TSTP Solution File: GEO268+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO268+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GEO268+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.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 : Wed Aug 31 07:39:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 tff(unequally_directed_lines_type, type, (
% 0.19/0.48 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.48 tff(reverse_line_type, type, (
% 0.19/0.48 reverse_line: $i > $i)).
% 0.19/0.48 tff(tptp_fun_M_0_type, type, (
% 0.19/0.48 tptp_fun_M_0: $i)).
% 0.19/0.48 tff(tptp_fun_L_1_type, type, (
% 0.19/0.48 tptp_fun_L_1: $i)).
% 0.19/0.48 tff(left_convergent_lines_type, type, (
% 0.19/0.48 left_convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.48 tff(unequally_directed_opposite_lines_type, type, (
% 0.19/0.48 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.19/0.48 tff(1,assumption,(left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0)))), introduced(assumption)).
% 0.19/0.48 tff(2,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(3,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.48 tff(4,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(5,axiom,(![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax11_basics')).
% 0.19/0.48 tff(6,plain,
% 0.19/0.48 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.48 tff(7,plain,(
% 0.19/0.48 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[6])).
% 0.19/0.48 tff(8,plain,
% 0.19/0.48 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.48 tff(9,plain,
% 0.19/0.48 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(10,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.48 tff(11,plain,(~(left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(12,plain,
% 0.19/0.48 ((left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0)))) | (~left_convergent_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(13,plain,
% 0.19/0.48 (~left_convergent_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.19/0.48 tff(14,assumption,(~unequally_directed_lines(L!1, M!0)), introduced(assumption)).
% 0.19/0.48 tff(15,assumption,(~unequally_directed_lines(L!1, reverse_line(M!0))), introduced(assumption)).
% 0.19/0.48 tff(16,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(17,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.48 tff(18,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(19,axiom,(![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','ax8_basics')).
% 0.19/0.48 tff(20,plain,
% 0.19/0.48 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.48 tff(21,plain,(
% 0.19/0.48 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[20])).
% 0.19/0.48 tff(22,plain,
% 0.19/0.48 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.48 tff(23,plain,
% 0.19/0.48 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(24,plain,
% 0.19/0.48 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(25,plain,
% 0.19/0.48 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.48 tff(26,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[25, 22, 14, 15])).
% 0.19/0.48 tff(27,plain,(unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, M!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(28,plain,
% 0.19/0.48 (unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[27, 14])).
% 0.19/0.48 tff(29,plain,
% 0.19/0.48 ((~(unequally_directed_lines(L!1, M!0) <=> unequally_directed_opposite_lines(L!1, reverse_line(M!0)))) <=> ((~unequally_directed_lines(L!1, M!0)) <=> unequally_directed_opposite_lines(L!1, reverse_line(M!0)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(30,plain,
% 0.19/0.48 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))) <=> (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(31,axiom,(~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.48 tff(32,plain,
% 0.19/0.48 (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.48 tff(33,plain,
% 0.19/0.48 (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[32, 30])).
% 0.19/0.48 tff(34,plain,
% 0.19/0.48 (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.19/0.48 tff(35,plain,
% 0.19/0.48 (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.48 tff(36,plain,
% 0.19/0.48 (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.19/0.48 tff(37,plain,
% 0.19/0.48 (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[36, 30])).
% 0.19/0.48 tff(38,plain,
% 0.19/0.48 (~![L: $i, M: $i] : (unequally_directed_lines(L, M) <=> unequally_directed_opposite_lines(L, reverse_line(M)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.48 tff(39,plain,(
% 0.19/0.48 ~(unequally_directed_lines(L!1, M!0) <=> unequally_directed_opposite_lines(L!1, reverse_line(M!0)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[38])).
% 0.19/0.49 tff(40,plain,
% 0.19/0.49 ((~unequally_directed_lines(L!1, M!0)) <=> unequally_directed_opposite_lines(L!1, reverse_line(M!0))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.19/0.49 tff(41,plain,
% 0.19/0.49 (unequally_directed_lines(L!1, M!0) | unequally_directed_opposite_lines(L!1, reverse_line(M!0)) | (~((~unequally_directed_lines(L!1, M!0)) <=> unequally_directed_opposite_lines(L!1, reverse_line(M!0))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(42,plain,
% 0.19/0.49 (unequally_directed_lines(L!1, M!0) | unequally_directed_opposite_lines(L!1, reverse_line(M!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.49 tff(43,plain,
% 0.19/0.49 (unequally_directed_opposite_lines(L!1, reverse_line(M!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[42, 14])).
% 0.19/0.49 tff(44,plain,
% 0.19/0.49 (^[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))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(45,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.49 tff(46,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(47,axiom,(![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a1_defns')).
% 0.19/0.49 tff(48,plain,
% 0.19/0.49 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.49 tff(49,plain,(
% 0.19/0.49 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[48])).
% 0.19/0.49 tff(50,plain,
% 0.19/0.49 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.19/0.49 tff(51,plain,
% 0.19/0.49 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!1, reverse_line(M!0)) <=> unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(52,plain,
% 0.19/0.49 (unequally_directed_opposite_lines(L!1, reverse_line(M!0)) <=> unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.49 tff(53,plain,
% 0.19/0.49 ((~(unequally_directed_opposite_lines(L!1, reverse_line(M!0)) <=> unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))) | (~unequally_directed_opposite_lines(L!1, reverse_line(M!0))) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(54,plain,
% 0.19/0.49 ((~unequally_directed_opposite_lines(L!1, reverse_line(M!0))) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.49 tff(55,plain,
% 0.19/0.49 (unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[54, 43])).
% 0.19/0.49 tff(56,plain,
% 0.19/0.49 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!1, M!0) | left_convergent_lines(L!1, reverse_line(M!0))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(57,plain,
% 0.19/0.49 (~(left_convergent_lines(L!1, M!0) | left_convergent_lines(L!1, reverse_line(M!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[56, 8])).
% 0.19/0.49 tff(58,plain,
% 0.19/0.49 ((left_convergent_lines(L!1, M!0) | left_convergent_lines(L!1, reverse_line(M!0))) | (~left_convergent_lines(L!1, reverse_line(M!0)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(59,plain,
% 0.19/0.49 (~left_convergent_lines(L!1, reverse_line(M!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.49 tff(60,plain,
% 0.19/0.49 (^[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)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(61,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.49 tff(62,plain,
% 0.19/0.49 (^[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))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(63,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.49 tff(64,plain,
% 0.19/0.49 (![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)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(65,plain,
% 0.19/0.49 (^[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))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(66,plain,
% 0.19/0.49 (![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)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.49 tff(67,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/sandbox2/benchmark/Axioms/GEO009+0.ax','ax9_basics')).
% 0.19/0.49 tff(68,plain,
% 0.19/0.49 (![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)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.49 tff(69,plain,
% 0.19/0.49 (![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)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.49 tff(70,plain,(
% 0.19/0.49 ![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)))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[69])).
% 0.19/0.49 tff(71,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.19/0.49 tff(72,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.19/0.49 tff(73,plain,
% 0.19/0.49 (((~![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!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!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!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(74,plain,
% 0.19/0.49 ((left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))) <=> ((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(75,plain,
% 0.19/0.49 (((~![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!1, reverse_line(reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!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!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[74])).
% 0.19/0.49 tff(76,plain,
% 0.19/0.49 (((~![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!1, reverse_line(reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!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!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[75, 73])).
% 0.19/0.49 tff(77,plain,
% 0.19/0.49 ((~![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!1, reverse_line(reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(78,plain,
% 0.19/0.49 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.49 tff(79,plain,
% 0.19/0.49 ((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[78, 72])).
% 0.19/0.49 tff(80,plain,
% 0.19/0.49 ((~unequally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))) | left_convergent_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[79, 59])).
% 0.19/0.49 tff(81,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[80, 55, 28, 13])).
% 0.19/0.49 tff(82,plain,(unequally_directed_lines(L!1, M!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(83,plain,
% 0.19/0.49 ((left_convergent_lines(L!1, M!0) | left_convergent_lines(L!1, reverse_line(M!0))) | (~left_convergent_lines(L!1, M!0))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(84,plain,
% 0.19/0.49 (~left_convergent_lines(L!1, M!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[83, 57])).
% 0.19/0.49 tff(85,plain,
% 0.19/0.49 (((~![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!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, M!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!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, M!0))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(86,plain,
% 0.19/0.49 ((left_convergent_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, M!0)) | left_convergent_lines(L!1, M!0) | (~unequally_directed_lines(L!1, reverse_line(M!0)))) <=> ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, M!0))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(87,plain,
% 0.19/0.49 (((~![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!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, M!0)) | left_convergent_lines(L!1, M!0) | (~unequally_directed_lines(L!1, reverse_line(M!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!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, M!0)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[86])).
% 0.19/0.49 tff(88,plain,
% 0.19/0.49 (((~![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!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, M!0)) | left_convergent_lines(L!1, M!0) | (~unequally_directed_lines(L!1, reverse_line(M!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!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, M!0))),
% 0.19/0.49 inference(transitivity,[status(thm)],[87, 85])).
% 0.19/0.49 tff(89,plain,
% 0.19/0.49 ((~![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!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, M!0)) | left_convergent_lines(L!1, M!0) | (~unequally_directed_lines(L!1, reverse_line(M!0))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(90,plain,
% 0.19/0.49 ((~![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!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | left_convergent_lines(L!1, reverse_line(M!0)) | left_convergent_lines(L!1, M!0)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.49 tff(91,plain,
% 0.19/0.49 ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[90, 72, 59, 84])).
% 0.19/0.49 tff(92,plain,
% 0.19/0.49 (~unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[91, 82])).
% 0.19/0.49 tff(93,plain,
% 0.19/0.49 ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_opposite_lines(L!1, reverse_line(M!0))) | (~((~unequally_directed_lines(L!1, M!0)) <=> unequally_directed_opposite_lines(L!1, reverse_line(M!0))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(94,plain,
% 0.19/0.49 ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_opposite_lines(L!1, reverse_line(M!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[93, 40])).
% 0.19/0.49 tff(95,plain,
% 0.19/0.49 (~unequally_directed_opposite_lines(L!1, reverse_line(M!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[94, 82])).
% 0.19/0.49 tff(96,plain,
% 0.19/0.49 ((~(unequally_directed_opposite_lines(L!1, reverse_line(M!0)) <=> unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))) | unequally_directed_opposite_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(97,plain,
% 0.19/0.49 (unequally_directed_opposite_lines(L!1, reverse_line(M!0)) | (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[96, 52])).
% 0.19/0.49 tff(98,plain,
% 0.19/0.49 (~unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[97, 95])).
% 0.19/0.49 tff(99,plain,
% 0.19/0.49 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(100,plain,
% 0.19/0.49 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(101,plain,
% 0.19/0.49 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.49 tff(102,plain,
% 0.19/0.49 (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, reverse_line(reverse_line(M!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[101, 22])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[102, 98, 92])).
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------