TSTP Solution File: GEO233+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO233+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Fri Sep 16 20:35:56 EDT 2022
% Result : Theorem 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO233+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 07:10:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(left_convergent_lines_type, type, (
% 0.21/0.47 left_convergent_lines: ( $i * $i ) > $o)).
% 0.21/0.47 tff(tptp_fun_L_0_type, type, (
% 0.21/0.47 tptp_fun_L_0: $i)).
% 0.21/0.47 tff(reverse_line_type, type, (
% 0.21/0.47 reverse_line: $i > $i)).
% 0.21/0.47 tff(unequally_directed_lines_type, type, (
% 0.21/0.47 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.21/0.47 tff(1,plain,
% 0.21/0.47 (^[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)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(2,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.47 tff(3,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(4,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')).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.47 tff(6,plain,(
% 0.21/0.47 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[5])).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.47 tff(8,plain,
% 0.21/0.47 ((~![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))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (~(left_convergent_lines(reverse_line(reverse_line(L!0)), L!0) | left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.47 tff(10,plain,
% 0.21/0.47 ((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))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(11,plain,
% 0.21/0.47 (~left_convergent_lines(reverse_line(reverse_line(L!0)), L!0)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.21/0.47 tff(12,plain,
% 0.21/0.47 ((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)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(13,plain,
% 0.21/0.47 (~left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[12, 9])).
% 0.21/0.47 tff(14,assumption,(unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(reverse_line(L!0)))), introduced(assumption)).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (^[L: $i] : refl((~unequally_directed_lines(L, L)) <=> (~unequally_directed_lines(L, L)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 (![L: $i] : (~unequally_directed_lines(L, L)) <=> ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(18,axiom,(![L: $i] : (~unequally_directed_lines(L, L))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag5')).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 (![L: $i] : (~unequally_directed_lines(L, L))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.47 tff(20,plain,(
% 0.21/0.47 ![L: $i] : (~unequally_directed_lines(L, L))),
% 0.21/0.47 inference(skolemize,[status(sab)],[19])).
% 0.21/0.47 tff(21,plain,
% 0.21/0.47 (![L: $i] : (~unequally_directed_lines(L, L))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 ((~![L: $i] : (~unequally_directed_lines(L, L))) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(reverse_line(L!0))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(23,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[22, 21, 14])).
% 0.21/0.47 tff(24,plain,(~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(25,plain,
% 0.21/0.47 ((~(~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0))) <=> unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 ((~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))) <=> (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(27,axiom,(~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.47 tff(28,plain,
% 0.21/0.47 (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.47 tff(29,plain,
% 0.21/0.47 (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[28, 26])).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.21/0.47 tff(31,plain,
% 0.21/0.47 (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.47 tff(32,plain,
% 0.21/0.47 (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.21/0.47 tff(33,plain,
% 0.21/0.47 (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.21/0.47 tff(34,plain,
% 0.21/0.47 (~![L: $i] : (~unequally_directed_lines(reverse_line(reverse_line(L)), L))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.21/0.47 tff(35,plain,(
% 0.21/0.47 ~(~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0))),
% 0.21/0.47 inference(skolemize,[status(sab)],[34])).
% 0.21/0.47 tff(36,plain,
% 0.21/0.47 (unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.21/0.47 tff(37,plain,
% 0.21/0.47 (^[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))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(38,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.47 tff(39,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(40,plain,
% 0.21/0.47 (^[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)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(41,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.47 tff(42,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')).
% 0.21/0.47 tff(43,plain,
% 0.21/0.47 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.21/0.47 tff(45,plain,(
% 0.21/0.47 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[44])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 (((~![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)), L!0)) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(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(reverse_line(L!0)), L!0)) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(reverse_line(L!0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 ((unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0))) <=> ((~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(reverse_line(L!0))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 (((~![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(reverse_line(L!0))) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(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)), L!0)) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(reverse_line(L!0)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[48])).
% 0.21/0.47 tff(50,plain,
% 0.21/0.47 (((~![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(reverse_line(L!0))) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(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)), L!0)) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(reverse_line(L!0))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[49, 47])).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 ((~![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(reverse_line(L!0))) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(52,plain,
% 0.21/0.47 ((~![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)), L!0)) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(reverse_line(L!0)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.47 tff(53,plain,
% 0.21/0.47 (unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(reverse_line(L!0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[52, 46, 36])).
% 0.21/0.47 tff(54,plain,
% 0.21/0.47 (unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[53, 24])).
% 0.21/0.47 tff(55,assumption,(left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))), introduced(assumption)).
% 0.21/0.47 tff(56,plain,
% 0.21/0.47 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[56, 7, 55])).
% 0.21/0.47 tff(58,plain,(~(left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(59,plain,
% 0.21/0.47 ((left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))) | (~left_convergent_lines(L!0, reverse_line(reverse_line(L!0))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(60,plain,
% 0.21/0.47 (~left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.21/0.47 tff(61,plain,
% 0.21/0.47 ((left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))) | (~left_convergent_lines(L!0, reverse_line(L!0)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(62,plain,
% 0.21/0.47 (~left_convergent_lines(L!0, reverse_line(L!0))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.21/0.47 tff(63,assumption,(unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))), introduced(assumption)).
% 0.21/0.47 tff(64,assumption,(unequally_directed_lines(L!0, reverse_line(L!0))), introduced(assumption)).
% 0.21/0.47 tff(65,plain,
% 0.21/0.47 (^[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)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(66,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.47 tff(67,plain,
% 0.21/0.47 (^[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))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(68,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.48 tff(69,plain,
% 0.21/0.48 (![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)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(70,plain,
% 0.21/0.48 (^[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))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(71,plain,
% 0.21/0.48 (![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)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[70])).
% 0.21/0.48 tff(72,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')).
% 0.21/0.48 tff(73,plain,
% 0.21/0.48 (![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)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.48 tff(74,plain,
% 0.21/0.48 (![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)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.21/0.48 tff(75,plain,(
% 0.21/0.48 ![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)))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[74])).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.21/0.48 tff(77,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[76, 66])).
% 0.21/0.48 tff(78,plain,
% 0.21/0.48 (((~![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(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(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))))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(79,plain,
% 0.21/0.48 ((left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_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(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(80,plain,
% 0.21/0.48 (((~![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(L!0, reverse_line(reverse_line(L!0))) | left_convergent_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)))))) <=> ((~![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(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.48 tff(81,plain,
% 0.21/0.48 (((~![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(L!0, reverse_line(reverse_line(L!0))) | left_convergent_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)))))) <=> ((~![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(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[80, 78])).
% 0.21/0.48 tff(82,plain,
% 0.21/0.48 ((~![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(L!0, reverse_line(reverse_line(L!0))) | left_convergent_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)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(83,plain,
% 0.21/0.48 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.48 tff(84,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[83, 77, 64, 63, 62, 60])).
% 0.21/0.48 tff(85,plain,((~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | (~unequally_directed_lines(L!0, reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(86,plain,
% 0.21/0.48 (~unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[85, 54])).
% 0.21/0.48 tff(87,plain,
% 0.21/0.48 (((~![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)), L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), 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(reverse_line(reverse_line(L!0)), L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 ((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)), L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(89,plain,
% 0.21/0.48 (((~![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)), L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[88])).
% 0.21/0.48 tff(90,plain,
% 0.21/0.48 (((~![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)), L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[89, 87])).
% 0.21/0.48 tff(91,plain,
% 0.21/0.48 ((~![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)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(92,plain,
% 0.21/0.48 ((~![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)), L!0)) | unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.48 tff(93,plain,
% 0.21/0.48 (unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[92, 46, 36])).
% 0.21/0.48 tff(94,plain,
% 0.21/0.48 (unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[93, 86])).
% 0.21/0.48 tff(95,plain,
% 0.21/0.48 (((~![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(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))) <=> ((~![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(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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(96,plain,
% 0.21/0.48 ((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)))) <=> ((~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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 (((~![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))))) | ((~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)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[96])).
% 0.21/0.48 tff(98,plain,
% 0.21/0.48 (((~![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))))) | (~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))),
% 0.21/0.48 inference(transitivity,[status(thm)],[97, 95])).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 ((~![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))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(100,plain,
% 0.21/0.48 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), L!0)) | (~unequally_directed_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0))) | left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | left_convergent_lines(reverse_line(reverse_line(L!0)), L!0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.48 tff(101,plain,
% 0.21/0.48 (left_convergent_lines(reverse_line(reverse_line(L!0)), reverse_line(L!0)) | left_convergent_lines(reverse_line(reverse_line(L!0)), L!0)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[100, 77, 36, 94])).
% 0.21/0.48 tff(102,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[101, 13, 11])).
% 0.21/0.48 % SZS output end Proof
%------------------------------------------------------------------------------