TSTP Solution File: GEO206+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO206+3 : TPTP v8.1.0. Bugfixed v4.0.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:35:39 EDT 2022
% Result : Theorem 0.14s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GEO206+3 : TPTP v8.1.0. Bugfixed v4.0.1.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 06:58:34 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(convergent_lines_type, type, (
% 0.14/0.41 convergent_lines: ( $i * $i ) > $o)).
% 0.14/0.41 tff(parallel_through_point_type, type, (
% 0.14/0.41 parallel_through_point: ( $i * $i ) > $i)).
% 0.14/0.41 tff(tptp_fun_X_2_type, type, (
% 0.14/0.41 tptp_fun_X_2: $i)).
% 0.14/0.41 tff(tptp_fun_Z_0_type, type, (
% 0.14/0.41 tptp_fun_Z_0: $i)).
% 0.14/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.14/0.41 tptp_fun_Y_1: $i)).
% 0.14/0.41 tff(parallel_lines_type, type, (
% 0.14/0.41 parallel_lines: ( $i * $i ) > $o)).
% 0.14/0.41 tff(incident_point_and_line_type, type, (
% 0.14/0.41 incident_point_and_line: ( $i * $i ) > $o)).
% 0.14/0.41 tff(equal_lines_type, type, (
% 0.14/0.41 equal_lines: ( $i * $i ) > $o)).
% 0.14/0.41 tff(distinct_lines_type, type, (
% 0.14/0.41 distinct_lines: ( $i * $i ) > $o)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 (^[X: $i, Y: $i] : refl((parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(4,axiom,(![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','a3')).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.14/0.41 tff(6,plain,(
% 0.14/0.41 ![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[5])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 ((~![X: $i, Y: $i] : (parallel_lines(X, Y) <=> (~convergent_lines(X, Y)))) | (parallel_lines(Y!1, Z!0) <=> (~convergent_lines(Y!1, Z!0)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (parallel_lines(Y!1, Z!0) <=> (~convergent_lines(Y!1, Z!0))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 ((~![X: $i, Y: $i, Z: $i] : ((~(incident_point_and_line(X, Y) & parallel_lines(Y, Z))) | equal_lines(Y, parallel_through_point(Z, X)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(incident_point_and_line(X, Y) & parallel_lines(Y, Z))) | equal_lines(Y, parallel_through_point(Z, X))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 ((~![X: $i, Y: $i, Z: $i] : ((incident_point_and_line(X, Y) & parallel_lines(Y, Z)) => equal_lines(Y, parallel_through_point(Z, X)))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(incident_point_and_line(X, Y) & parallel_lines(Y, Z))) | equal_lines(Y, parallel_through_point(Z, X))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(12,axiom,(~![X: $i, Y: $i, Z: $i] : ((incident_point_and_line(X, Y) & parallel_lines(Y, Z)) => equal_lines(Y, parallel_through_point(Z, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(incident_point_and_line(X, Y) & parallel_lines(Y, Z))) | equal_lines(Y, parallel_through_point(Z, X)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(incident_point_and_line(X, Y) & parallel_lines(Y, Z))) | equal_lines(Y, parallel_through_point(Z, X)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(incident_point_and_line(X, Y) & parallel_lines(Y, Z))) | equal_lines(Y, parallel_through_point(Z, X)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.14/0.41 tff(16,plain,
% 0.14/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(incident_point_and_line(X, Y) & parallel_lines(Y, Z))) | equal_lines(Y, parallel_through_point(Z, X)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(incident_point_and_line(X, Y) & parallel_lines(Y, Z))) | equal_lines(Y, parallel_through_point(Z, X)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(incident_point_and_line(X, Y) & parallel_lines(Y, Z))) | equal_lines(Y, parallel_through_point(Z, X)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (~![X: $i, Y: $i, Z: $i] : ((~(incident_point_and_line(X, Y) & parallel_lines(Y, Z))) | equal_lines(Y, parallel_through_point(Z, X)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.14/0.41 tff(20,plain,(
% 0.14/0.41 ~((~(incident_point_and_line(X!2, Y!1) & parallel_lines(Y!1, Z!0))) | equal_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[19])).
% 0.14/0.41 tff(21,plain,
% 0.14/0.41 (incident_point_and_line(X!2, Y!1) & parallel_lines(Y!1, Z!0)),
% 0.14/0.41 inference(or_elim,[status(thm)],[20])).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 (parallel_lines(Y!1, Z!0)),
% 0.14/0.41 inference(and_elim,[status(thm)],[21])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 ((~(parallel_lines(Y!1, Z!0) <=> (~convergent_lines(Y!1, Z!0)))) | (~parallel_lines(Y!1, Z!0)) | (~convergent_lines(Y!1, Z!0))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 ((~(parallel_lines(Y!1, Z!0) <=> (~convergent_lines(Y!1, Z!0)))) | (~convergent_lines(Y!1, Z!0))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 (~convergent_lines(Y!1, Z!0)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[24, 9])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(29,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.14/0.41 tff(30,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.14/0.41 tff(31,plain,(
% 0.14/0.41 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.14/0.41 inference(skolemize,[status(sab)],[30])).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(Z!0, X!2), Z!0))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(34,plain,
% 0.14/0.41 (~convergent_lines(parallel_through_point(Z!0, X!2), Z!0)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.14/0.41 tff(35,plain,
% 0.14/0.41 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(36,plain,
% 0.14/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.14/0.41 tff(37,plain,
% 0.14/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(38,plain,
% 0.14/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(39,plain,
% 0.22/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.22/0.41 tff(40,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.22/0.41 tff(41,plain,
% 0.22/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.22/0.41 tff(42,plain,
% 0.22/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.22/0.41 tff(43,plain,(
% 0.22/0.41 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.41 inference(skolemize,[status(sab)],[42])).
% 0.22/0.41 tff(44,plain,
% 0.22/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.22/0.41 tff(45,plain,
% 0.22/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(46,plain,
% 0.22/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(47,plain,
% 0.22/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | convergent_lines(Y!1, Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.22/0.41 tff(48,plain,
% 0.22/0.41 (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[47, 44, 34, 25])).
% 0.22/0.41 tff(49,plain,
% 0.22/0.41 (^[X: $i, Y: $i] : refl((equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> (equal_lines(X, Y) <=> (~distinct_lines(X, Y))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(50,plain,
% 0.22/0.41 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.22/0.41 tff(51,plain,
% 0.22/0.41 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(52,axiom,(![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax','ax2')).
% 0.22/0.41 tff(53,plain,
% 0.22/0.41 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.22/0.41 tff(54,plain,(
% 0.22/0.41 ![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))),
% 0.22/0.41 inference(skolemize,[status(sab)],[53])).
% 0.22/0.41 tff(55,plain,
% 0.22/0.41 (![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.22/0.41 tff(56,plain,
% 0.22/0.41 ((~![X: $i, Y: $i] : (equal_lines(X, Y) <=> (~distinct_lines(X, Y)))) | (equal_lines(Y!1, parallel_through_point(Z!0, X!2)) <=> (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(57,plain,
% 0.22/0.42 (equal_lines(Y!1, parallel_through_point(Z!0, X!2)) <=> (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.22/0.42 tff(58,plain,
% 0.22/0.42 (~equal_lines(Y!1, parallel_through_point(Z!0, X!2))),
% 0.22/0.42 inference(or_elim,[status(thm)],[20])).
% 0.22/0.42 tff(59,plain,
% 0.22/0.42 ((~(equal_lines(Y!1, parallel_through_point(Z!0, X!2)) <=> (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))))) | equal_lines(Y!1, parallel_through_point(Z!0, X!2)) | distinct_lines(Y!1, parallel_through_point(Z!0, X!2))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(60,plain,
% 0.22/0.42 ((~(equal_lines(Y!1, parallel_through_point(Z!0, X!2)) <=> (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))))) | distinct_lines(Y!1, parallel_through_point(Z!0, X!2))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.22/0.42 tff(61,plain,
% 0.22/0.42 (distinct_lines(Y!1, parallel_through_point(Z!0, X!2))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.22/0.42 tff(62,plain,
% 0.22/0.42 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(63,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.22/0.42 tff(64,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(65,plain,
% 0.22/0.42 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(66,plain,
% 0.22/0.42 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.22/0.42 tff(67,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.22/0.42 tff(68,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.22/0.42 tff(69,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.22/0.42 tff(70,plain,(
% 0.22/0.42 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.22/0.42 inference(skolemize,[status(sab)],[69])).
% 0.22/0.42 tff(71,plain,
% 0.22/0.42 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.22/0.42 tff(72,plain,
% 0.22/0.42 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(73,plain,
% 0.22/0.42 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(74,plain,
% 0.22/0.42 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.22/0.42 tff(75,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[74, 71, 61, 48])).
% 0.22/0.42 % SZS output end Proof
%------------------------------------------------------------------------------