TSTP Solution File: GEO196+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO196+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:35:32 EDT 2022
% Result : Theorem 1.27s 1.08s
% Output : Proof 1.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO196+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.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 07:06:32 EDT 2022
% 0.13/0.34 % 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.
% 1.27/1.08 % SZS status Theorem
% 1.27/1.08 % SZS output start Proof
% 1.27/1.08 tff(apart_point_and_line_type, type, (
% 1.27/1.08 apart_point_and_line: ( $i * $i ) > $o)).
% 1.27/1.08 tff(tptp_fun_X_3_type, type, (
% 1.27/1.08 tptp_fun_X_3: $i)).
% 1.27/1.08 tff(intersection_point_type, type, (
% 1.27/1.08 intersection_point: ( $i * $i ) > $i)).
% 1.27/1.08 tff(tptp_fun_V_0_type, type, (
% 1.27/1.08 tptp_fun_V_0: $i)).
% 1.27/1.08 tff(tptp_fun_U_1_type, type, (
% 1.27/1.08 tptp_fun_U_1: $i)).
% 1.27/1.08 tff(distinct_points_type, type, (
% 1.27/1.08 distinct_points: ( $i * $i ) > $o)).
% 1.27/1.08 tff(tptp_fun_Y_2_type, type, (
% 1.27/1.08 tptp_fun_Y_2: $i)).
% 1.27/1.08 tff(distinct_lines_type, type, (
% 1.27/1.08 distinct_lines: ( $i * $i ) > $o)).
% 1.27/1.08 tff(convergent_lines_type, type, (
% 1.27/1.08 convergent_lines: ( $i * $i ) > $o)).
% 1.27/1.08 tff(1,assumption,(convergent_lines(U!1, U!1)), introduced(assumption)).
% 1.27/1.08 tff(2,plain,
% 1.27/1.08 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(3,plain,
% 1.27/1.08 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[2])).
% 1.27/1.08 tff(4,plain,
% 1.27/1.08 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(5,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','apart3')).
% 1.27/1.08 tff(6,plain,
% 1.27/1.08 (![X: $i] : (~convergent_lines(X, X))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.27/1.08 tff(7,plain,(
% 1.27/1.08 ![X: $i] : (~convergent_lines(X, X))),
% 1.27/1.08 inference(skolemize,[status(sab)],[6])).
% 1.27/1.08 tff(8,plain,
% 1.27/1.08 (![X: $i] : (~convergent_lines(X, X))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.27/1.08 tff(9,plain,
% 1.27/1.08 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(U!1, U!1))),
% 1.27/1.08 inference(quant_inst,[status(thm)],[])).
% 1.27/1.08 tff(10,plain,
% 1.27/1.08 ($false),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 1.27/1.08 tff(11,plain,(~convergent_lines(U!1, U!1)), inference(lemma,lemma(discharge,[]))).
% 1.27/1.08 tff(12,assumption,(~distinct_lines(V!0, U!1)), introduced(assumption)).
% 1.27/1.08 tff(13,plain,
% 1.27/1.08 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(intersection_point(X, Y), U)) & (~apart_point_and_line(intersection_point(X, Y), V)))) | ((~apart_point_and_line(intersection_point(U, V), X)) & (~apart_point_and_line(intersection_point(U, V), Y))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(intersection_point(X, Y), U)) & (~apart_point_and_line(intersection_point(X, Y), V)))) | ((~apart_point_and_line(intersection_point(U, V), X)) & (~apart_point_and_line(intersection_point(U, V), Y)))))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(14,plain,
% 1.27/1.08 ((~![X: $i, Y: $i, U: $i, V: $i] : ((((convergent_lines(X, Y) & convergent_lines(U, V)) & (~apart_point_and_line(intersection_point(X, Y), U))) & (~apart_point_and_line(intersection_point(X, Y), V))) => ((~apart_point_and_line(intersection_point(U, V), X)) & (~apart_point_and_line(intersection_point(U, V), Y))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(intersection_point(X, Y), U)) & (~apart_point_and_line(intersection_point(X, Y), V)))) | ((~apart_point_and_line(intersection_point(U, V), X)) & (~apart_point_and_line(intersection_point(U, V), Y)))))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(15,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : ((((convergent_lines(X, Y) & convergent_lines(U, V)) & (~apart_point_and_line(intersection_point(X, Y), U))) & (~apart_point_and_line(intersection_point(X, Y), V))) => ((~apart_point_and_line(intersection_point(U, V), X)) & (~apart_point_and_line(intersection_point(U, V), Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 1.27/1.08 tff(16,plain,
% 1.27/1.08 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(intersection_point(X, Y), U)) & (~apart_point_and_line(intersection_point(X, Y), V)))) | ((~apart_point_and_line(intersection_point(U, V), X)) & (~apart_point_and_line(intersection_point(U, V), Y))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[15, 14])).
% 1.27/1.08 tff(17,plain,
% 1.27/1.08 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(intersection_point(X, Y), U)) & (~apart_point_and_line(intersection_point(X, Y), V)))) | ((~apart_point_and_line(intersection_point(U, V), X)) & (~apart_point_and_line(intersection_point(U, V), Y))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[16, 13])).
% 1.27/1.08 tff(18,plain,
% 1.27/1.08 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(intersection_point(X, Y), U)) & (~apart_point_and_line(intersection_point(X, Y), V)))) | ((~apart_point_and_line(intersection_point(U, V), X)) & (~apart_point_and_line(intersection_point(U, V), Y))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.27/1.08 tff(19,plain,
% 1.27/1.08 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(intersection_point(X, Y), U)) & (~apart_point_and_line(intersection_point(X, Y), V)))) | ((~apart_point_and_line(intersection_point(U, V), X)) & (~apart_point_and_line(intersection_point(U, V), Y))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[18, 13])).
% 1.27/1.08 tff(20,plain,
% 1.27/1.08 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(intersection_point(X, Y), U)) & (~apart_point_and_line(intersection_point(X, Y), V)))) | ((~apart_point_and_line(intersection_point(U, V), X)) & (~apart_point_and_line(intersection_point(U, V), Y))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[19, 13])).
% 1.27/1.08 tff(21,plain,
% 1.27/1.08 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(intersection_point(X, Y), U)) & (~apart_point_and_line(intersection_point(X, Y), V)))) | ((~apart_point_and_line(intersection_point(U, V), X)) & (~apart_point_and_line(intersection_point(U, V), Y))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.27/1.08 tff(22,plain,
% 1.27/1.08 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(convergent_lines(X, Y) & convergent_lines(U, V) & (~apart_point_and_line(intersection_point(X, Y), U)) & (~apart_point_and_line(intersection_point(X, Y), V)))) | ((~apart_point_and_line(intersection_point(U, V), X)) & (~apart_point_and_line(intersection_point(U, V), Y))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[21, 13])).
% 1.27/1.08 tff(23,plain,(
% 1.27/1.08 ~((~(convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)) & (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)))) | ((~apart_point_and_line(intersection_point(U!1, V!0), X!3)) & (~apart_point_and_line(intersection_point(U!1, V!0), Y!2))))),
% 1.27/1.08 inference(skolemize,[status(sab)],[22])).
% 1.27/1.08 tff(24,plain,
% 1.27/1.08 (convergent_lines(X!3, Y!2) & convergent_lines(U!1, V!0) & (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)) & (~apart_point_and_line(intersection_point(X!3, Y!2), V!0))),
% 1.27/1.08 inference(or_elim,[status(thm)],[23])).
% 1.27/1.08 tff(25,plain,
% 1.27/1.08 (convergent_lines(U!1, V!0)),
% 1.27/1.08 inference(and_elim,[status(thm)],[24])).
% 1.27/1.08 tff(26,plain,
% 1.27/1.08 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(27,plain,
% 1.27/1.08 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[26])).
% 1.27/1.08 tff(28,plain,
% 1.27/1.08 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(29,plain,
% 1.27/1.08 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(30,plain,
% 1.27/1.08 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[29])).
% 1.27/1.08 tff(31,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 1.27/1.08 tff(32,plain,
% 1.27/1.08 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.27/1.08 tff(33,plain,
% 1.27/1.08 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[32, 28])).
% 1.27/1.08 tff(34,plain,(
% 1.27/1.08 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 1.27/1.08 inference(skolemize,[status(sab)],[33])).
% 1.27/1.08 tff(35,plain,
% 1.27/1.08 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[34, 27])).
% 1.27/1.08 tff(36,plain,
% 1.27/1.08 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(37,plain,
% 1.27/1.08 ((distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0))) <=> ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(38,plain,
% 1.27/1.08 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1)))),
% 1.27/1.08 inference(monotonicity,[status(thm)],[37])).
% 1.27/1.08 tff(39,plain,
% 1.27/1.08 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1))),
% 1.27/1.08 inference(transitivity,[status(thm)],[38, 36])).
% 1.27/1.08 tff(40,plain,
% 1.27/1.08 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1) | (~convergent_lines(U!1, V!0)))),
% 1.27/1.08 inference(quant_inst,[status(thm)],[])).
% 1.27/1.08 tff(41,plain,
% 1.27/1.08 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(U!1, V!0)) | distinct_lines(V!0, U!1) | convergent_lines(U!1, U!1)),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[40, 39])).
% 1.27/1.08 tff(42,plain,
% 1.27/1.08 ($false),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[41, 35, 25, 12, 11])).
% 1.27/1.08 tff(43,plain,(distinct_lines(V!0, U!1)), inference(lemma,lemma(discharge,[]))).
% 1.27/1.08 tff(44,plain,
% 1.27/1.08 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(45,plain,
% 1.27/1.08 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[44])).
% 1.27/1.08 tff(46,plain,
% 1.27/1.08 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(47,plain,
% 1.27/1.08 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(48,plain,
% 1.27/1.08 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[47])).
% 1.27/1.08 tff(49,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), X)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci3')).
% 1.27/1.08 tff(50,plain,
% 1.27/1.08 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.27/1.08 tff(51,plain,
% 1.27/1.08 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.27/1.08 tff(52,plain,(
% 1.27/1.08 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 1.27/1.08 inference(skolemize,[status(sab)],[51])).
% 1.27/1.08 tff(53,plain,
% 1.27/1.08 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.27/1.08 tff(54,plain,
% 1.27/1.08 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(55,plain,
% 1.27/1.08 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1)))),
% 1.27/1.08 inference(quant_inst,[status(thm)],[])).
% 1.27/1.08 tff(56,plain,
% 1.27/1.08 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), U!1))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.27/1.08 tff(57,plain,
% 1.27/1.08 (~apart_point_and_line(intersection_point(U!1, V!0), U!1)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[56, 53, 25])).
% 1.27/1.08 tff(58,plain,
% 1.27/1.08 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(59,plain,
% 1.27/1.08 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[58])).
% 1.27/1.08 tff(60,plain,
% 1.27/1.08 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(61,plain,
% 1.27/1.08 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(62,plain,
% 1.27/1.08 (![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y))) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[61])).
% 1.27/1.08 tff(63,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => (~apart_point_and_line(intersection_point(X, Y), Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ci4')).
% 1.27/1.08 tff(64,plain,
% 1.27/1.08 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.27/1.08 tff(65,plain,
% 1.27/1.08 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.27/1.08 tff(66,plain,(
% 1.27/1.08 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 1.27/1.08 inference(skolemize,[status(sab)],[65])).
% 1.27/1.08 tff(67,plain,
% 1.27/1.08 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[66, 59])).
% 1.27/1.08 tff(68,plain,
% 1.27/1.08 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(69,plain,
% 1.27/1.08 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0)))),
% 1.27/1.08 inference(quant_inst,[status(thm)],[])).
% 1.27/1.08 tff(70,plain,
% 1.27/1.08 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(U!1, V!0)) | (~apart_point_and_line(intersection_point(U!1, V!0), V!0))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[69, 68])).
% 1.27/1.08 tff(71,plain,
% 1.27/1.08 (~apart_point_and_line(intersection_point(U!1, V!0), V!0)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[70, 67, 25])).
% 1.27/1.08 tff(72,plain,
% 1.27/1.08 (~apart_point_and_line(intersection_point(X!3, Y!2), V!0)),
% 1.27/1.08 inference(and_elim,[status(thm)],[24])).
% 1.27/1.08 tff(73,plain,
% 1.27/1.08 (~apart_point_and_line(intersection_point(X!3, Y!2), U!1)),
% 1.27/1.08 inference(and_elim,[status(thm)],[24])).
% 1.27/1.08 tff(74,plain,
% 1.27/1.08 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(75,plain,
% 1.27/1.08 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[74])).
% 1.27/1.08 tff(76,plain,
% 1.27/1.08 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(77,plain,
% 1.27/1.08 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[76])).
% 1.27/1.08 tff(78,plain,
% 1.27/1.08 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(79,plain,
% 1.27/1.08 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(80,plain,
% 1.27/1.08 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[79])).
% 1.27/1.08 tff(81,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','cu1')).
% 1.27/1.08 tff(82,plain,
% 1.27/1.08 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.27/1.08 tff(83,plain,
% 1.27/1.08 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[82, 78])).
% 1.27/1.08 tff(84,plain,(
% 1.27/1.08 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 1.27/1.08 inference(skolemize,[status(sab)],[83])).
% 1.27/1.08 tff(85,plain,
% 1.27/1.08 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[84, 77])).
% 1.27/1.08 tff(86,plain,
% 1.27/1.08 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[85, 75])).
% 1.27/1.08 tff(87,plain,
% 1.27/1.08 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(88,plain,
% 1.27/1.08 ((apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, U!1))) <=> (apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(89,plain,
% 1.27/1.08 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, U!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))))),
% 1.27/1.08 inference(monotonicity,[status(thm)],[88])).
% 1.27/1.08 tff(90,plain,
% 1.27/1.08 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, U!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))))),
% 1.27/1.08 inference(transitivity,[status(thm)],[89, 87])).
% 1.27/1.08 tff(91,plain,
% 1.27/1.08 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))) | (~distinct_lines(V!0, U!1)))),
% 1.27/1.08 inference(quant_inst,[status(thm)],[])).
% 1.27/1.08 tff(92,plain,
% 1.27/1.08 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(intersection_point(X!3, Y!2), U!1) | apart_point_and_line(intersection_point(X!3, Y!2), V!0) | apart_point_and_line(intersection_point(U!1, V!0), V!0) | apart_point_and_line(intersection_point(U!1, V!0), U!1) | (~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.27/1.08 tff(93,plain,
% 1.27/1.08 ((~distinct_lines(V!0, U!1)) | (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[92, 86, 73, 72, 71, 57])).
% 1.27/1.08 tff(94,plain,
% 1.27/1.08 (~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[93, 43])).
% 1.27/1.08 tff(95,plain,
% 1.27/1.08 (convergent_lines(X!3, Y!2)),
% 1.27/1.08 inference(and_elim,[status(thm)],[24])).
% 1.27/1.08 tff(96,plain,
% 1.27/1.08 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(97,plain,
% 1.27/1.08 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | ((~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)))),
% 1.27/1.08 inference(quant_inst,[status(thm)],[])).
% 1.27/1.08 tff(98,plain,
% 1.27/1.08 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), X)))) | (~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), X!3))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.27/1.08 tff(99,plain,
% 1.27/1.08 (~apart_point_and_line(intersection_point(X!3, Y!2), X!3)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[98, 53, 95])).
% 1.27/1.08 tff(100,plain,
% 1.27/1.08 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(101,plain,
% 1.27/1.08 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[100])).
% 1.27/1.08 tff(102,plain,
% 1.27/1.08 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(103,plain,
% 1.27/1.08 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | apart_point_and_line(Z, Y)) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))))), rewrite((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))), ((apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))))),
% 1.27/1.08 inference(bind,[status(th)],[])).
% 1.27/1.08 tff(104,plain,
% 1.27/1.08 (![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 1.27/1.08 inference(quant_intro,[status(thm)],[103])).
% 1.27/1.08 tff(105,axiom,(![X: $i, Y: $i, Z: $i] : (apart_point_and_line(X, Y) => (distinct_points(X, Z) | apart_point_and_line(Z, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax','ceq1')).
% 1.27/1.08 tff(106,plain,
% 1.27/1.08 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.27/1.08 tff(107,plain,
% 1.27/1.08 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[106, 102])).
% 1.27/1.09 tff(108,plain,(
% 1.27/1.09 ![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 1.27/1.09 inference(skolemize,[status(sab)],[107])).
% 1.27/1.09 tff(109,plain,
% 1.27/1.09 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[108, 101])).
% 1.27/1.09 tff(110,plain,
% 1.27/1.09 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(111,plain,
% 1.27/1.09 ((distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3))) <=> ((~apart_point_and_line(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(112,plain,
% 1.27/1.09 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))))),
% 1.27/1.09 inference(monotonicity,[status(thm)],[111])).
% 1.27/1.09 tff(113,plain,
% 1.27/1.09 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))),
% 1.27/1.09 inference(transitivity,[status(thm)],[112, 110])).
% 1.27/1.09 tff(114,plain,
% 1.27/1.09 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)))),
% 1.27/1.09 inference(quant_inst,[status(thm)],[])).
% 1.27/1.09 tff(115,plain,
% 1.27/1.09 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(U!1, V!0), X!3)) | apart_point_and_line(intersection_point(X!3, Y!2), X!3) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.27/1.09 tff(116,plain,
% 1.27/1.09 ((~apart_point_and_line(intersection_point(U!1, V!0), X!3)) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[115, 109, 99])).
% 1.27/1.09 tff(117,plain,
% 1.27/1.09 (~apart_point_and_line(intersection_point(U!1, V!0), X!3)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[116, 94])).
% 1.27/1.09 tff(118,assumption,(~distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))), introduced(assumption)).
% 1.27/1.09 tff(119,plain,
% 1.27/1.09 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(120,plain,
% 1.27/1.09 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | ((~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)))),
% 1.27/1.09 inference(quant_inst,[status(thm)],[])).
% 1.27/1.09 tff(121,plain,
% 1.27/1.09 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | (~apart_point_and_line(intersection_point(X, Y), Y)))) | (~convergent_lines(X!3, Y!2)) | (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.27/1.09 tff(122,plain,
% 1.27/1.09 (~apart_point_and_line(intersection_point(X!3, Y!2), Y!2)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[121, 67, 95])).
% 1.27/1.09 tff(123,assumption,(apart_point_and_line(intersection_point(U!1, V!0), Y!2)), introduced(assumption)).
% 1.27/1.09 tff(124,plain,
% 1.27/1.09 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(U!1, V!0), Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(125,plain,
% 1.27/1.09 ((distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2))) <=> ((~apart_point_and_line(intersection_point(U!1, V!0), Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(126,plain,
% 1.27/1.09 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(intersection_point(U!1, V!0), Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))))),
% 1.27/1.09 inference(monotonicity,[status(thm)],[125])).
% 1.27/1.09 tff(127,plain,
% 1.27/1.09 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)))),
% 1.27/1.09 inference(transitivity,[status(thm)],[126, 124])).
% 1.27/1.09 tff(128,plain,
% 1.27/1.09 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 1.37/1.09 inference(quant_inst,[status(thm)],[])).
% 1.37/1.09 tff(129,plain,
% 1.37/1.09 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Z) | apart_point_and_line(Z, Y) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)) | apart_point_and_line(intersection_point(X!3, Y!2), Y!2) | distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2))),
% 1.37/1.09 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.37/1.09 tff(130,plain,
% 1.37/1.09 ($false),
% 1.37/1.09 inference(unit_resolution,[status(thm)],[129, 109, 123, 122, 118])).
% 1.37/1.09 tff(131,plain,(distinct_points(intersection_point(U!1, V!0), intersection_point(X!3, Y!2)) | (~apart_point_and_line(intersection_point(U!1, V!0), Y!2))), inference(lemma,lemma(discharge,[]))).
% 1.37/1.09 tff(132,plain,
% 1.37/1.09 (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 1.37/1.09 inference(unit_resolution,[status(thm)],[131, 94])).
% 1.37/1.09 tff(133,plain,
% 1.37/1.09 ((~(~(apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) <=> (apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2))),
% 1.37/1.09 inference(rewrite,[status(thm)],[])).
% 1.37/1.09 tff(134,plain,
% 1.37/1.09 (((~apart_point_and_line(intersection_point(U!1, V!0), X!3)) & (~apart_point_and_line(intersection_point(U!1, V!0), Y!2))) <=> (~(apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 1.37/1.09 inference(rewrite,[status(thm)],[])).
% 1.37/1.09 tff(135,plain,
% 1.37/1.09 ((~((~apart_point_and_line(intersection_point(U!1, V!0), X!3)) & (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) <=> (~(~(apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2))))),
% 1.37/1.09 inference(monotonicity,[status(thm)],[134])).
% 1.37/1.09 tff(136,plain,
% 1.37/1.09 ((~((~apart_point_and_line(intersection_point(U!1, V!0), X!3)) & (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))) <=> (apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2))),
% 1.37/1.09 inference(transitivity,[status(thm)],[135, 133])).
% 1.37/1.09 tff(137,plain,
% 1.37/1.09 (~((~apart_point_and_line(intersection_point(U!1, V!0), X!3)) & (~apart_point_and_line(intersection_point(U!1, V!0), Y!2)))),
% 1.37/1.09 inference(or_elim,[status(thm)],[23])).
% 1.37/1.09 tff(138,plain,
% 1.37/1.09 (apart_point_and_line(intersection_point(U!1, V!0), X!3) | apart_point_and_line(intersection_point(U!1, V!0), Y!2)),
% 1.37/1.09 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.37/1.09 tff(139,plain,
% 1.37/1.09 ($false),
% 1.37/1.09 inference(unit_resolution,[status(thm)],[138, 132, 117])).
% 1.37/1.09 % SZS output end Proof
%------------------------------------------------------------------------------