TSTP Solution File: GEO269+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO269+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:36:12 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO269+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 07:59:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(unequally_directed_lines_type, type, (
% 0.20/0.41 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_L_0_type, type, (
% 0.20/0.41 tptp_fun_L_0: $i)).
% 0.20/0.41 tff(reverse_line_type, type, (
% 0.20/0.41 reverse_line: $i > $i)).
% 0.20/0.41 tff(left_convergent_lines_type, type, (
% 0.20/0.41 left_convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(unequally_directed_opposite_lines_type, type, (
% 0.20/0.41 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(equally_directed_opposite_lines_type, type, (
% 0.20/0.41 equally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,assumption,(left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[L: $i, M: $i] : refl((~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(5,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax11_basics')).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.41 tff(7,plain,(
% 0.20/0.41 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.41 tff(11,plain,(~(left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 ((left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))) | (~left_convergent_lines(L!0, reverse_line(L!0)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (~left_convergent_lines(L!0, reverse_line(L!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 ((left_convergent_lines(L!0, reverse_line(L!0)) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))) | (~left_convergent_lines(L!0, reverse_line(reverse_line(L!0))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (~left_convergent_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : refl((unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(19,axiom,(![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a1_defns')).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.41 tff(21,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (unequally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : refl((equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))) <=> (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))) <=> ![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))) <=> ![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(28,axiom,(![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a5_defns')).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.41 tff(30,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[29])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))) | (equally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> (~unequally_directed_opposite_lines(L!0, reverse_line(L!0))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (equally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> (~unequally_directed_opposite_lines(L!0, reverse_line(L!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 ((~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))) <=> (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(35,axiom,(~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[40, 34])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (~![L: $i] : equally_directed_opposite_lines(L, reverse_line(L))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.20/0.41 tff(43,plain,(
% 0.20/0.41 ~equally_directed_opposite_lines(L!0, reverse_line(L!0))),
% 0.20/0.41 inference(skolemize,[status(sab)],[42])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((~(equally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> (~unequally_directed_opposite_lines(L!0, reverse_line(L!0))))) | equally_directed_opposite_lines(L!0, reverse_line(L!0)) | unequally_directed_opposite_lines(L!0, reverse_line(L!0))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 ((~(equally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> (~unequally_directed_opposite_lines(L!0, reverse_line(L!0))))) | unequally_directed_opposite_lines(L!0, reverse_line(L!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (unequally_directed_opposite_lines(L!0, reverse_line(L!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[45, 33])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 ((~(unequally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))))) | (~unequally_directed_opposite_lines(L!0, reverse_line(L!0))) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 ((~(unequally_directed_opposite_lines(L!0, reverse_line(L!0)) <=> unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))))) | unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[48, 24])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (^[L: $i, M: $i] : refl((left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (^[L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((~(~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))), ((~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))), rewrite((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))), ((left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (^[L: $i, M: $i] : rewrite(((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.41 tff(57,axiom,(![L: $i, M: $i] : ((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) => (left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax9_basics')).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.41 tff(60,plain,(
% 0.20/0.41 ![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | left_convergent_lines(L, M) | (~(unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[59])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 ((left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0))))) <=> ((~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | ((~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))))) <=> ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!0, reverse_line(L!0))) | (~unequally_directed_lines(L!0, reverse_line(reverse_line(L!0)))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((~unequally_directed_lines(L!0, reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(reverse_line(L!0))) | left_convergent_lines(L!0, reverse_line(L!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[68, 62, 49])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (~unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[69, 15, 13])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (^[L: $i, M: $i, N: $i] : refl((unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(L, N) | unequally_directed_lines(M, N)) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))))), rewrite((unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.41 tff(76,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/GEO009+0.ax','ax6_basics')).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.20/0.41 tff(79,plain,(
% 0.20/0.41 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[78])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (((~![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, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 ((unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0))) <=> (unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[82])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[83, 81])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (~unequally_directed_lines(L!0, L!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[86, 80, 70])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (^[L: $i, M: $i] : refl((unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(91,axiom,(![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax8_basics')).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.42 tff(93,plain,(
% 0.20/0.42 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[92])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[97, 94, 70, 87])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------