%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO234+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO234+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.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 14:43:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(unequally_directed_lines_type, type, (
% 0.19/0.41 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_M_1_type, type, (
% 0.19/0.41 tptp_fun_M_1: $i)).
% 0.19/0.41 tff(reverse_line_type, type, (
% 0.19/0.41 reverse_line: $i > $i)).
% 0.19/0.41 tff(tptp_fun_L_2_type, type, (
% 0.19/0.41 tptp_fun_L_2: $i)).
% 0.19/0.41 tff(tptp_fun_N_0_type, type, (
% 0.19/0.41 tptp_fun_N_0: $i)).
% 0.19/0.41 tff(left_convergent_lines_type, type, (
% 0.19/0.41 left_convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.41 tff(1,assumption,(~unequally_directed_lines(reverse_line(M!1), M!1)), introduced(assumption)).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 ((~(unequally_directed_lines(M!1, reverse_line(N!0)) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1))))) <=> (~(unequally_directed_lines(M!1, reverse_line(N!0)) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, reverse_line(N)) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, reverse_line(M))))) <=> (~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, reverse_line(N)) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 ((~![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, N) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(5,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')).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, reverse_line(N)) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, reverse_line(N)) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, reverse_line(N)) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, reverse_line(N)) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.19/0.41 tff(10,plain,(
% 0.19/0.41 ~(unequally_directed_lines(M!1, reverse_line(N!0)) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[9])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (~(unequally_directed_lines(M!1, reverse_line(N!0)) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (~unequally_directed_lines(L!2, N!0)),
% 0.19/0.41 inference(or_elim,[status(thm)],[11])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (((~unequally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, reverse_line(N!0)))) | unequally_directed_lines(L!2, N!0)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 ((~unequally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, reverse_line(N!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (~unequally_directed_lines(M!1, reverse_line(N!0))),
% 0.19/0.41 inference(or_elim,[status(thm)],[11])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0)))) | unequally_directed_lines(M!1, reverse_line(N!0))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 ((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (unequally_directed_lines(L!2, reverse_line(M!1))),
% 0.19/0.41 inference(or_elim,[status(thm)],[11])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (^[L: $i, M: $i, N: $i] : refl(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) <=> (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N)))))), rewrite((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) <=> (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N)))))), trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite(((~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))), (((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite(((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))), (((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))))), rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))), (((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))))) <=> ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.41 tff(26,axiom,(![L: $i, M: $i, N: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => ((unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N)))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag7')).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.41 tff(29,plain,(
% 0.19/0.41 ![L: $i, M: $i, N: $i] : ((unequally_directed_lines(M, N) & unequally_directed_lines(M, reverse_line(N))) | (unequally_directed_lines(L, N) & unequally_directed_lines(L, reverse_line(N))) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[28])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | ((~unequally_directed_lines(L!2, reverse_line(M!1))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(L!2, M!1)) | (~((~unequally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, reverse_line(N!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(L!2, M!1)) | (~((~unequally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, reverse_line(N!0))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (((~unequally_directed_lines(L!2, M!1)) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~((~unequally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, reverse_line(N!0)))))) <=> ((~unequally_directed_lines(L!2, reverse_line(M!1))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(L!2, M!1)) | (~((~unequally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, reverse_line(N!0))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | ((~unequally_directed_lines(L!2, M!1)) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~((~unequally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, reverse_line(N!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | ((~unequally_directed_lines(L!2, reverse_line(M!1))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(L!2, M!1)) | (~((~unequally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, reverse_line(N!0)))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | ((~unequally_directed_lines(L!2, M!1)) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~((~unequally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, reverse_line(N!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(L!2, M!1)) | (~((~unequally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, reverse_line(N!0))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[34, 32])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | ((~unequally_directed_lines(L!2, M!1)) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~((~unequally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, reverse_line(N!0))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))) | (~((~unequally_directed_lines(M, N)) | (~unequally_directed_lines(M, reverse_line(N))))) | (~((~unequally_directed_lines(L, N)) | (~unequally_directed_lines(L, reverse_line(N))))))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | (~((~unequally_directed_lines(M!1, N!0)) | (~unequally_directed_lines(M!1, reverse_line(N!0))))) | (~unequally_directed_lines(L!2, M!1)) | (~((~unequally_directed_lines(L!2, N!0)) | (~unequally_directed_lines(L!2, reverse_line(N!0)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (~unequally_directed_lines(L!2, M!1)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[37, 31, 18, 17, 14])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(40,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))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.42 tff(41,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))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.42 tff(44,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')).
% 0.19/0.42 tff(45,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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.42 tff(46,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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.42 tff(47,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)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[46])).
% 0.19/0.42 tff(48,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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.42 tff(49,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(L!2, M!1) | unequally_directed_lines(reverse_line(M!1), M!1))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(L!2, M!1) | unequally_directed_lines(reverse_line(M!1), M!1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 ((unequally_directed_lines(reverse_line(M!1), M!1) | unequally_directed_lines(L!2, M!1) | (~unequally_directed_lines(L!2, reverse_line(M!1)))) <=> ((~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(L!2, M!1) | unequally_directed_lines(reverse_line(M!1), M!1))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(51,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(M!1), M!1) | unequally_directed_lines(L!2, M!1) | (~unequally_directed_lines(L!2, reverse_line(M!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(L!2, M!1) | unequally_directed_lines(reverse_line(M!1), M!1)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.42 tff(52,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(M!1), M!1) | unequally_directed_lines(L!2, M!1) | (~unequally_directed_lines(L!2, reverse_line(M!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(L!2, M!1) | unequally_directed_lines(reverse_line(M!1), M!1))),
% 0.19/0.42 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.42 tff(53,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(M!1), M!1) | unequally_directed_lines(L!2, M!1) | (~unequally_directed_lines(L!2, reverse_line(M!1))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(L!2, M!1) | unequally_directed_lines(reverse_line(M!1), M!1)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[54, 48, 18, 38, 1])).
% 0.19/0.42 tff(56,plain,(unequally_directed_lines(reverse_line(M!1), M!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(60,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')).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.42 tff(62,plain,(
% 0.19/0.42 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[61])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(M!1), N!0) | left_convergent_lines(reverse_line(M!1), reverse_line(N!0))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (~(left_convergent_lines(reverse_line(M!1), N!0) | left_convergent_lines(reverse_line(M!1), reverse_line(N!0)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 ((left_convergent_lines(reverse_line(M!1), N!0) | left_convergent_lines(reverse_line(M!1), reverse_line(N!0))) | (~left_convergent_lines(reverse_line(M!1), N!0))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (~left_convergent_lines(reverse_line(M!1), N!0)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 ((left_convergent_lines(reverse_line(M!1), N!0) | left_convergent_lines(reverse_line(M!1), reverse_line(N!0))) | (~left_convergent_lines(reverse_line(M!1), reverse_line(N!0)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (~left_convergent_lines(reverse_line(M!1), reverse_line(N!0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.19/0.42 tff(70,assumption,(~unequally_directed_lines(reverse_line(M!1), N!0)), introduced(assumption)).
% 0.19/0.42 tff(71,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(L!2, reverse_line(M!1))) | unequally_directed_lines(reverse_line(M!1), N!0))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(reverse_line(M!1), N!0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((unequally_directed_lines(reverse_line(M!1), N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1)))) <=> (unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(reverse_line(M!1), N!0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(73,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(M!1), N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(reverse_line(M!1), N!0)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[72])).
% 0.19/0.42 tff(74,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(M!1), N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1))))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(reverse_line(M!1), N!0))),
% 0.19/0.42 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.42 tff(75,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(M!1), N!0) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!2, N!0) | (~unequally_directed_lines(L!2, reverse_line(M!1))) | unequally_directed_lines(reverse_line(M!1), N!0)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[76, 48, 12, 18, 70])).
% 0.19/0.42 tff(78,plain,(unequally_directed_lines(reverse_line(M!1), N!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (^[L: $i, M: $i] : refl((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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(80,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, 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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (^[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, 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))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(82,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, 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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.42 tff(83,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, 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)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (^[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))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (![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)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.42 tff(86,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')).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 (![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)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 (![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)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.43 tff(89,plain,(
% 0.19/0.43 ![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)))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[88])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 (((~![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))))) | ((~unequally_directed_lines(reverse_line(M!1), reverse_line(N!0))) | (~unequally_directed_lines(reverse_line(M!1), N!0)) | left_convergent_lines(reverse_line(M!1), reverse_line(N!0)) | left_convergent_lines(reverse_line(M!1), N!0))) <=> ((~![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))))) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(N!0))) | (~unequally_directed_lines(reverse_line(M!1), N!0)) | left_convergent_lines(reverse_line(M!1), reverse_line(N!0)) | left_convergent_lines(reverse_line(M!1), N!0))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 ((left_convergent_lines(reverse_line(M!1), reverse_line(N!0)) | left_convergent_lines(reverse_line(M!1), N!0) | (~unequally_directed_lines(reverse_line(M!1), N!0)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(N!0)))) <=> ((~unequally_directed_lines(reverse_line(M!1), reverse_line(N!0))) | (~unequally_directed_lines(reverse_line(M!1), N!0)) | left_convergent_lines(reverse_line(M!1), reverse_line(N!0)) | left_convergent_lines(reverse_line(M!1), N!0))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 (((~![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))))) | (left_convergent_lines(reverse_line(M!1), reverse_line(N!0)) | left_convergent_lines(reverse_line(M!1), N!0) | (~unequally_directed_lines(reverse_line(M!1), N!0)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(N!0))))) <=> ((~![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))))) | ((~unequally_directed_lines(reverse_line(M!1), reverse_line(N!0))) | (~unequally_directed_lines(reverse_line(M!1), N!0)) | left_convergent_lines(reverse_line(M!1), reverse_line(N!0)) | left_convergent_lines(reverse_line(M!1), N!0)))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (((~![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))))) | (left_convergent_lines(reverse_line(M!1), reverse_line(N!0)) | left_convergent_lines(reverse_line(M!1), N!0) | (~unequally_directed_lines(reverse_line(M!1), N!0)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(N!0))))) <=> ((~![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))))) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(N!0))) | (~unequally_directed_lines(reverse_line(M!1), N!0)) | left_convergent_lines(reverse_line(M!1), reverse_line(N!0)) | left_convergent_lines(reverse_line(M!1), N!0))),
% 0.19/0.43 inference(transitivity,[status(thm)],[94, 92])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 ((~![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))))) | (left_convergent_lines(reverse_line(M!1), reverse_line(N!0)) | left_convergent_lines(reverse_line(M!1), N!0) | (~unequally_directed_lines(reverse_line(M!1), N!0)) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(N!0))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 ((~![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))))) | (~unequally_directed_lines(reverse_line(M!1), reverse_line(N!0))) | (~unequally_directed_lines(reverse_line(M!1), N!0)) | left_convergent_lines(reverse_line(M!1), reverse_line(N!0)) | left_convergent_lines(reverse_line(M!1), N!0)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (~unequally_directed_lines(reverse_line(M!1), reverse_line(N!0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[97, 91, 78, 69, 67])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (((~![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(reverse_line(M!1), M!1)) | unequally_directed_lines(reverse_line(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(reverse_line(M!1), M!1)) | unequally_directed_lines(reverse_line(M!1), reverse_line(N!0)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 ((unequally_directed_lines(M!1, reverse_line(N!0)) | unequally_directed_lines(reverse_line(M!1), reverse_line(N!0)) | (~unequally_directed_lines(reverse_line(M!1), M!1))) <=> (unequally_directed_lines(M!1, reverse_line(N!0)) | (~unequally_directed_lines(reverse_line(M!1), M!1)) | unequally_directed_lines(reverse_line(M!1), reverse_line(N!0)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (((~![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(reverse_line(M!1), reverse_line(N!0)) | (~unequally_directed_lines(reverse_line(M!1), 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(reverse_line(M!1), M!1)) | unequally_directed_lines(reverse_line(M!1), reverse_line(N!0))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[100])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (((~![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(reverse_line(M!1), reverse_line(N!0)) | (~unequally_directed_lines(reverse_line(M!1), 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(reverse_line(M!1), M!1)) | unequally_directed_lines(reverse_line(M!1), reverse_line(N!0)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[101, 99])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 ((~![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(reverse_line(M!1), reverse_line(N!0)) | (~unequally_directed_lines(reverse_line(M!1), M!1)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(M!1, reverse_line(N!0)) | (~unequally_directed_lines(reverse_line(M!1), M!1)) | unequally_directed_lines(reverse_line(M!1), reverse_line(N!0))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[104, 48, 15, 98, 56])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------