TSTP Solution File: GEO206+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO206+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO206+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.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 07:18:32 EDT 2022
% 0.13/0.35 % 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.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(convergent_lines_type, type, (
% 0.13/0.40 convergent_lines: ( $i * $i ) > $o)).
% 0.13/0.40 tff(parallel_through_point_type, type, (
% 0.13/0.40 parallel_through_point: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_X_2_type, type, (
% 0.13/0.40 tptp_fun_X_2: $i)).
% 0.13/0.40 tff(tptp_fun_Z_0_type, type, (
% 0.13/0.40 tptp_fun_Z_0: $i)).
% 0.13/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.40 tptp_fun_Y_1: $i)).
% 0.13/0.40 tff(apart_point_and_line_type, type, (
% 0.13/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.13/0.40 tff(distinct_lines_type, type, (
% 0.13/0.40 distinct_lines: ( $i * $i ) > $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,axiom,(![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cp1')).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.40 tff(6,plain,(
% 0.13/0.40 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.13/0.40 inference(skolemize,[status(sab)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(Z!0, X!2), Z!0))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (~convergent_lines(parallel_through_point(Z!0, X!2), Z!0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 ((~![X: $i, Y: $i, Z: $i] : (((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z))) => (~distinct_lines(Y, parallel_through_point(Z, X))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z))))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(12,axiom,(~![X: $i, Y: $i, Z: $i] : (((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z))) => (~distinct_lines(Y, parallel_through_point(Z, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Y, parallel_through_point(Z, X))) | (~((~apart_point_and_line(X, Y)) & (~convergent_lines(Y, Z)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.13/0.40 tff(20,plain,(
% 0.13/0.40 ~((~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | (~((~apart_point_and_line(X!2, Y!1)) & (~convergent_lines(Y!1, Z!0)))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[19])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 ((~apart_point_and_line(X!2, Y!1)) & (~convergent_lines(Y!1, Z!0))),
% 0.13/0.40 inference(or_elim,[status(thm)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (~convergent_lines(Y!1, Z!0)),
% 0.13/0.40 inference(and_elim,[status(thm)],[21])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (^[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))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.40 tff(28,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.40 tff(31,plain,(
% 0.13/0.40 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[30])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!1, Z!0) | convergent_lines(parallel_through_point(Z!0, X!2), 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(Y!1, Z!0) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 ((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)))) <=> (convergent_lines(Y!1, Z!0) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (((~![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(Y!1, Z!0) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (((~![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(Y!1, Z!0) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[35, 33])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 ((~![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))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(Y!1, Z!0) | convergent_lines(parallel_through_point(Z!0, X!2), Z!0) | (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (~convergent_lines(Y!1, parallel_through_point(Z!0, X!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[38, 32, 22, 9])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (^[X: $i, Y: $i] : refl((~apart_point_and_line(X, parallel_through_point(Y, X))) <=> (~apart_point_and_line(X, parallel_through_point(Y, X))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X))) <=> ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(43,axiom,(![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cp2')).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.13/0.41 tff(45,plain,(
% 0.13/0.41 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[44])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (~apart_point_and_line(X!2, parallel_through_point(Z!0, X!2))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 (~apart_point_and_line(X!2, Y!1)),
% 0.13/0.41 inference(and_elim,[status(thm)],[21])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (distinct_lines(Y!1, parallel_through_point(Z!0, X!2))),
% 0.13/0.41 inference(or_elim,[status(thm)],[20])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) <=> (apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> ((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)))), rewrite(((apart_point_and_line(X, Z) | apart_point_and_line(X, Y)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))), (((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))))), rewrite((distinct_lines(Y, Z) => (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))), ((distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.13/0.41 tff(56,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) => ((apart_point_and_line(X, Y) | apart_point_and_line(X, Z)) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax','cup1')).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.13/0.41 tff(59,plain,(
% 0.13/0.41 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[58])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | ((~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 ((convergent_lines(Y!1, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2)))) <=> ((~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Y!1, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | ((~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[62])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Y!1, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[63, 61])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (convergent_lines(Y!1, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | apart_point_and_line(X!2, Y!1) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | apart_point_and_line(X, Z) | apart_point_and_line(X, Y) | (~distinct_lines(Y, Z)))) | (~distinct_lines(Y!1, parallel_through_point(Z!0, X!2))) | apart_point_and_line(X!2, Y!1) | apart_point_and_line(X!2, parallel_through_point(Z!0, X!2)) | convergent_lines(Y!1, parallel_through_point(Z!0, X!2))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[66, 60, 50, 49, 48, 39])).
% 0.13/0.41 % SZS output end Proof
%------------------------------------------------------------------------------