TSTP Solution File: GEO177+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO177+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 20:35:18 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : GEO177+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n006.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 06:44:09 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35 Usage: tptp [options] [-file:]file
% 0.19/0.35 -h, -? prints this message.
% 0.19/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.35 -m, -model generate model.
% 0.19/0.35 -p, -proof generate proof.
% 0.19/0.35 -c, -core generate unsat core of named formulas.
% 0.19/0.35 -st, -statistics display statistics.
% 0.19/0.35 -t:timeout set timeout (in second).
% 0.19/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35 -<param>:<value> configuration parameter and value.
% 0.19/0.35 -o:<output-file> file to place output in.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(distinct_points_type, type, (
% 0.19/0.46 distinct_points: ( $i * $i ) > $o)).
% 0.19/0.46 tff(tptp_fun_V_0_type, type, (
% 0.19/0.46 tptp_fun_V_0: $i)).
% 0.19/0.46 tff(apart_point_and_line_type, type, (
% 0.19/0.46 apart_point_and_line: ( $i * $i ) > $o)).
% 0.19/0.46 tff(line_connecting_type, type, (
% 0.19/0.46 line_connecting: ( $i * $i ) > $i)).
% 0.19/0.46 tff(tptp_fun_U_1_type, type, (
% 0.19/0.46 tptp_fun_U_1: $i)).
% 0.19/0.46 tff(distinct_lines_type, type, (
% 0.19/0.46 distinct_lines: ( $i * $i ) > $o)).
% 0.19/0.46 tff(tptp_fun_Y_2_type, type, (
% 0.19/0.46 tptp_fun_Y_2: $i)).
% 0.19/0.46 tff(tptp_fun_X_3_type, type, (
% 0.19/0.46 tptp_fun_X_3: $i)).
% 0.19/0.46 tff(1,assumption,(~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))), introduced(assumption)).
% 0.19/0.46 tff(2,assumption,(distinct_points(Y!2, Y!2)), introduced(assumption)).
% 0.19/0.46 tff(3,plain,
% 0.19/0.46 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(4,plain,
% 0.19/0.46 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.46 tff(5,plain,
% 0.19/0.46 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(6,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.19/0.46 tff(7,plain,
% 0.19/0.46 (![X: $i] : (~distinct_points(X, X))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.46 tff(8,plain,(
% 0.19/0.46 ![X: $i] : (~distinct_points(X, X))),
% 0.19/0.46 inference(skolemize,[status(sab)],[7])).
% 0.19/0.46 tff(9,plain,
% 0.19/0.46 (![X: $i] : (~distinct_points(X, X))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.46 tff(10,plain,
% 0.19/0.46 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Y!2, Y!2))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(11,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.19/0.46 tff(12,plain,(~distinct_points(Y!2, Y!2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(13,plain,
% 0.19/0.46 (((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))) | distinct_points(Y!2, Y!2)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 ((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.19/0.46 tff(15,assumption,(apart_point_and_line(Y!2, line_connecting(X!3, Y!2))), introduced(assumption)).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 ((~(apart_point_and_line(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | (~(apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | apart_point_and_line(X!3, line_connecting(U!1, V!0)))) | (~(distinct_points(X!3, Y!2) & distinct_points(U!1, V!0))))) <=> (~(apart_point_and_line(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | (~(apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | apart_point_and_line(X!3, line_connecting(U!1, V!0)))) | (~(distinct_points(X!3, Y!2) & distinct_points(U!1, V!0)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(V, line_connecting(X, Y)) | apart_point_and_line(U, line_connecting(X, Y)) | (~(apart_point_and_line(Y, line_connecting(U, V)) | apart_point_and_line(X, line_connecting(U, V)))) | (~(distinct_points(X, Y) & distinct_points(U, V))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(V, line_connecting(X, Y)) | apart_point_and_line(U, line_connecting(X, Y)) | (~(apart_point_and_line(Y, line_connecting(U, V)) | apart_point_and_line(X, line_connecting(U, V)))) | (~(distinct_points(X, Y) & distinct_points(U, V)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(18,plain,
% 0.19/0.46 ((~![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_points(U, V)) => ((apart_point_and_line(X, line_connecting(U, V)) | apart_point_and_line(Y, line_connecting(U, V))) => (apart_point_and_line(U, line_connecting(X, Y)) | apart_point_and_line(V, line_connecting(X, Y)))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(V, line_connecting(X, Y)) | apart_point_and_line(U, line_connecting(X, Y)) | (~(apart_point_and_line(Y, line_connecting(U, V)) | apart_point_and_line(X, line_connecting(U, V)))) | (~(distinct_points(X, Y) & distinct_points(U, V)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(19,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_points(U, V)) => ((apart_point_and_line(X, line_connecting(U, V)) | apart_point_and_line(Y, line_connecting(U, V))) => (apart_point_and_line(U, line_connecting(X, Y)) | apart_point_and_line(V, line_connecting(X, Y)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.19/0.47 tff(20,plain,
% 0.19/0.47 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(V, line_connecting(X, Y)) | apart_point_and_line(U, line_connecting(X, Y)) | (~(apart_point_and_line(Y, line_connecting(U, V)) | apart_point_and_line(X, line_connecting(U, V)))) | (~(distinct_points(X, Y) & distinct_points(U, V))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.47 tff(21,plain,
% 0.19/0.47 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(V, line_connecting(X, Y)) | apart_point_and_line(U, line_connecting(X, Y)) | (~(apart_point_and_line(Y, line_connecting(U, V)) | apart_point_and_line(X, line_connecting(U, V)))) | (~(distinct_points(X, Y) & distinct_points(U, V))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.19/0.47 tff(22,plain,
% 0.19/0.47 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(V, line_connecting(X, Y)) | apart_point_and_line(U, line_connecting(X, Y)) | (~(apart_point_and_line(Y, line_connecting(U, V)) | apart_point_and_line(X, line_connecting(U, V)))) | (~(distinct_points(X, Y) & distinct_points(U, V))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.47 tff(23,plain,
% 0.19/0.47 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(V, line_connecting(X, Y)) | apart_point_and_line(U, line_connecting(X, Y)) | (~(apart_point_and_line(Y, line_connecting(U, V)) | apart_point_and_line(X, line_connecting(U, V)))) | (~(distinct_points(X, Y) & distinct_points(U, V))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.19/0.47 tff(24,plain,
% 0.19/0.47 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(V, line_connecting(X, Y)) | apart_point_and_line(U, line_connecting(X, Y)) | (~(apart_point_and_line(Y, line_connecting(U, V)) | apart_point_and_line(X, line_connecting(U, V)))) | (~(distinct_points(X, Y) & distinct_points(U, V))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[23, 17])).
% 0.19/0.47 tff(25,plain,
% 0.19/0.47 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(V, line_connecting(X, Y)) | apart_point_and_line(U, line_connecting(X, Y)) | (~(apart_point_and_line(Y, line_connecting(U, V)) | apart_point_and_line(X, line_connecting(U, V)))) | (~(distinct_points(X, Y) & distinct_points(U, V))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.47 tff(26,plain,
% 0.19/0.47 (~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(V, line_connecting(X, Y)) | apart_point_and_line(U, line_connecting(X, Y)) | (~(apart_point_and_line(Y, line_connecting(U, V)) | apart_point_and_line(X, line_connecting(U, V)))) | (~(distinct_points(X, Y) & distinct_points(U, V))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.19/0.47 tff(27,plain,(
% 0.19/0.47 ~(apart_point_and_line(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | (~(apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | apart_point_and_line(X!3, line_connecting(U!1, V!0)))) | (~(distinct_points(X!3, Y!2) & distinct_points(U!1, V!0))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[26])).
% 0.19/0.47 tff(28,plain,
% 0.19/0.47 (~(apart_point_and_line(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | (~(apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | apart_point_and_line(X!3, line_connecting(U!1, V!0)))) | (~(distinct_points(X!3, Y!2) & distinct_points(U!1, V!0))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[27, 16])).
% 0.19/0.47 tff(29,plain,
% 0.19/0.47 (distinct_points(X!3, Y!2) & distinct_points(U!1, V!0)),
% 0.19/0.47 inference(or_elim,[status(thm)],[28])).
% 0.19/0.47 tff(30,plain,
% 0.19/0.47 (distinct_points(X!3, Y!2)),
% 0.19/0.47 inference(and_elim,[status(thm)],[29])).
% 0.19/0.47 tff(31,plain,
% 0.19/0.47 (^[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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(32,plain,
% 0.19/0.47 (![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)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.47 tff(33,plain,
% 0.19/0.47 (^[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)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(34,plain,
% 0.19/0.47 (![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)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.47 tff(35,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(36,plain,
% 0.19/0.47 (^[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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(37,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.47 tff(38,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')).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.47 tff(41,plain,(
% 0.19/0.47 ![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))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[40])).
% 0.19/0.47 tff(42,plain,
% 0.19/0.47 (![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)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 (![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)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 (((~![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)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 ((~![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)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(46,plain,
% 0.19/0.47 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))) | (~((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[46, 43, 30, 15, 14])).
% 0.19/0.47 tff(48,plain,(~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(49,plain,
% 0.19/0.47 (^[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))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(52,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.47 tff(54,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')).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.47 tff(56,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.47 tff(57,plain,(
% 0.19/0.47 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[56])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.19/0.47 tff(59,plain,
% 0.19/0.47 (((~![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(Y!2, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | 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)))) | (~apart_point_and_line(Y!2, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(60,plain,
% 0.19/0.47 ((distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(U!1, V!0)))) <=> ((~apart_point_and_line(Y!2, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 (((~![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(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(U!1, V!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(Y!2, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.47 tff(62,plain,
% 0.19/0.47 (((~![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(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(U!1, V!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(Y!2, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[61, 59])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 ((~![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(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(U!1, V!0))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 ((~![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(Y!2, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 ((~apart_point_and_line(Y!2, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[64, 58])).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 ((~apart_point_and_line(Y!2, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[65, 48])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 (~apart_point_and_line(Y!2, line_connecting(U!1, V!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[66, 1])).
% 0.19/0.47 tff(68,assumption,(distinct_points(X!3, X!3)), introduced(assumption)).
% 0.19/0.47 tff(69,plain,
% 0.19/0.47 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(X!3, X!3))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(70,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[69, 9, 68])).
% 0.19/0.47 tff(71,plain,(~distinct_points(X!3, X!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(72,plain,
% 0.19/0.47 (((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2))) | distinct_points(X!3, X!3)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 ((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.47 tff(74,assumption,(apart_point_and_line(X!3, line_connecting(X!3, Y!2))), introduced(assumption)).
% 0.19/0.48 tff(75,plain,
% 0.19/0.48 (((~![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)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(76,plain,
% 0.19/0.48 ((~![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)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(77,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))) | (~((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.48 tff(78,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[77, 43, 30, 74, 73])).
% 0.19/0.48 tff(79,plain,(~apart_point_and_line(X!3, line_connecting(X!3, Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(80,plain,
% 0.19/0.48 (((~![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(X!3, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | 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)))) | (~apart_point_and_line(X!3, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(81,plain,
% 0.19/0.48 ((distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(U!1, V!0)))) <=> ((~apart_point_and_line(X!3, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(82,plain,
% 0.19/0.48 (((~![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(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(U!1, V!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | ((~apart_point_and_line(X!3, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.48 tff(83,plain,
% 0.19/0.48 (((~![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(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(U!1, V!0))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(X!3, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.48 tff(84,plain,
% 0.19/0.48 ((~![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(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(U!1, V!0))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(85,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (~apart_point_and_line(X!3, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.48 tff(86,plain,
% 0.19/0.48 ((~apart_point_and_line(X!3, line_connecting(U!1, V!0))) | distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[85, 58])).
% 0.19/0.48 tff(87,plain,
% 0.19/0.48 (~apart_point_and_line(X!3, line_connecting(U!1, V!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[86, 1, 79])).
% 0.19/0.48 tff(88,plain,
% 0.19/0.48 (apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | apart_point_and_line(X!3, line_connecting(U!1, V!0))),
% 0.19/0.48 inference(or_elim,[status(thm)],[28])).
% 0.19/0.48 tff(89,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[88, 87, 67])).
% 0.19/0.48 tff(90,plain,(distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(91,assumption,(~distinct_points(V!0, U!1)), introduced(assumption)).
% 0.19/0.48 tff(92,assumption,(distinct_points(U!1, U!1)), introduced(assumption)).
% 0.19/0.48 tff(93,plain,
% 0.19/0.48 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(U!1, U!1))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(94,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[93, 9, 92])).
% 0.19/0.48 tff(95,plain,(~distinct_points(U!1, U!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(96,plain,
% 0.19/0.48 (distinct_points(U!1, V!0)),
% 0.19/0.48 inference(and_elim,[status(thm)],[29])).
% 0.19/0.48 tff(97,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(98,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.48 tff(99,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(100,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(101,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.48 tff(102,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (distinct_points(X, Z) | distinct_points(Y, Z)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart4')).
% 0.19/0.48 tff(103,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.48 tff(104,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.19/0.48 tff(105,plain,(
% 0.19/0.48 ![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[104])).
% 0.19/0.48 tff(106,plain,
% 0.19/0.48 (![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(U!1, V!0)) | distinct_points(U!1, U!1) | distinct_points(V!0, U!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(U!1, V!0)) | distinct_points(U!1, U!1) | distinct_points(V!0, U!1))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 ((distinct_points(V!0, U!1) | distinct_points(U!1, U!1) | (~distinct_points(U!1, V!0))) <=> ((~distinct_points(U!1, V!0)) | distinct_points(U!1, U!1) | distinct_points(V!0, U!1))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(V!0, U!1) | distinct_points(U!1, U!1) | (~distinct_points(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | ((~distinct_points(U!1, V!0)) | distinct_points(U!1, U!1) | distinct_points(V!0, U!1)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(V!0, U!1) | distinct_points(U!1, U!1) | (~distinct_points(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(U!1, V!0)) | distinct_points(U!1, U!1) | distinct_points(V!0, U!1))),
% 0.19/0.48 inference(transitivity,[status(thm)],[109, 107])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (distinct_points(V!0, U!1) | distinct_points(U!1, U!1) | (~distinct_points(U!1, V!0)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Y, Z) | distinct_points(X, Z) | (~distinct_points(X, Y)))) | (~distinct_points(U!1, V!0)) | distinct_points(U!1, U!1) | distinct_points(V!0, U!1)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[112, 106, 96, 95, 91])).
% 0.19/0.48 tff(114,plain,(distinct_points(V!0, U!1)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(115,plain,
% 0.19/0.48 (((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0))) | distinct_points(U!1, U!1)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 ((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[115, 95])).
% 0.19/0.48 tff(117,assumption,(apart_point_and_line(U!1, line_connecting(U!1, V!0))), introduced(assumption)).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 (((~![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(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0))) | (~((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0)))))) <=> ((~![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(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0))) | (~((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(119,plain,
% 0.19/0.48 ((~![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(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0))) | (~((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(120,plain,
% 0.19/0.48 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0))) | (~((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.48 tff(121,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[120, 43, 96, 117, 116])).
% 0.19/0.48 tff(122,plain,(~apart_point_and_line(U!1, line_connecting(U!1, V!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(123,plain,
% 0.19/0.48 (~apart_point_and_line(U!1, line_connecting(X!3, Y!2))),
% 0.19/0.48 inference(or_elim,[status(thm)],[28])).
% 0.19/0.48 tff(124,plain,
% 0.19/0.48 (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))),
% 0.19/0.48 inference(or_elim,[status(thm)],[28])).
% 0.19/0.48 tff(125,plain,
% 0.19/0.48 (^[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))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(126,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[125])).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(128,plain,
% 0.19/0.48 (![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)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[127])).
% 0.19/0.48 tff(129,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(130,plain,
% 0.19/0.48 (^[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))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(131,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.49 tff(132,axiom,(![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','cu1')).
% 0.19/0.49 tff(133,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.49 tff(134,plain,
% 0.19/0.49 (![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))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.19/0.49 tff(135,plain,(
% 0.19/0.49 ![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))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[134])).
% 0.19/0.49 tff(136,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.19/0.49 tff(137,plain,
% 0.19/0.49 (![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)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[136, 126])).
% 0.19/0.49 tff(138,plain,
% 0.19/0.49 (((~![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(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~distinct_points(V!0, U!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~distinct_points(V!0, U!1)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(139,plain,
% 0.19/0.49 ((apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~distinct_points(V!0, U!1)) | (~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2)))) <=> (apart_point_and_line(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~distinct_points(V!0, U!1)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(140,plain,
% 0.19/0.49 (((~![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(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~distinct_points(V!0, U!1)) | (~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~distinct_points(V!0, U!1))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[139])).
% 0.19/0.49 tff(141,plain,
% 0.19/0.49 (((~![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(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~distinct_points(V!0, U!1)) | (~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | apart_point_and_line(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~distinct_points(V!0, U!1)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[140, 138])).
% 0.19/0.49 tff(142,plain,
% 0.19/0.49 ((~![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(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~distinct_points(V!0, U!1)) | (~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(143,plain,
% 0.19/0.50 ((~![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(V!0, line_connecting(X!3, Y!2)) | apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~distinct_points(V!0, U!1))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.50 tff(144,plain,
% 0.19/0.50 ((~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~distinct_points(V!0, U!1))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[143, 137, 124, 123, 122])).
% 0.19/0.50 tff(145,plain,
% 0.19/0.50 ((~distinct_lines(line_connecting(U!1, V!0), line_connecting(X!3, Y!2))) | apart_point_and_line(V!0, line_connecting(U!1, V!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[144, 114])).
% 0.19/0.50 tff(146,plain,
% 0.19/0.50 (apart_point_and_line(V!0, line_connecting(U!1, V!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[145, 90])).
% 0.19/0.50 tff(147,assumption,(~distinct_points(V!0, V!0)), introduced(assumption)).
% 0.19/0.50 tff(148,plain,
% 0.19/0.50 (((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0))) | distinct_points(V!0, V!0)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(149,plain,
% 0.19/0.50 ((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.19/0.50 tff(150,assumption,(apart_point_and_line(V!0, line_connecting(U!1, V!0))), introduced(assumption)).
% 0.19/0.50 tff(151,plain,
% 0.19/0.50 (((~![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(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0))) | (~((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0)))))) <=> ((~![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(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0))) | (~((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(152,plain,
% 0.19/0.50 ((~![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(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0))) | (~((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(153,plain,
% 0.19/0.50 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0))) | (~((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.50 tff(154,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[153, 43, 96, 150, 149])).
% 0.19/0.50 tff(155,plain,((~apart_point_and_line(V!0, line_connecting(U!1, V!0))) | distinct_points(V!0, V!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(156,plain,
% 0.19/0.50 (distinct_points(V!0, V!0)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[155, 146])).
% 0.19/0.50 tff(157,plain,
% 0.19/0.50 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(V!0, V!0))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(158,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[157, 9, 156])).
% 0.19/0.50 % SZS output end Proof
%------------------------------------------------------------------------------