TSTP Solution File: GEO174+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO174+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 20:35:15 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO174+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 06:30:01 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(distinct_points_type, type, (
% 0.21/0.44 distinct_points: ( $i * $i ) > $o)).
% 0.21/0.44 tff(tptp_fun_Y_2_type, type, (
% 0.21/0.44 tptp_fun_Y_2: $i)).
% 0.21/0.44 tff(tptp_fun_X_3_type, type, (
% 0.21/0.44 tptp_fun_X_3: $i)).
% 0.21/0.44 tff(apart_point_and_line_type, type, (
% 0.21/0.44 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.44 tff(line_connecting_type, type, (
% 0.21/0.44 line_connecting: ( $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_U_1_type, type, (
% 0.21/0.44 tptp_fun_U_1: $i)).
% 0.21/0.44 tff(convergent_lines_type, type, (
% 0.21/0.44 convergent_lines: ( $i * $i ) > $o)).
% 0.21/0.44 tff(tptp_fun_V_0_type, type, (
% 0.21/0.44 tptp_fun_V_0: $i)).
% 0.21/0.44 tff(distinct_lines_type, type, (
% 0.21/0.44 distinct_lines: ( $i * $i ) > $o)).
% 0.21/0.44 tff(1,assumption,(distinct_points(X!3, X!3)), introduced(assumption)).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.21/0.44 tff(6,plain,
% 0.21/0.44 (![X: $i] : (~distinct_points(X, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.44 tff(7,plain,(
% 0.21/0.44 ![X: $i] : (~distinct_points(X, X))),
% 0.21/0.44 inference(skolemize,[status(sab)],[6])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (![X: $i] : (~distinct_points(X, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(X!3, X!3))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.44 tff(11,plain,(~distinct_points(X!3, X!3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2))) | distinct_points(X!3, X!3)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 ((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.21/0.44 tff(14,assumption,(distinct_points(Y!2, Y!2)), introduced(assumption)).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Y!2, Y!2))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[15, 8, 14])).
% 0.21/0.44 tff(17,plain,(~distinct_points(Y!2, Y!2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))) | distinct_points(Y!2, Y!2)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 ((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.21/0.44 tff(20,assumption,(apart_point_and_line(Y!2, line_connecting(X!3, Y!2))), introduced(assumption)).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 ((distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1))) <=> (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(22,plain,
% 0.21/0.44 ((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) <=> (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[21])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2))) <=> ((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 ((~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)))) <=> (~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(26,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(X, U) | apart_point_and_line(Y, U))) => distinct_lines(U, line_connecting(X, Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(27,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(X, U) | apart_point_and_line(Y, U))) => distinct_lines(U, line_connecting(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.21/0.44 tff(30,plain,
% 0.21/0.44 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.21/0.44 tff(35,plain,(
% 0.21/0.44 ~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[34])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[35, 24])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1))),
% 0.21/0.44 inference(or_elim,[status(thm)],[36])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (distinct_points(X!3, Y!2)),
% 0.21/0.44 inference(and_elim,[status(thm)],[37])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (^[X: $i, Y: $i, Z: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(Z, X) & distinct_points(Z, Y)) <=> (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))), rewrite(((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))) <=> ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> (distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))))), rewrite((distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.44 tff(46,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con1')).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.44 tff(49,plain,(
% 0.21/0.44 ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[48])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))) | (~((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))) | (~((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))) | (~((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))) | (~((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[54, 51, 38, 20, 19])).
% 0.21/0.44 tff(56,plain,(~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (~distinct_lines(U!1, line_connecting(X!3, Y!2))),
% 0.21/0.44 inference(or_elim,[status(thm)],[36])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 (^[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)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.45 tff(63,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/GEO008+0.ax','ceq2')).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.21/0.45 tff(66,plain,(
% 0.21/0.45 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[65])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.21/0.45 tff(68,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 ((distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1))) <=> (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[69])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[70, 68])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 ((~apart_point_and_line(Y!2, U!1)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[73, 67, 57])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (~apart_point_and_line(Y!2, U!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[74, 56])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)),
% 0.21/0.45 inference(and_elim,[status(thm)],[37])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (apart_point_and_line(X!3, U!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 ((distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1))) <=> (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[80, 78])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 ((~apart_point_and_line(X!3, U!1)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[83, 67, 57])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[84, 77])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))) | (~((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))) | (~((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))) | (~((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))) | (~((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[88, 51, 38, 85, 13])).
% 0.21/0.45 % SZS output end Proof
%------------------------------------------------------------------------------