%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO233+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO233+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:47:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(unequally_directed_lines_type, type, (
% 0.19/0.39 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_L_0_type, type, (
% 0.19/0.39 tptp_fun_L_0: $i)).
% 0.19/0.39 tff(reverse_line_type, type, (
% 0.19/0.39 reverse_line: $i > $i)).
% 0.19/0.39 tff(left_convergent_lines_type, type, (
% 0.19/0.39 left_convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.39 tff(1,assumption,(~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))), introduced(assumption)).
% 0.19/0.39 tff(2,assumption,(left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))), introduced(assumption)).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(6,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')).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.39 tff(8,plain,(
% 0.19/0.39 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[7])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.19/0.39 tff(12,plain,(~(left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 ((left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))) | (~left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (~left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 ((left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))) | (~left_convergent_lines(reverse_line(reverse_line(L!0)), L!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (~left_convergent_lines(reverse_line(reverse_line(L!0)), L!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[15, 12])).
% 0.19/0.39 tff(17,assumption,(unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))), introduced(assumption)).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 ((~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))) <=> (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(19,axiom,(~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[20, 18])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.39 tff(24,plain,(
% 0.19/0.39 unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)),
% 0.19/0.39 inference(skolemize,[status(sab)],[23])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (^[L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | 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))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.40 tff(32,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')).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.40 tff(35,plain,(
% 0.19/0.40 ![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)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[34])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (((~![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(reverse_line(L!0)), reverse_line(L!0)) | left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!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))))) | left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 ((left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)))) <=> (left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (((~![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(reverse_line(L!0)), reverse_line(L!0)) | left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!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))))) | (left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (((~![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(reverse_line(L!0)), reverse_line(L!0)) | left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!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))))) | left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[40, 38])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 ((~![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(reverse_line(L!0)), reverse_line(L!0)) | left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[43, 37, 24, 17, 16, 14])).
% 0.19/0.40 tff(45,plain,(~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (^[L: $i] : refl((~unequally_directed_lines(L, L)) <=> (~unequally_directed_lines(L, L)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(49,axiom,(![L: $i] : (~unequally_directed_lines(L, L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag5')).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![L: $i] : (~unequally_directed_lines(L, L))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.40 tff(51,plain,(
% 0.19/0.40 ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.19/0.40 inference(skolemize,[status(sab)],[50])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![L: $i] : (~unequally_directed_lines(L, L))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (~unequally_directed_lines(reverse_line(L!0), reverse_line(L!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.40 tff(60,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')).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.40 tff(63,plain,(
% 0.19/0.40 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[62])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (((~![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(L!0), reverse_line(L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(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(reverse_line(L!0), reverse_line(L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ((unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0))))) <=> (unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (((~![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(reverse_line(L!0)), reverse_line(L!0)) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(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(reverse_line(L!0), reverse_line(L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (((~![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(reverse_line(L!0)), reverse_line(L!0)) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(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(reverse_line(L!0), reverse_line(L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((~![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(reverse_line(L!0)), reverse_line(L!0)) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 ((~![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(L!0), reverse_line(L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (~unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[70, 64, 54, 45])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (((~![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(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)) | unequally_directed_lines(L!0, reverse_line(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(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0))) <=> (unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((~![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(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(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(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)) | unequally_directed_lines(L!0, reverse_line(L!0))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[73])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (((~![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(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(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(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[74, 72])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~![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(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((~![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(reverse_line(L!0)), reverse_line(L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)) | unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[77, 64, 24])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[78, 45])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (((~![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(reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(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, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((unequally_directed_lines(reverse_line(L!0), reverse_line(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(L!0))) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (((~![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(L!0), reverse_line(reverse_line(L!0))) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(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, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (((~![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(L!0), reverse_line(reverse_line(L!0))) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(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, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 ((~![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(L!0), reverse_line(reverse_line(L!0))) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(L!0))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(L!0), reverse_line(reverse_line(L!0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[85, 64, 79, 71, 1])).
% 0.19/0.41 tff(87,plain,(unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (((~unequally_directed_lines(reverse_line(L!0), L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)))) | unequally_directed_lines(reverse_line(L!0), reverse_line(L!0))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~unequally_directed_lines(reverse_line(L!0), L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(L!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[88, 54])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (^[L: $i, M: $i, N: $i] : refl(((~unequally_directed_lines(L, 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, reverse_line(M)))) <=> ((~unequally_directed_lines(L, 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, reverse_line(M)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, 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, reverse_line(M)))) <=> ![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, 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, reverse_line(M))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.41 tff(92,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(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, 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(L, 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, reverse_line(M))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(93,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(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, reverse_line(M))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.41 tff(94,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(95,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(96,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)],[95])).
% 0.19/0.41 tff(97,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(98,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)],[97, 96])).
% 0.19/0.41 tff(99,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)],[98, 94])).
% 0.19/0.41 tff(100,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)],[99])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, 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, reverse_line(M))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, 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, reverse_line(M))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[101, 91])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, 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, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!0), L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(L!0))))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | (~((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0))))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, 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, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!0), L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(L!0))))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | (~((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (((~unequally_directed_lines(L!0, reverse_line(L!0))) | (~((~unequally_directed_lines(reverse_line(L!0), L!0)) | (~unequally_directed_lines(reverse_line(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, reverse_line(reverse_line(L!0))))) <=> ((~((~unequally_directed_lines(reverse_line(L!0), L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(L!0))))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | (~((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, 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, reverse_line(M))))) | ((~unequally_directed_lines(L!0, reverse_line(L!0))) | (~((~unequally_directed_lines(reverse_line(L!0), L!0)) | (~unequally_directed_lines(reverse_line(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, reverse_line(reverse_line(L!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, 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, reverse_line(M))))) | ((~((~unequally_directed_lines(reverse_line(L!0), L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(L!0))))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | (~((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[104])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, 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, reverse_line(M))))) | ((~unequally_directed_lines(L!0, reverse_line(L!0))) | (~((~unequally_directed_lines(reverse_line(L!0), L!0)) | (~unequally_directed_lines(reverse_line(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, reverse_line(reverse_line(L!0)))))) <=> ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, 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, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!0), L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(L!0))))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | (~((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[105, 103])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, 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, reverse_line(M))))) | ((~unequally_directed_lines(L!0, reverse_line(L!0))) | (~((~unequally_directed_lines(reverse_line(L!0), L!0)) | (~unequally_directed_lines(reverse_line(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, reverse_line(reverse_line(L!0)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 ((~![L: $i, M: $i, N: $i] : ((~unequally_directed_lines(L, 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, reverse_line(M))))) | (~((~unequally_directed_lines(reverse_line(L!0), L!0)) | (~unequally_directed_lines(reverse_line(L!0), reverse_line(L!0))))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | (~((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 ((~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | (~((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[108, 102, 89, 79])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 (~((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[109, 87])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (((~unequally_directed_lines(L!0, L!0)) | (~unequally_directed_lines(L!0, reverse_line(L!0)))) | unequally_directed_lines(L!0, L!0)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (unequally_directed_lines(L!0, L!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(L!0, L!0))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[113, 52, 112])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------