TSTP Solution File: GEO195+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO195+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 20:35:31 EDT 2022
% Result : Theorem 0.63s 0.64s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO195+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n028.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 07:00:34 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.63/0.64 % SZS status Theorem
% 0.63/0.64 % SZS output start Proof
% 0.63/0.64 tff(distinct_lines_type, type, (
% 0.63/0.64 distinct_lines: ( $i * $i ) > $o)).
% 0.63/0.64 tff(parallel_through_point_type, type, (
% 0.63/0.64 parallel_through_point: ( $i * $i ) > $i)).
% 0.63/0.64 tff(intersection_point_type, type, (
% 0.63/0.64 intersection_point: ( $i * $i ) > $i)).
% 0.63/0.64 tff(tptp_fun_Y_1_type, type, (
% 0.63/0.64 tptp_fun_Y_1: $i)).
% 0.63/0.64 tff(tptp_fun_X_2_type, type, (
% 0.63/0.64 tptp_fun_X_2: $i)).
% 0.63/0.64 tff(tptp_fun_Z_0_type, type, (
% 0.63/0.64 tptp_fun_Z_0: $i)).
% 0.63/0.64 tff(convergent_lines_type, type, (
% 0.63/0.64 convergent_lines: ( $i * $i ) > $o)).
% 0.63/0.64 tff(apart_point_and_line_type, type, (
% 0.63/0.64 apart_point_and_line: ( $i * $i ) > $o)).
% 0.63/0.64 tff(1,plain,
% 0.63/0.64 (^[X: $i, Y: $i] : refl((~convergent_lines(parallel_through_point(Y, X), Y)) <=> (~convergent_lines(parallel_through_point(Y, X), Y)))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(2,plain,
% 0.63/0.64 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[1])).
% 0.63/0.64 tff(3,plain,
% 0.63/0.64 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y)) <=> ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 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')).
% 0.63/0.64 tff(5,plain,
% 0.63/0.64 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.63/0.64 tff(6,plain,(
% 0.63/0.64 ![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.63/0.64 inference(skolemize,[status(sab)],[5])).
% 0.63/0.64 tff(7,plain,
% 0.63/0.64 (![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.63/0.64 tff(8,plain,
% 0.63/0.64 ((~![X: $i, Y: $i] : (~convergent_lines(parallel_through_point(Y, X), Y))) | (~convergent_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(9,plain,
% 0.63/0.64 (~convergent_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.63/0.64 tff(10,plain,
% 0.63/0.64 (^[X: $i, Y: $i] : refl(((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(11,plain,
% 0.63/0.64 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[10])).
% 0.63/0.64 tff(12,plain,
% 0.63/0.64 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(13,plain,
% 0.63/0.64 (^[X: $i, Y: $i] : rewrite((distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ((~distinct_lines(X, Y)) | convergent_lines(X, Y)))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(14,plain,
% 0.63/0.64 (![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[13])).
% 0.63/0.64 tff(15,axiom,(![X: $i, Y: $i] : (distinct_lines(X, Y) => convergent_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax','p1')).
% 0.63/0.64 tff(16,plain,
% 0.63/0.64 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.63/0.64 tff(17,plain,
% 0.63/0.64 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.63/0.64 tff(18,plain,(
% 0.63/0.64 ![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.63/0.64 inference(skolemize,[status(sab)],[17])).
% 0.63/0.64 tff(19,plain,
% 0.63/0.64 (![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.63/0.64 tff(20,plain,
% 0.63/0.64 (((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)) | convergent_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0))) <=> ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)) | convergent_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(21,plain,
% 0.63/0.64 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | ((~distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)) | convergent_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(22,plain,
% 0.63/0.64 ((~![X: $i, Y: $i] : ((~distinct_lines(X, Y)) | convergent_lines(X, Y))) | (~distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)) | convergent_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.63/0.64 tff(23,plain,
% 0.63/0.64 (~distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0)),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.63/0.64 tff(24,assumption,(distinct_lines(Z!0, Z!0)), introduced(assumption)).
% 0.63/0.64 tff(25,plain,
% 0.63/0.64 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(26,plain,
% 0.63/0.64 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[25])).
% 0.63/0.64 tff(27,plain,
% 0.63/0.64 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(28,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart2')).
% 0.63/0.64 tff(29,plain,
% 0.63/0.64 (![X: $i] : (~distinct_lines(X, X))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.63/0.64 tff(30,plain,(
% 0.63/0.64 ![X: $i] : (~distinct_lines(X, X))),
% 0.63/0.64 inference(skolemize,[status(sab)],[29])).
% 0.63/0.64 tff(31,plain,
% 0.63/0.64 (![X: $i] : (~distinct_lines(X, X))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.63/0.64 tff(32,plain,
% 0.63/0.64 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(Z!0, Z!0))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(33,plain,
% 0.63/0.64 ($false),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[32, 31, 24])).
% 0.63/0.64 tff(34,plain,(~distinct_lines(Z!0, Z!0)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.64 tff(35,plain,
% 0.63/0.64 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(36,plain,
% 0.63/0.64 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[35])).
% 0.63/0.64 tff(37,plain,
% 0.63/0.64 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(38,plain,
% 0.63/0.64 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(39,plain,
% 0.63/0.64 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[38])).
% 0.63/0.64 tff(40,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart5')).
% 0.63/0.64 tff(41,plain,
% 0.63/0.64 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.63/0.64 tff(42,plain,
% 0.63/0.64 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.63/0.64 tff(43,plain,(
% 0.63/0.64 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.63/0.64 inference(skolemize,[status(sab)],[42])).
% 0.63/0.64 tff(44,plain,
% 0.63/0.64 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.63/0.64 tff(45,plain,
% 0.63/0.64 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(46,plain,
% 0.63/0.64 ((distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))) <=> (distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(47,plain,
% 0.63/0.64 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))))),
% 0.63/0.64 inference(monotonicity,[status(thm)],[46])).
% 0.63/0.64 tff(48,plain,
% 0.63/0.64 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))),
% 0.63/0.64 inference(transitivity,[status(thm)],[47, 45])).
% 0.63/0.64 tff(49,plain,
% 0.63/0.64 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0) | distinct_lines(Z!0, Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(50,plain,
% 0.63/0.64 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(Z!0, Z!0) | distinct_lines(parallel_through_point(Z!0, intersection_point(X!2, Y!1)), Z!0) | (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.63/0.64 tff(51,plain,
% 0.63/0.64 (~distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[50, 44, 34, 23])).
% 0.63/0.64 tff(52,plain,
% 0.63/0.64 (^[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))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(53,plain,
% 0.63/0.64 (![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)))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[52])).
% 0.63/0.64 tff(54,plain,
% 0.63/0.64 (![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)))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(55,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')).
% 0.63/0.64 tff(56,plain,
% 0.63/0.64 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.63/0.64 tff(57,plain,(
% 0.63/0.64 ![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.63/0.64 inference(skolemize,[status(sab)],[56])).
% 0.63/0.64 tff(58,plain,
% 0.63/0.64 (![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.63/0.64 tff(59,plain,
% 0.63/0.64 ((~![X: $i, Y: $i] : (~apart_point_and_line(X, parallel_through_point(Y, X)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(60,plain,
% 0.63/0.64 (~apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1)))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.63/0.64 tff(61,plain,
% 0.63/0.64 ((~(apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0))))) <=> (~(apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0)))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(62,plain,
% 0.63/0.64 ((~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z)))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(63,plain,
% 0.63/0.64 ((~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) => (apart_point_and_line(intersection_point(X, Y), Z) => apart_point_and_line(intersection_point(Y, X), Z)))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z)))))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(64,axiom,(~![X: $i, Y: $i, Z: $i] : (((convergent_lines(X, Y) & convergent_lines(Z, Y)) & convergent_lines(X, Z)) => (apart_point_and_line(intersection_point(X, Y), Z) => apart_point_and_line(intersection_point(Y, X), Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.63/0.65 tff(65,plain,
% 0.63/0.65 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.63/0.65 tff(66,plain,
% 0.63/0.65 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[65, 62])).
% 0.63/0.65 tff(67,plain,
% 0.63/0.65 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.63/0.65 tff(68,plain,
% 0.63/0.65 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[67, 62])).
% 0.63/0.65 tff(69,plain,
% 0.63/0.65 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[68, 62])).
% 0.63/0.65 tff(70,plain,
% 0.63/0.65 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.63/0.65 tff(71,plain,
% 0.63/0.65 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(intersection_point(Y, X), Z) | (~apart_point_and_line(intersection_point(X, Y), Z)) | (~(convergent_lines(X, Y) & convergent_lines(Z, Y) & convergent_lines(X, Z))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[70, 62])).
% 0.63/0.65 tff(72,plain,(
% 0.63/0.65 ~(apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0))))),
% 0.63/0.65 inference(skolemize,[status(sab)],[71])).
% 0.63/0.65 tff(73,plain,
% 0.63/0.65 (~(apart_point_and_line(intersection_point(Y!1, X!2), Z!0) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | (~(convergent_lines(X!2, Y!1) & convergent_lines(Z!0, Y!1) & convergent_lines(X!2, Z!0))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[72, 61])).
% 0.63/0.65 tff(74,plain,
% 0.63/0.65 (apart_point_and_line(intersection_point(X!2, Y!1), Z!0)),
% 0.63/0.65 inference(or_elim,[status(thm)],[73])).
% 0.63/0.65 tff(75,plain,
% 0.63/0.65 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(76,plain,
% 0.63/0.65 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[75])).
% 0.63/0.65 tff(77,plain,
% 0.63/0.65 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(78,plain,
% 0.63/0.65 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | apart_point_and_line(X, Z)) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))))), rewrite((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(79,plain,
% 0.63/0.65 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[78])).
% 0.63/0.65 tff(80,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_lines(Y, Z) | apart_point_and_line(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq2')).
% 0.63/0.65 tff(81,plain,
% 0.63/0.65 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.63/0.65 tff(82,plain,
% 0.63/0.65 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.63/0.65 tff(83,plain,(
% 0.63/0.65 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.63/0.65 inference(skolemize,[status(sab)],[82])).
% 0.63/0.65 tff(84,plain,
% 0.63/0.65 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.63/0.65 tff(85,plain,
% 0.63/0.65 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(86,plain,
% 0.63/0.65 ((distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0))) <=> ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(87,plain,
% 0.63/0.65 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[86])).
% 0.63/0.65 tff(88,plain,
% 0.63/0.65 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))))),
% 0.63/0.65 inference(transitivity,[status(thm)],[87, 85])).
% 0.63/0.65 tff(89,plain,
% 0.63/0.65 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(90,plain,
% 0.63/0.65 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(X!2, Y!1), Z!0)) | apart_point_and_line(intersection_point(X!2, Y!1), parallel_through_point(Z!0, intersection_point(X!2, Y!1))) | distinct_lines(Z!0, parallel_through_point(Z!0, intersection_point(X!2, Y!1)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.63/0.65 tff(91,plain,
% 0.63/0.65 ($false),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[90, 84, 74, 60, 51])).
% 0.63/0.65 % SZS output end Proof
%------------------------------------------------------------------------------