TSTP Solution File: GEO182+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO182+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 20:35:21 EDT 2022
% Result : Theorem 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO182+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n026.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Aug 31 07:01:21 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(distinct_points_type, type, (
% 0.18/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.18/0.40 tff(tptp_fun_X_2_type, type, (
% 0.18/0.40 tptp_fun_X_2: $i)).
% 0.18/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.18/0.40 tptp_fun_Y_1: $i)).
% 0.18/0.40 tff(apart_point_and_line_type, type, (
% 0.18/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.18/0.40 tff(line_connecting_type, type, (
% 0.18/0.40 line_connecting: ( $i * $i ) > $i)).
% 0.18/0.40 tff(tptp_fun_Z_0_type, type, (
% 0.18/0.40 tptp_fun_Z_0: $i)).
% 0.18/0.40 tff(distinct_lines_type, type, (
% 0.18/0.40 distinct_lines: ( $i * $i ) > $o)).
% 0.18/0.40 tff(1,assumption,(distinct_points(Y!1, Y!1)), introduced(assumption)).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(5,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.18/0.40 tff(6,plain,
% 0.18/0.40 (![X: $i] : (~distinct_points(X, X))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.40 tff(7,plain,(
% 0.18/0.40 ![X: $i] : (~distinct_points(X, X))),
% 0.18/0.40 inference(skolemize,[status(sab)],[6])).
% 0.18/0.40 tff(8,plain,
% 0.18/0.40 (![X: $i] : (~distinct_points(X, X))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.40 tff(9,plain,
% 0.18/0.40 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Y!1, Y!1))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.40 tff(11,plain,(~distinct_points(Y!1, Y!1)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(12,plain,
% 0.18/0.40 (((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, X!2))) | distinct_points(Y!1, Y!1)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 ((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, X!2))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.18/0.40 tff(14,assumption,(~distinct_points(X!2, X!2)), introduced(assumption)).
% 0.18/0.40 tff(15,plain,
% 0.18/0.40 (((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1))) | distinct_points(X!2, X!2)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(16,plain,
% 0.18/0.40 ((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.18/0.40 tff(17,assumption,(apart_point_and_line(X!2, line_connecting(X!2, Y!1))), introduced(assumption)).
% 0.18/0.40 tff(18,plain,
% 0.18/0.40 ((~(apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> (~(apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(19,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(20,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => apart_point_and_line(Z, line_connecting(Y, X))))) <=> (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(21,axiom,(~![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => apart_point_and_line(Z, line_connecting(Y, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.18/0.40 tff(22,plain,
% 0.18/0.40 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.40 tff(23,plain,
% 0.18/0.40 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.18/0.40 tff(24,plain,
% 0.18/0.40 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.18/0.40 tff(25,plain,
% 0.18/0.40 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.18/0.40 tff(26,plain,
% 0.18/0.40 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.18/0.40 tff(27,plain,
% 0.18/0.40 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.18/0.40 tff(28,plain,
% 0.18/0.40 (~![X: $i, Y: $i, Z: $i] : (apart_point_and_line(Z, line_connecting(Y, X)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.18/0.40 tff(29,plain,(
% 0.18/0.40 ~(apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[28])).
% 0.18/0.40 tff(30,plain,
% 0.18/0.40 (~(apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[29, 18])).
% 0.18/0.40 tff(31,plain,
% 0.18/0.40 (distinct_points(X!2, Y!1)),
% 0.18/0.40 inference(or_elim,[status(thm)],[30])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 (^[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))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 (^[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)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (^[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))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[37])).
% 0.18/0.40 tff(39,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/sandbox/benchmark/Axioms/GEO008+0.ax','con1')).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.18/0.40 tff(42,plain,(
% 0.18/0.40 ![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))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[41])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 (((~![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!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))))) <=> ((~![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!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 ((~![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!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[47, 44, 31, 17, 16])).
% 0.18/0.40 tff(49,plain,((~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | distinct_points(X!2, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(50,plain,
% 0.18/0.40 (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[49, 14])).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1))) | distinct_points(Y!1, Y!1)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 ((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[51, 11])).
% 0.18/0.40 tff(53,assumption,(apart_point_and_line(Y!1, line_connecting(X!2, Y!1))), introduced(assumption)).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 (((~![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!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))) | (~((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1)))))) <=> ((~![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!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))) | (~((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 ((~![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!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))) | (~((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))) | (~((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[56, 44, 31, 53, 52])).
% 0.18/0.40 tff(58,plain,(~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 (((~distinct_points(X!2, Y!1)) | (~distinct_points(X!2, X!2))) | distinct_points(X!2, X!2)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 ((~distinct_points(X!2, Y!1)) | (~distinct_points(X!2, X!2))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[59, 14])).
% 0.18/0.40 tff(61,assumption,(apart_point_and_line(X!2, line_connecting(Y!1, X!2))), introduced(assumption)).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(X, Z) | distinct_points(Y, Z)) <=> (distinct_points(Y, Z) | distinct_points(X, Z))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))))), rewrite((distinct_points(X, Y) => (distinct_points(Y, Z) | distinct_points(X, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))), ((distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.40 tff(67,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart4')).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.18/0.40 tff(70,plain,(
% 0.18/0.40 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[69])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(X!2, Y!1)) | distinct_points(X!2, X!2) | distinct_points(Y!1, X!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | distinct_points(X!2, X!2) | distinct_points(Y!1, X!2))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 ((distinct_points(Y!1, X!2) | distinct_points(X!2, X!2) | (~distinct_points(X!2, Y!1))) <=> ((~distinct_points(X!2, Y!1)) | distinct_points(X!2, X!2) | distinct_points(Y!1, X!2))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, X!2) | distinct_points(X!2, X!2) | (~distinct_points(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(X!2, Y!1)) | distinct_points(X!2, X!2) | distinct_points(Y!1, X!2)))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[73])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, X!2) | distinct_points(X!2, X!2) | (~distinct_points(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | distinct_points(X!2, X!2) | distinct_points(Y!1, X!2))),
% 0.18/0.40 inference(transitivity,[status(thm)],[74, 72])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(Y!1, X!2) | distinct_points(X!2, X!2) | (~distinct_points(X!2, Y!1)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(X!2, Y!1)) | distinct_points(X!2, X!2) | distinct_points(Y!1, X!2)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.41 tff(78,plain,
% 0.18/0.41 (distinct_points(X!2, X!2) | distinct_points(Y!1, X!2)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[77, 71, 31])).
% 0.18/0.41 tff(79,plain,
% 0.18/0.41 (distinct_points(Y!1, X!2)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[78, 14])).
% 0.18/0.41 tff(80,plain,
% 0.18/0.41 (((~![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(Y!1, X!2)) | (~apart_point_and_line(X!2, line_connecting(Y!1, X!2))) | (~((~distinct_points(X!2, Y!1)) | (~distinct_points(X!2, X!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(Y!1, X!2)) | (~apart_point_and_line(X!2, line_connecting(Y!1, X!2))) | (~((~distinct_points(X!2, Y!1)) | (~distinct_points(X!2, X!2)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(81,plain,
% 0.18/0.41 ((~![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(Y!1, X!2)) | (~apart_point_and_line(X!2, line_connecting(Y!1, X!2))) | (~((~distinct_points(X!2, Y!1)) | (~distinct_points(X!2, X!2)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(82,plain,
% 0.18/0.41 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(Y!1, X!2)) | (~apart_point_and_line(X!2, line_connecting(Y!1, X!2))) | (~((~distinct_points(X!2, Y!1)) | (~distinct_points(X!2, X!2))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.41 tff(83,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[82, 44, 79, 61, 60])).
% 0.18/0.41 tff(84,plain,((~apart_point_and_line(X!2, line_connecting(Y!1, X!2))) | distinct_points(X!2, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 (~apart_point_and_line(X!2, line_connecting(Y!1, X!2))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[84, 14])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 (apart_point_and_line(Z!0, line_connecting(X!2, Y!1))),
% 0.18/0.41 inference(or_elim,[status(thm)],[30])).
% 0.18/0.41 tff(87,plain,
% 0.18/0.41 (~apart_point_and_line(Z!0, line_connecting(Y!1, X!2))),
% 0.18/0.41 inference(or_elim,[status(thm)],[30])).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 (^[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))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(89,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[88])).
% 0.18/0.41 tff(90,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(91,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(92,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[91])).
% 0.18/0.41 tff(93,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/sandbox/benchmark/Axioms/GEO008+0.ax','ceq2')).
% 0.18/0.41 tff(94,plain,
% 0.18/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.41 tff(95,plain,
% 0.18/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.18/0.41 tff(96,plain,(
% 0.18/0.41 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.18/0.41 inference(skolemize,[status(sab)],[95])).
% 0.18/0.41 tff(97,plain,
% 0.18/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.18/0.41 tff(98,plain,
% 0.18/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 ((distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2)) | apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1)))) <=> (apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(100,plain,
% 0.18/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2)) | apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[99])).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2)) | apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[100, 98])).
% 0.18/0.41 tff(102,plain,
% 0.18/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2)) | apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(103,plain,
% 0.18/0.41 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | apart_point_and_line(Z!0, line_connecting(Y!1, X!2)) | (~apart_point_and_line(Z!0, line_connecting(X!2, Y!1))) | distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 (distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[103, 97, 87, 86])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 (^[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))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[105])).
% 0.18/0.41 tff(107,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(108,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[107])).
% 0.18/0.41 tff(109,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(110,plain,
% 0.18/0.41 (^[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))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(111,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[110])).
% 0.18/0.41 tff(112,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/sandbox/benchmark/Axioms/GEO008+0.ax','cu1')).
% 0.18/0.41 tff(113,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.18/0.41 tff(114,plain,
% 0.18/0.41 (![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))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.18/0.41 tff(115,plain,(
% 0.18/0.41 ![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))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[114])).
% 0.18/0.41 tff(116,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.18/0.42 tff(117,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.18/0.42 tff(118,plain,
% 0.18/0.42 (((~![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)))) | ((~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2))) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!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)))) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2))) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(119,plain,
% 0.18/0.42 ((apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2)))) <=> ((~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2))) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(120,plain,
% 0.18/0.42 (((~![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(Y!1, line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!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)))) | ((~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2))) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[119])).
% 0.18/0.42 tff(121,plain,
% 0.18/0.42 (((~![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(Y!1, line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!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)))) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2))) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)))),
% 0.18/0.42 inference(transitivity,[status(thm)],[120, 118])).
% 0.18/0.42 tff(122,plain,
% 0.18/0.42 ((~![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(Y!1, line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(123,plain,
% 0.18/0.42 ((~![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)))) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(line_connecting(X!2, Y!1), line_connecting(Y!1, X!2))) | apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.18/0.42 tff(124,plain,
% 0.18/0.42 (apart_point_and_line(X!2, line_connecting(Y!1, X!2)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(Y!1, X!2)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[123, 117, 31, 104])).
% 0.18/0.42 tff(125,plain,
% 0.18/0.42 (apart_point_and_line(Y!1, line_connecting(Y!1, X!2))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[124, 85, 58, 50])).
% 0.18/0.42 tff(126,plain,
% 0.18/0.42 (((~![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(Y!1, X!2)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, X!2))) | (~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, X!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(Y!1, X!2)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, X!2))) | (~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, X!2)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(127,plain,
% 0.18/0.42 ((~![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(Y!1, X!2)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, X!2))) | (~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, X!2)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(128,plain,
% 0.18/0.42 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(Y!1, X!2)) | (~apart_point_and_line(Y!1, line_connecting(Y!1, X!2))) | (~((~distinct_points(Y!1, Y!1)) | (~distinct_points(Y!1, X!2))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.18/0.42 tff(129,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[128, 44, 79, 125, 13])).
% 0.18/0.42 tff(130,plain,(distinct_points(X!2, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(131,plain,
% 0.18/0.42 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(X!2, X!2))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(132,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[131, 8, 130])).
% 0.18/0.42 % SZS output end Proof
%------------------------------------------------------------------------------