption)).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (~unequally_directed_lines(L!2, N!0)),
% 0.19/0.42 inference(and_elim,[status(thm)],[77])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (((~![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(M!1, N!0) | (~unequally_directed_lines(M!1, L!2)))) <=> ((~![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(M!1, N!0) | (~unequally_directed_lines(M!1, L!2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 ((~![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(M!1, N!0) | (~unequally_directed_lines(M!1, L!2)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | unequally_directed_lines(M!1, N!0) | (~unequally_directed_lines(M!1, L!2))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[95, 33, 92, 91, 90])).
% 0.19/0.42 tff(97,plain,(unequally_directed_lines(M!1, N!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 ((~![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))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (~(left_convergent_lines(M!1, N!0) | left_convergent_lines(M!1, reverse_line(N!0)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[98, 49])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 ((left_convergent_lines(M!1, N!0) | left_convergent_lines(M!1, reverse_line(N!0))) | (~left_convergent_lines(M!1, N!0))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (~left_convergent_lines(M!1, N!0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 ((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)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (~left_convergent_lines(M!1, reverse_line(N!0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[102, 99])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, 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)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 ((left_convergent_lines(M!1, reverse_line(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))) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (left_convergent_lines(M!1, reverse_line(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)))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[105])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (left_convergent_lines(M!1, reverse_line(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)))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0))),
% 0.19/0.42 inference(transitivity,[status(thm)],[106, 104])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (left_convergent_lines(M!1, reverse_line(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)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(M!1, reverse_line(N!0))) | (~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((~unequally_directed_lines(M!1, N!0)) | left_convergent_lines(M!1, reverse_line(N!0)) | left_convergent_lines(M!1, N!0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[109, 68, 23])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[110, 103, 101, 97])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------