TSTP Solution File: GEO261+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO261+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 20:36:09 EDT 2022
% Result : Theorem 0.84s 0.77s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO261+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 07:16:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.84/0.77 % SZS status Theorem
% 0.84/0.77 % SZS output start Proof
% 0.84/0.77 tff(left_convergent_lines_type, type, (
% 0.84/0.77 left_convergent_lines: ( $i * $i ) > $o)).
% 0.84/0.77 tff(tptp_fun_M_3_type, type, (
% 0.84/0.77 tptp_fun_M_3: $i)).
% 0.84/0.77 tff(tptp_fun_L_4_type, type, (
% 0.84/0.77 tptp_fun_L_4: $i)).
% 0.84/0.77 tff(reverse_line_type, type, (
% 0.84/0.77 reverse_line: $i > $i)).
% 0.84/0.77 tff(unequally_directed_lines_type, type, (
% 0.84/0.77 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.84/0.77 tff(unequally_directed_opposite_lines_type, type, (
% 0.84/0.77 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.84/0.77 tff(convergent_lines_type, type, (
% 0.84/0.77 convergent_lines: ( $i * $i ) > $o)).
% 0.84/0.77 tff(incident_point_and_line_type, type, (
% 0.84/0.77 incident_point_and_line: ( $i * $i ) > $o)).
% 0.84/0.77 tff(tptp_fun_B_1_type, type, (
% 0.84/0.77 tptp_fun_B_1: $i)).
% 0.84/0.77 tff(between_on_line_type, type, (
% 0.84/0.77 between_on_line: ( $i * $i * $i * $i ) > $o)).
% 0.84/0.77 tff(tptp_fun_C_0_type, type, (
% 0.84/0.77 tptp_fun_C_0: $i)).
% 0.84/0.77 tff(tptp_fun_A_2_type, type, (
% 0.84/0.77 tptp_fun_A_2: $i)).
% 0.84/0.77 tff(divides_points_type, type, (
% 0.84/0.77 divides_points: ( $i * $i * $i ) > $o)).
% 0.84/0.77 tff(1,plain,
% 0.84/0.77 (^[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)))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(2,plain,
% 0.84/0.77 (![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))))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[1])).
% 0.84/0.77 tff(3,plain,
% 0.84/0.77 (![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))))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 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/GEO009+0.ax','ax11_basics')).
% 0.84/0.77 tff(5,plain,
% 0.84/0.77 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.84/0.77 tff(6,plain,(
% 0.84/0.77 ![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.84/0.77 inference(skolemize,[status(sab)],[5])).
% 0.84/0.77 tff(7,plain,
% 0.84/0.77 (![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.84/0.77 tff(8,plain,
% 0.84/0.77 ((~![L: $i, M: $i] : (~(left_convergent_lines(L, M) | left_convergent_lines(L, reverse_line(M))))) | (~(left_convergent_lines(L!4, M!3) | left_convergent_lines(L!4, reverse_line(M!3))))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(9,plain,
% 0.84/0.77 (~(left_convergent_lines(L!4, M!3) | left_convergent_lines(L!4, reverse_line(M!3)))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.84/0.77 tff(10,plain,
% 0.84/0.77 ((left_convergent_lines(L!4, M!3) | left_convergent_lines(L!4, reverse_line(M!3))) | (~left_convergent_lines(L!4, M!3))),
% 0.84/0.77 inference(tautology,[status(thm)],[])).
% 0.84/0.77 tff(11,plain,
% 0.84/0.77 (~left_convergent_lines(L!4, M!3)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.84/0.77 tff(12,plain,
% 0.84/0.77 ((left_convergent_lines(L!4, M!3) | left_convergent_lines(L!4, reverse_line(M!3))) | (~left_convergent_lines(L!4, reverse_line(M!3)))),
% 0.84/0.77 inference(tautology,[status(thm)],[])).
% 0.84/0.77 tff(13,plain,
% 0.84/0.77 (~left_convergent_lines(L!4, reverse_line(M!3))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[12, 9])).
% 0.84/0.77 tff(14,plain,
% 0.84/0.77 (^[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))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(15,plain,
% 0.84/0.77 (![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)))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[14])).
% 0.84/0.77 tff(16,plain,
% 0.84/0.77 (![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)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(17,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')).
% 0.84/0.77 tff(18,plain,
% 0.84/0.77 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.84/0.77 tff(19,plain,(
% 0.84/0.77 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.84/0.77 inference(skolemize,[status(sab)],[18])).
% 0.84/0.77 tff(20,plain,
% 0.84/0.77 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.84/0.77 tff(21,plain,
% 0.84/0.77 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!4, M!3) <=> unequally_directed_lines(L!4, reverse_line(M!3)))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(22,plain,
% 0.84/0.77 (unequally_directed_opposite_lines(L!4, M!3) <=> unequally_directed_lines(L!4, reverse_line(M!3))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.84/0.77 tff(23,plain,
% 0.84/0.77 (^[L: $i, M: $i] : refl((convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))))) <=> (convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(24,plain,
% 0.84/0.77 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))))) <=> ![L: $i, M: $i] : (convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M)))))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[23])).
% 0.84/0.77 tff(25,plain,
% 0.84/0.77 (^[L: $i, M: $i] : rewrite((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> (convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M))))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(26,plain,
% 0.84/0.77 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> ![L: $i, M: $i] : (convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M)))))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[25])).
% 0.84/0.77 tff(27,plain,
% 0.84/0.77 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M))) <=> ![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(28,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a7_defns')).
% 0.84/0.77 tff(29,plain,
% 0.84/0.77 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.84/0.77 tff(30,plain,(
% 0.84/0.77 ![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_opposite_lines(L, M)))),
% 0.84/0.77 inference(skolemize,[status(sab)],[29])).
% 0.84/0.77 tff(31,plain,
% 0.84/0.77 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M)))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.84/0.77 tff(32,plain,
% 0.84/0.77 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M)))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.84/0.77 tff(33,plain,
% 0.84/0.77 ((~![L: $i, M: $i] : (convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_opposite_lines(L, M)))))) | (convergent_lines(L!4, M!3) <=> (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3)))))),
% 0.84/0.77 inference(quant_inst,[status(thm)],[])).
% 0.84/0.77 tff(34,plain,
% 0.84/0.77 (convergent_lines(L!4, M!3) <=> (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3))))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.84/0.77 tff(35,plain,
% 0.84/0.77 ((~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C))) <=> (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(36,plain,
% 0.84/0.77 ((~![L: $i, M: $i, A: $i, B: $i, C: $i] : (((between_on_line(L, A, B, C) & convergent_lines(L, M)) & incident_point_and_line(B, M)) => divides_points(M, A, C))) <=> (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C)))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(37,axiom,(~![L: $i, M: $i, A: $i, B: $i, C: $i] : (((between_on_line(L, A, B, C) & convergent_lines(L, M)) & incident_point_and_line(B, M)) => divides_points(M, A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.84/0.77 tff(38,plain,
% 0.84/0.77 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.84/0.77 tff(39,plain,
% 0.84/0.77 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.84/0.77 tff(40,plain,
% 0.84/0.77 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.84/0.77 tff(41,plain,
% 0.84/0.77 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.84/0.77 tff(42,plain,
% 0.84/0.77 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.84/0.77 tff(43,plain,
% 0.84/0.77 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.84/0.77 tff(44,plain,
% 0.84/0.77 (~![L: $i, M: $i, A: $i, B: $i, C: $i] : ((~(between_on_line(L, A, B, C) & convergent_lines(L, M) & incident_point_and_line(B, M))) | divides_points(M, A, C))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[43, 35])).
% 0.84/0.77 tff(45,plain,(
% 0.84/0.77 ~((~(between_on_line(L!4, A!2, B!1, C!0) & convergent_lines(L!4, M!3) & incident_point_and_line(B!1, M!3))) | divides_points(M!3, A!2, C!0))),
% 0.84/0.77 inference(skolemize,[status(sab)],[44])).
% 0.84/0.77 tff(46,plain,
% 0.84/0.77 (between_on_line(L!4, A!2, B!1, C!0) & convergent_lines(L!4, M!3) & incident_point_and_line(B!1, M!3)),
% 0.84/0.77 inference(or_elim,[status(thm)],[45])).
% 0.84/0.77 tff(47,plain,
% 0.84/0.77 (convergent_lines(L!4, M!3)),
% 0.84/0.77 inference(and_elim,[status(thm)],[46])).
% 0.84/0.77 tff(48,plain,
% 0.84/0.77 ((~(convergent_lines(L!4, M!3) <=> (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3)))))) | (~convergent_lines(L!4, M!3)) | (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3))))),
% 0.84/0.77 inference(tautology,[status(thm)],[])).
% 0.84/0.77 tff(49,plain,
% 0.84/0.77 ((~(convergent_lines(L!4, M!3) <=> (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3)))))) | (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3))))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.84/0.77 tff(50,plain,
% 0.84/0.77 (~((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3)))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[49, 34])).
% 0.84/0.77 tff(51,plain,
% 0.84/0.77 (((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3))) | unequally_directed_opposite_lines(L!4, M!3)),
% 0.84/0.77 inference(tautology,[status(thm)],[])).
% 0.84/0.77 tff(52,plain,
% 0.84/0.77 (unequally_directed_opposite_lines(L!4, M!3)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.84/0.77 tff(53,plain,
% 0.84/0.77 ((~(unequally_directed_opposite_lines(L!4, M!3) <=> unequally_directed_lines(L!4, reverse_line(M!3)))) | (~unequally_directed_opposite_lines(L!4, M!3)) | unequally_directed_lines(L!4, reverse_line(M!3))),
% 0.84/0.77 inference(tautology,[status(thm)],[])).
% 0.84/0.77 tff(54,plain,
% 0.84/0.77 ((~(unequally_directed_opposite_lines(L!4, M!3) <=> unequally_directed_lines(L!4, reverse_line(M!3)))) | unequally_directed_lines(L!4, reverse_line(M!3))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.84/0.77 tff(55,plain,
% 0.84/0.77 (unequally_directed_lines(L!4, reverse_line(M!3))),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[54, 22])).
% 0.84/0.77 tff(56,plain,
% 0.84/0.77 (((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_opposite_lines(L!4, M!3))) | unequally_directed_lines(L!4, M!3)),
% 0.84/0.77 inference(tautology,[status(thm)],[])).
% 0.84/0.77 tff(57,plain,
% 0.84/0.77 (unequally_directed_lines(L!4, M!3)),
% 0.84/0.77 inference(unit_resolution,[status(thm)],[56, 50])).
% 0.84/0.77 tff(58,plain,
% 0.84/0.77 (^[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)))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(59,plain,
% 0.84/0.77 (![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))))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[58])).
% 0.84/0.77 tff(60,plain,
% 0.84/0.77 (^[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))))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(61,plain,
% 0.84/0.77 (![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))))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[60])).
% 0.84/0.77 tff(62,plain,
% 0.84/0.77 (![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)))))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(63,plain,
% 0.84/0.77 (^[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))))))),
% 0.84/0.77 inference(bind,[status(th)],[])).
% 0.84/0.77 tff(64,plain,
% 0.84/0.77 (![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)))))),
% 0.84/0.77 inference(quant_intro,[status(thm)],[63])).
% 0.84/0.77 tff(65,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')).
% 0.84/0.77 tff(66,plain,
% 0.84/0.77 (![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)))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.84/0.77 tff(67,plain,
% 0.84/0.77 (![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)))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.84/0.77 tff(68,plain,(
% 0.84/0.77 ![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)))))),
% 0.84/0.77 inference(skolemize,[status(sab)],[67])).
% 0.84/0.77 tff(69,plain,
% 0.84/0.77 (![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))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.84/0.77 tff(70,plain,
% 0.84/0.77 (![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))))),
% 0.84/0.77 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.84/0.77 tff(71,plain,
% 0.84/0.77 (((~![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!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3))) <=> ((~![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!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3))),
% 0.84/0.77 inference(rewrite,[status(thm)],[])).
% 0.84/0.77 tff(72,plain,
% 0.84/0.77 ((left_convergent_lines(L!4, reverse_line(M!3)) | (~unequally_directed_lines(L!4, M!3)) | left_convergent_lines(L!4, M!3) | (~unequally_directed_lines(L!4, reverse_line(M!3)))) <=> ((~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(73,plain,
% 0.84/0.78 (((~![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!4, reverse_line(M!3)) | (~unequally_directed_lines(L!4, M!3)) | left_convergent_lines(L!4, M!3) | (~unequally_directed_lines(L!4, reverse_line(M!3))))) <=> ((~![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!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3)))),
% 0.84/0.78 inference(monotonicity,[status(thm)],[72])).
% 0.84/0.78 tff(74,plain,
% 0.84/0.78 (((~![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!4, reverse_line(M!3)) | (~unequally_directed_lines(L!4, M!3)) | left_convergent_lines(L!4, M!3) | (~unequally_directed_lines(L!4, reverse_line(M!3))))) <=> ((~![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!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3))),
% 0.84/0.78 inference(transitivity,[status(thm)],[73, 71])).
% 0.84/0.78 tff(75,plain,
% 0.84/0.78 ((~![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!4, reverse_line(M!3)) | (~unequally_directed_lines(L!4, M!3)) | left_convergent_lines(L!4, M!3) | (~unequally_directed_lines(L!4, reverse_line(M!3))))),
% 0.84/0.78 inference(quant_inst,[status(thm)],[])).
% 0.84/0.78 tff(76,plain,
% 0.84/0.78 ((~![L: $i, M: $i] : (left_convergent_lines(L, reverse_line(M)) | (~unequally_directed_lines(L, M)) | left_convergent_lines(L, M) | (~unequally_directed_lines(L, reverse_line(M))))) | (~unequally_directed_lines(L!4, M!3)) | (~unequally_directed_lines(L!4, reverse_line(M!3))) | left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3)),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.84/0.78 tff(77,plain,
% 0.84/0.78 (left_convergent_lines(L!4, reverse_line(M!3)) | left_convergent_lines(L!4, M!3)),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[76, 70, 57, 55])).
% 0.84/0.78 tff(78,plain,
% 0.84/0.78 ($false),
% 0.84/0.78 inference(unit_resolution,[status(thm)],[77, 13, 11])).
% 0.84/0.78 % SZS output end Proof
%------------------------------------------------------------------------------