TSTP Solution File: GEO215+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO215+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 20:35:45 EDT 2022
% Result : Theorem 0.84s 0.79s
% Output : Proof 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO215+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 07:00:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.84/0.79 % SZS status Theorem
% 0.84/0.79 % SZS output start Proof
% 0.84/0.79 tff(apart_point_and_line_type, type, (
% 0.84/0.79 apart_point_and_line: ( $i * $i ) > $o)).
% 0.84/0.79 tff(tptp_fun_L_2_type, type, (
% 0.84/0.79 tptp_fun_L_2: $i)).
% 0.84/0.79 tff(intersection_point_type, type, (
% 0.84/0.79 intersection_point: ( $i * $i ) > $i)).
% 0.84/0.79 tff(tptp_fun_M_1_type, type, (
% 0.84/0.79 tptp_fun_M_1: $i)).
% 0.84/0.79 tff(distinct_points_type, type, (
% 0.84/0.79 distinct_points: ( $i * $i ) > $o)).
% 0.84/0.79 tff(convergent_lines_type, type, (
% 0.84/0.79 convergent_lines: ( $i * $i ) > $o)).
% 0.84/0.79 tff(unorthogonal_lines_type, type, (
% 0.84/0.79 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.84/0.79 tff(tptp_fun_N_0_type, type, (
% 0.84/0.79 tptp_fun_N_0: $i)).
% 0.84/0.79 tff(distinct_lines_type, type, (
% 0.84/0.79 distinct_lines: ( $i * $i ) > $o)).
% 0.84/0.79 tff(1,assumption,(distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1))), introduced(assumption)).
% 0.84/0.79 tff(2,plain,
% 0.84/0.79 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(3,plain,
% 0.84/0.79 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[2])).
% 0.84/0.79 tff(4,plain,
% 0.84/0.79 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.84/0.79 tff(6,plain,
% 0.84/0.79 (![X: $i] : (~distinct_points(X, X))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.84/0.79 tff(7,plain,(
% 0.84/0.79 ![X: $i] : (~distinct_points(X, X))),
% 0.84/0.79 inference(skolemize,[status(sab)],[6])).
% 0.84/0.79 tff(8,plain,
% 0.84/0.79 (![X: $i] : (~distinct_points(X, X))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.84/0.79 tff(9,plain,
% 0.84/0.79 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(10,plain,
% 0.84/0.79 ($false),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.84/0.79 tff(11,plain,(~distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1))), inference(lemma,lemma(discharge,[]))).
% 0.84/0.79 tff(12,plain,
% 0.84/0.79 ((~(unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))) <=> (~(unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(L!2, M!1))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(13,plain,
% 0.84/0.79 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))) <=> (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(14,plain,
% 0.84/0.79 ((~![L: $i, M: $i, N: $i] : (convergent_lines(L, M) => (unorthogonal_lines(L, N) | unorthogonal_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(15,axiom,(~![L: $i, M: $i, N: $i] : (convergent_lines(L, M) => (unorthogonal_lines(L, N) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.84/0.79 tff(16,plain,
% 0.84/0.79 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.84/0.79 tff(17,plain,
% 0.84/0.79 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.84/0.79 tff(18,plain,
% 0.84/0.79 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.84/0.79 tff(19,plain,
% 0.84/0.79 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.84/0.79 tff(20,plain,
% 0.84/0.79 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.84/0.79 tff(21,plain,
% 0.84/0.79 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.84/0.79 tff(22,plain,
% 0.84/0.79 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.84/0.79 tff(23,plain,(
% 0.84/0.79 ~(unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.84/0.79 inference(skolemize,[status(sab)],[22])).
% 0.84/0.79 tff(24,plain,
% 0.84/0.79 (~(unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[23, 12])).
% 0.84/0.79 tff(25,plain,
% 0.84/0.79 (convergent_lines(L!2, M!1)),
% 0.84/0.79 inference(or_elim,[status(thm)],[24])).
% 0.84/0.79 tff(26,plain,
% 0.84/0.79 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(27,plain,
% 0.84/0.79 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[26])).
% 0.84/0.79 tff(28,plain,
% 0.84/0.79 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(29,plain,
% 0.84/0.79 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) <=> (apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))))), rewrite(((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))))), rewrite((convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(30,plain,
% 0.84/0.79 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[29])).
% 0.84/0.79 tff(31,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.84/0.80 tff(32,plain,
% 0.84/0.80 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.84/0.80 tff(33,plain,
% 0.84/0.80 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.84/0.80 tff(34,plain,(
% 0.84/0.80 ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.84/0.80 inference(skolemize,[status(sab)],[33])).
% 0.84/0.80 tff(35,plain,
% 0.84/0.80 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.84/0.80 tff(36,plain,
% 0.84/0.80 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(L!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(L!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(37,plain,
% 0.84/0.80 ((distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))) <=> ((~convergent_lines(L!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(38,plain,
% 0.84/0.80 ((~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))) <=> (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(39,plain,
% 0.84/0.80 ((distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))) <=> (distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))),
% 0.84/0.80 inference(monotonicity,[status(thm)],[38])).
% 0.84/0.80 tff(40,plain,
% 0.84/0.80 ((distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))) <=> ((~convergent_lines(L!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))),
% 0.84/0.80 inference(transitivity,[status(thm)],[39, 37])).
% 0.84/0.80 tff(41,plain,
% 0.84/0.80 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | ((~convergent_lines(L!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))))),
% 0.84/0.80 inference(monotonicity,[status(thm)],[40])).
% 0.84/0.80 tff(42,plain,
% 0.84/0.80 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(L!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))),
% 0.84/0.80 inference(transitivity,[status(thm)],[41, 36])).
% 0.84/0.80 tff(43,plain,
% 0.84/0.80 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))),
% 0.84/0.80 inference(quant_inst,[status(thm)],[])).
% 0.84/0.80 tff(44,plain,
% 0.84/0.80 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(L!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.84/0.80 tff(45,plain,
% 0.84/0.80 (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[44, 35, 25, 11])).
% 0.84/0.80 tff(46,plain,
% 0.84/0.80 ((apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)) | (~apart_point_and_line(intersection_point(L!2, M!1), L!2))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(47,plain,
% 0.84/0.80 (~apart_point_and_line(intersection_point(L!2, M!1), L!2)),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.84/0.80 tff(48,assumption,(apart_point_and_line(intersection_point(L!2, M!1), M!1)), introduced(assumption)).
% 0.84/0.80 tff(49,plain,
% 0.84/0.80 ((apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)) | (~apart_point_and_line(intersection_point(L!2, M!1), M!1))),
% 0.84/0.80 inference(tautology,[status(thm)],[])).
% 0.84/0.80 tff(50,plain,
% 0.84/0.80 (apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.84/0.80 tff(51,assumption,(~distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1))), introduced(assumption)).
% 0.84/0.80 tff(52,plain,
% 0.84/0.80 ($false),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[44, 35, 25, 51, 50])).
% 0.84/0.80 tff(53,plain,(distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~apart_point_and_line(intersection_point(L!2, M!1), M!1))), inference(lemma,lemma(discharge,[]))).
% 0.84/0.80 tff(54,plain,
% 0.84/0.80 (~apart_point_and_line(intersection_point(L!2, M!1), M!1)),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[53, 11])).
% 0.84/0.80 tff(55,plain,
% 0.84/0.80 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(56,plain,
% 0.84/0.80 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[55])).
% 0.84/0.80 tff(57,plain,
% 0.84/0.80 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(58,plain,
% 0.84/0.80 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(59,plain,
% 0.84/0.80 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[58])).
% 0.84/0.80 tff(60,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.84/0.80 tff(61,plain,
% 0.84/0.80 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.84/0.80 tff(62,plain,
% 0.84/0.80 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.84/0.80 tff(63,plain,(
% 0.84/0.80 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.84/0.80 inference(skolemize,[status(sab)],[62])).
% 0.84/0.80 tff(64,plain,
% 0.84/0.80 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.84/0.80 tff(65,plain,
% 0.84/0.80 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(L!2, M!1)) | distinct_lines(L!2, M!1))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(L!2, M!1)) | distinct_lines(L!2, M!1))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(66,plain,
% 0.84/0.80 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(L!2, M!1)) | distinct_lines(L!2, M!1))),
% 0.84/0.80 inference(quant_inst,[status(thm)],[])).
% 0.84/0.80 tff(67,plain,
% 0.84/0.80 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(L!2, M!1)) | distinct_lines(L!2, M!1)),
% 0.84/0.80 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.84/0.80 tff(68,plain,
% 0.84/0.80 (distinct_lines(L!2, M!1)),
% 0.84/0.80 inference(unit_resolution,[status(thm)],[67, 64, 25])).
% 0.84/0.80 tff(69,plain,
% 0.84/0.80 (~unorthogonal_lines(L!2, N!0)),
% 0.84/0.80 inference(or_elim,[status(thm)],[24])).
% 0.84/0.80 tff(70,plain,
% 0.84/0.80 (~unorthogonal_lines(M!1, N!0)),
% 0.84/0.80 inference(or_elim,[status(thm)],[24])).
% 0.84/0.80 tff(71,plain,
% 0.84/0.80 (^[A: $i, L: $i, M: $i, N: $i] : refl((apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))))),
% 0.84/0.80 inference(bind,[status(th)],[])).
% 0.84/0.80 tff(72,plain,
% 0.84/0.80 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.84/0.80 inference(quant_intro,[status(thm)],[71])).
% 0.84/0.80 tff(73,plain,
% 0.84/0.80 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(74,plain,
% 0.84/0.80 (^[A: $i, L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(A, L) | apart_point_and_line(A, M)) <=> (apart_point_and_line(A, M) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> ((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)))), rewrite(((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> ((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)))), rewrite(((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))))), rewrite((distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))))),
% 0.89/0.80 inference(bind,[status(th)],[])).
% 0.89/0.80 tff(75,plain,
% 0.89/0.80 (![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.89/0.80 inference(quant_intro,[status(thm)],[74])).
% 0.89/0.80 tff(76,axiom,(![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax','ouo1')).
% 0.89/0.80 tff(77,plain,
% 0.89/0.80 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.89/0.80 tff(78,plain,
% 0.89/0.80 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.89/0.80 tff(79,plain,(
% 0.89/0.80 ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.89/0.80 inference(skolemize,[status(sab)],[78])).
% 0.89/0.80 tff(80,plain,
% 0.89/0.80 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.89/0.80 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.89/0.80 tff(81,plain,
% 0.89/0.80 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~distinct_lines(L!2, M!1)) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~distinct_lines(L!2, M!1)) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))),
% 0.89/0.81 inference(rewrite,[status(thm)],[])).
% 0.89/0.81 tff(82,plain,
% 0.89/0.81 ((apart_point_and_line(intersection_point(L!2, M!1), M!1) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | apart_point_and_line(intersection_point(L!2, M!1), L!2) | (~distinct_lines(L!2, M!1))) <=> (unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~distinct_lines(L!2, M!1)) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))),
% 0.89/0.81 inference(rewrite,[status(thm)],[])).
% 0.89/0.81 tff(83,plain,
% 0.89/0.81 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(L!2, M!1), M!1) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | apart_point_and_line(intersection_point(L!2, M!1), L!2) | (~distinct_lines(L!2, M!1)))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~distinct_lines(L!2, M!1)) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))),
% 0.89/0.81 inference(monotonicity,[status(thm)],[82])).
% 0.89/0.81 tff(84,plain,
% 0.89/0.81 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(L!2, M!1), M!1) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | apart_point_and_line(intersection_point(L!2, M!1), L!2) | (~distinct_lines(L!2, M!1)))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~distinct_lines(L!2, M!1)) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))),
% 0.89/0.81 inference(transitivity,[status(thm)],[83, 81])).
% 0.89/0.81 tff(85,plain,
% 0.89/0.81 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(L!2, M!1), M!1) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | apart_point_and_line(intersection_point(L!2, M!1), L!2) | (~distinct_lines(L!2, M!1)))),
% 0.89/0.81 inference(quant_inst,[status(thm)],[])).
% 0.89/0.81 tff(86,plain,
% 0.89/0.81 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~distinct_lines(L!2, M!1)) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)),
% 0.89/0.81 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.89/0.81 tff(87,plain,
% 0.89/0.81 ($false),
% 0.89/0.81 inference(unit_resolution,[status(thm)],[86, 80, 70, 69, 68, 54, 47])).
% 0.89/0.81 % SZS output end Proof
%------------------------------------------------------------------------------