%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO174+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 05:05:45 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO174+2 : TPTP v9.0.0. Released v3.3.0.
% 0.10/0.11 % 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 14:39:33 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(distinct_points_type, type, (
% 0.12/0.39 distinct_points: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_Y_2_type, type, (
% 0.12/0.39 tptp_fun_Y_2: $i)).
% 0.12/0.39 tff(tptp_fun_X_3_type, type, (
% 0.12/0.39 tptp_fun_X_3: $i)).
% 0.12/0.39 tff(apart_point_and_line_type, type, (
% 0.12/0.39 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.39 tff(line_connecting_type, type, (
% 0.12/0.39 line_connecting: ( $i * $i ) > $i)).
% 0.12/0.39 tff(distinct_lines_type, type, (
% 0.12/0.39 distinct_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_U_1_type, type, (
% 0.12/0.39 tptp_fun_U_1: $i)).
% 0.12/0.39 tff(convergent_lines_type, type, (
% 0.12/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_V_0_type, type, (
% 0.12/0.39 tptp_fun_V_0: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![X: $i] : (~distinct_points(X, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.39 tff(6,plain,(
% 0.12/0.39 ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.39 inference(skolemize,[status(sab)],[5])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![X: $i] : (~distinct_points(X, X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Y!2, Y!2))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~distinct_points(Y!2, Y!2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))) | distinct_points(Y!2, Y!2)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 ((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 ((distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1))) <=> (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 ((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) <=> (~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2))) <=> ((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 ((~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)))) <=> (~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[14])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 ((~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(X, U) | apart_point_and_line(Y, U))) => distinct_lines(U, line_connecting(X, Y)))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(18,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (apart_point_and_line(X, U) | apart_point_and_line(Y, U))) => distinct_lines(U, line_connecting(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (apart_point_and_line(Y, U) | apart_point_and_line(X, U)))) | distinct_lines(U, line_connecting(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.12/0.39 tff(23,plain,(
% 0.12/0.39 ~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (~distinct_lines(U!1, line_connecting(X!3, Y!2))),
% 0.12/0.39 inference(or_elim,[status(thm)],[24])).
% 0.12/0.39 tff(26,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(27,plain,
% 0.12/0.39 (~distinct_points(X!3, X!3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[26, 7])).
% 0.12/0.39 tff(28,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(29,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)],[28, 27])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1))),
% 0.12/0.39 inference(or_elim,[status(thm)],[24])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (distinct_points(X!3, Y!2)),
% 0.12/0.39 inference(and_elim,[status(thm)],[30])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(33,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(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (^[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)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(35,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)))) <=> ![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(quant_intro,[status(thm)],[34])).
% 0.12/0.39 tff(36,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)))) <=> ![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(37,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(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)))) <=> ![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)],[37])).
% 0.12/0.39 tff(39,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','con1')).
% 0.12/0.39 tff(40,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)],[39, 38])).
% 0.12/0.39 tff(41,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)],[40, 36])).
% 0.12/0.39 tff(42,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)],[41])).
% 0.12/0.39 tff(43,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)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!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)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!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)))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (~apart_point_and_line(X!3, line_connecting(X!3, Y!2))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[47, 44, 31, 29])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (^[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))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (^[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)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![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)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.40 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/sandbox/benchmark/Axioms/GEO008+0.ax','ceq2')).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.12/0.40 tff(57,plain,(
% 0.12/0.40 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[56])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(X!3, line_connecting(X!3, Y!2)) | (~apart_point_and_line(X!3, U!1))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (~apart_point_and_line(X!3, U!1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[61, 58, 25, 48])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (apart_point_and_line(Y!2, U!1) | apart_point_and_line(X!3, U!1)),
% 0.12/0.40 inference(and_elim,[status(thm)],[30])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (apart_point_and_line(Y!2, U!1)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | (distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | apart_point_and_line(X, Z) | (~apart_point_and_line(X, Y)))) | distinct_lines(U!1, line_connecting(X!3, Y!2)) | apart_point_and_line(Y!2, line_connecting(X!3, Y!2)) | (~apart_point_and_line(Y!2, U!1))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (apart_point_and_line(Y!2, line_connecting(X!3, Y!2))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[67, 58, 64, 25])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!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)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!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)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!3, Y!2)) | (~apart_point_and_line(Y!2, line_connecting(X!3, Y!2))) | (~((~distinct_points(Y!2, X!3)) | (~distinct_points(Y!2, Y!2))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[71, 44, 31, 68, 11])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------