%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO187+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 : Sat Jun 21 05:05:49 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO187+2 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n009.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 : Thu Jun 19 14:40:18 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(apart_point_and_line_type, type, (
% 0.12/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.38 tff(line_connecting_type, type, (
% 0.12/0.38 line_connecting: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_Y_2_type, type, (
% 0.12/0.38 tptp_fun_Y_2: $i)).
% 0.12/0.38 tff(tptp_fun_X_3_type, type, (
% 0.12/0.38 tptp_fun_X_3: $i)).
% 0.12/0.38 tff(tptp_fun_U_1_type, type, (
% 0.12/0.38 tptp_fun_U_1: $i)).
% 0.12/0.38 tff(distinct_lines_type, type, (
% 0.12/0.38 distinct_lines: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_V_0_type, type, (
% 0.12/0.38 tptp_fun_V_0: $i)).
% 0.12/0.38 tff(distinct_points_type, type, (
% 0.12/0.38 distinct_points: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X: $i] : (~distinct_points(X, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,(
% 0.12/0.38 ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.38 inference(skolemize,[status(sab)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![X: $i] : (~distinct_points(X, X))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Y!2, Y!2))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~distinct_points(Y!2, Y!2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))) | distinct_points(Y!2, Y!2)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.12/0.38 tff(12,assumption,(apart_point_and_line(Y!2, line_connecting(X!3, Y!2))), introduced(assumption)).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ((~![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] : ((~(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))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 ((~![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] : ((~(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))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(15,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/sandbox/benchmark/theBenchmark.p','con')).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (~![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)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (~![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)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (~![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)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (~![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)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.12/0.38 tff(20,plain,(
% 0.12/0.38 ~((~(distinct_points(X!3, Y!2) & distinct_points(U!1, V!0) & (~apart_point_and_line(X!3, line_connecting(U!1, V!0))) & (~apart_point_and_line(Y!2, line_connecting(U!1, V!0))))) | ((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) & (~apart_point_and_line(V!0, line_connecting(X!3, Y!2)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (distinct_points(X!3, Y!2) & distinct_points(U!1, V!0) & (~apart_point_and_line(X!3, line_connecting(U!1, V!0))) & (~apart_point_and_line(Y!2, line_connecting(U!1, V!0)))),
% 0.12/0.38 inference(or_elim,[status(thm)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (distinct_points(X!3, Y!2)),
% 0.12/0.38 inference(and_elim,[status(thm)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (^[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))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![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)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (^[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)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (![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)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.12/0.39 tff(30,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')).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.12/0.39 tff(33,plain,(
% 0.12/0.39 ![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))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[32])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[34, 24])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (((~![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)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 ((~![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)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))) | (~((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 35, 22, 12, 11])).
% 0.12/0.39 tff(40,plain,(~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(X!3, X!3))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (~distinct_points(X!3, X!3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[41, 7])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2))) | distinct_points(X!3, X!3)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 ((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.12/0.39 tff(45,assumption,(apart_point_and_line(X!3, line_connecting(X!3, Y!2))), introduced(assumption)).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (((~![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)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 ((~![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)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))) | (~((~distinct_points(X!3, X!3)) | (~distinct_points(X!3, Y!2))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[48, 35, 22, 45, 44])).
% 0.12/0.39 tff(50,plain,(~apart_point_and_line(X!3, line_connecting(X!3, Y!2))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (~apart_point_and_line(Y!2, line_connecting(U!1, V!0))),
% 0.12/0.39 inference(and_elim,[status(thm)],[21])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (~apart_point_and_line(X!3, line_connecting(U!1, V!0))),
% 0.12/0.39 inference(and_elim,[status(thm)],[21])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (^[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)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.18/0.39 tff(60,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')).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.18/0.39 tff(63,plain,(
% 0.18/0.39 ![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))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[62])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 (((~![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(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | (~distinct_points(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))) | apart_point_and_line(Y!2, 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(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | (~distinct_points(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 ((apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, 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(X!3, Y!2)) | (~distinct_points(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)))) <=> (apart_point_and_line(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | (~distinct_points(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 (((~![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!2, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, 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(X!3, Y!2)) | (~distinct_points(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))))) <=> ((~![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(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | (~distinct_points(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[67])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 (((~![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!2, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, 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(X!3, Y!2)) | (~distinct_points(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))))) <=> ((~![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(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | (~distinct_points(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[68, 66])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 ((~![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!2, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, 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(X!3, Y!2)) | (~distinct_points(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.40 ((~![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(X!3, line_connecting(U!1, V!0)) | apart_point_and_line(Y!2, line_connecting(U!1, V!0)) | (~distinct_points(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[71, 65, 22, 52, 51])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (~distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[72, 50, 40])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(U!1, U!1))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (~distinct_points(U!1, U!1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[74, 7])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 (((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0))) | distinct_points(U!1, U!1)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 ((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.18/0.40 tff(78,assumption,(apart_point_and_line(U!1, line_connecting(U!1, V!0))), introduced(assumption)).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 (distinct_points(U!1, V!0)),
% 0.18/0.40 inference(and_elim,[status(thm)],[21])).
% 0.18/0.40 tff(80,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(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)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(81,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(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)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(U!1, V!0))) | (~((~distinct_points(U!1, U!1)) | (~distinct_points(U!1, V!0))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[82, 35, 79, 78, 77])).
% 0.18/0.40 tff(84,plain,(~apart_point_and_line(U!1, line_connecting(U!1, V!0))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 (^[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))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[85])).
% 0.18/0.40 tff(87,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(88,plain,
% 0.18/0.40 (^[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)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[88])).
% 0.18/0.40 tff(90,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')).
% 0.18/0.40 tff(91,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.18/0.40 tff(93,plain,(
% 0.18/0.40 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[92])).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 (((~![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(U!1, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, 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(U!1, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 ((distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(X!3, Y!2)))) <=> ((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (((~![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!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | (~apart_point_and_line(U!1, 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(U!1, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[96])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (((~![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!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | (~apart_point_and_line(U!1, 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(U!1, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[97, 95])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 ((~![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!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0)) | (~apart_point_and_line(U!1, line_connecting(X!3, Y!2))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 ((~![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(U!1, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 ((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(U!1, line_connecting(U!1, V!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[100, 94])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 ((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[101, 84])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 (~apart_point_and_line(U!1, line_connecting(X!3, Y!2))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[102, 73])).
% 0.18/0.40 tff(104,assumption,(distinct_points(V!0, V!0)), introduced(assumption)).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(V!0, V!0))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[105, 7, 104])).
% 0.18/0.40 tff(107,plain,(~distinct_points(V!0, V!0)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(108,plain,
% 0.18/0.40 (((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0))) | distinct_points(V!0, V!0)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(109,plain,
% 0.18/0.40 ((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.18/0.40 tff(110,assumption,(apart_point_and_line(V!0, line_connecting(U!1, V!0))), introduced(assumption)).
% 0.18/0.40 tff(111,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(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)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(112,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(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)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(113,plain,
% 0.18/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(U!1, V!0))) | (~((~distinct_points(V!0, U!1)) | (~distinct_points(V!0, V!0))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.18/0.40 tff(114,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[113, 35, 79, 110, 109])).
% 0.18/0.40 tff(115,plain,(~apart_point_and_line(V!0, line_connecting(U!1, V!0))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(116,plain,
% 0.18/0.40 (((~![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(V!0, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, 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(V!0, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(117,plain,
% 0.18/0.40 ((distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, 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(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(118,plain,
% 0.18/0.40 (((~![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!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~apart_point_and_line(V!0, 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(V!0, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[117])).
% 0.18/0.40 tff(119,plain,
% 0.18/0.40 (((~![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!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~apart_point_and_line(V!0, 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(V!0, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[118, 116])).
% 0.18/0.40 tff(120,plain,
% 0.18/0.40 ((~![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!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0)) | (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(121,plain,
% 0.18/0.40 ((~![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(V!0, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.18/0.40 tff(122,plain,
% 0.18/0.40 ((~apart_point_and_line(V!0, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0)) | apart_point_and_line(V!0, line_connecting(U!1, V!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[121, 94])).
% 0.18/0.40 tff(123,plain,
% 0.18/0.40 ((~apart_point_and_line(V!0, line_connecting(X!3, Y!2))) | distinct_lines(line_connecting(X!3, Y!2), line_connecting(U!1, V!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[122, 115])).
% 0.18/0.40 tff(124,plain,
% 0.18/0.40 (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[123, 73])).
% 0.18/0.40 tff(125,plain,
% 0.18/0.40 ((~(~(apart_point_and_line(U!1, 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)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 (((~apart_point_and_line(U!1, 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)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(127,plain,
% 0.18/0.41 ((~((~apart_point_and_line(U!1, 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)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[126])).
% 0.18/0.41 tff(128,plain,
% 0.18/0.41 ((~((~apart_point_and_line(U!1, 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)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[127, 125])).
% 0.18/0.41 tff(129,plain,
% 0.18/0.41 (~((~apart_point_and_line(U!1, line_connecting(X!3, Y!2))) & (~apart_point_and_line(V!0, line_connecting(X!3, Y!2))))),
% 0.18/0.41 inference(or_elim,[status(thm)],[20])).
% 0.18/0.41 tff(130,plain,
% 0.18/0.41 (apart_point_and_line(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(V!0, line_connecting(X!3, Y!2))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[130, 124, 103])).
% 0.18/0.41 % SZS output end Proof
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------