%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO170+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:05:43 AM UTC 2025
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : GEO170+2 : TPTP v9.0.0. Released v3.3.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.21/0.35 % WCLimit : 300
% 0.21/0.35 % DateTime : Thu Jun 19 14:38:41 EDT 2025
% 0.21/0.36 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(distinct_points_type, type, (
% 0.21/0.40 distinct_points: ( $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.40 tptp_fun_Y_1: $i)).
% 0.21/0.40 tff(tptp_fun_X_2_type, type, (
% 0.21/0.40 tptp_fun_X_2: $i)).
% 0.21/0.40 tff(apart_point_and_line_type, type, (
% 0.21/0.40 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.40 tff(line_connecting_type, type, (
% 0.21/0.40 line_connecting: ( $i * $i ) > $i)).
% 0.21/0.40 tff(tptp_fun_Z_0_type, type, (
% 0.21/0.40 tptp_fun_Z_0: $i)).
% 0.21/0.40 tff(distinct_lines_type, type, (
% 0.21/0.40 distinct_lines: ( $i * $i ) > $o)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(4,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (![X: $i] : (~distinct_points(X, X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.40 tff(6,plain,(
% 0.21/0.40 ![X: $i] : (~distinct_points(X, X))),
% 0.21/0.40 inference(skolemize,[status(sab)],[5])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (![X: $i] : (~distinct_points(X, X))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(Y!1, Y!1))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (~distinct_points(Y!1, Y!1)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1))) | distinct_points(Y!1, Y!1)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 ((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(X!2, X!2))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (~distinct_points(X!2, X!2)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[12, 7])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1))) | distinct_points(X!2, X!2)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 ((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.21/0.40 tff(16,assumption,(apart_point_and_line(X!2, line_connecting(X!2, Y!1))), introduced(assumption)).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Z, line_connecting(X, Y))) | (~(distinct_points(X, Y) & (~apart_point_and_line(X, Z)) & (~apart_point_and_line(Y, Z)))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Z, line_connecting(X, Y))) | (~(distinct_points(X, Y) & (~apart_point_and_line(X, Z)) & (~apart_point_and_line(Y, Z))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 ((~![X: $i, Y: $i, Z: $i] : (((distinct_points(X, Y) & (~apart_point_and_line(X, Z))) & (~apart_point_and_line(Y, Z))) => (~distinct_lines(Z, line_connecting(X, Y))))) <=> (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Z, line_connecting(X, Y))) | (~(distinct_points(X, Y) & (~apart_point_and_line(X, Z)) & (~apart_point_and_line(Y, Z))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(19,axiom,(~![X: $i, Y: $i, Z: $i] : (((distinct_points(X, Y) & (~apart_point_and_line(X, Z))) & (~apart_point_and_line(Y, Z))) => (~distinct_lines(Z, line_connecting(X, Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Z, line_connecting(X, Y))) | (~(distinct_points(X, Y) & (~apart_point_and_line(X, Z)) & (~apart_point_and_line(Y, Z)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Z, line_connecting(X, Y))) | (~(distinct_points(X, Y) & (~apart_point_and_line(X, Z)) & (~apart_point_and_line(Y, Z)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Z, line_connecting(X, Y))) | (~(distinct_points(X, Y) & (~apart_point_and_line(X, Z)) & (~apart_point_and_line(Y, Z)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (~![X: $i, Y: $i, Z: $i] : ((~distinct_lines(Z, line_connecting(X, Y))) | (~(distinct_points(X, Y) & (~apart_point_and_line(X, Z)) & (~apart_point_and_line(Y, Z)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.21/0.41 tff(24,plain,(
% 0.21/0.41 ~((~distinct_lines(Z!0, line_connecting(X!2, Y!1))) | (~(distinct_points(X!2, Y!1) & (~apart_point_and_line(X!2, Z!0)) & (~apart_point_and_line(Y!1, Z!0)))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[23])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (distinct_points(X!2, Y!1) & (~apart_point_and_line(X!2, Z!0)) & (~apart_point_and_line(Y!1, Z!0))),
% 0.21/0.41 inference(or_elim,[status(thm)],[24])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (distinct_points(X!2, Y!1)),
% 0.21/0.41 inference(and_elim,[status(thm)],[25])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (^[X: $i, Y: $i, Z: $i] : refl(((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_points(Z, X) & distinct_points(Z, Y)) <=> (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))))), rewrite(((~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))), (((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))) <=> ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> (distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))))), rewrite((distinct_points(X, Y) => ((~apart_point_and_line(Z, line_connecting(X, Y))) | (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))), ((distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y)))) <=> ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.41 tff(34,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_points(X, Y) => (apart_point_and_line(Z, line_connecting(X, Y)) => (distinct_points(Z, X) & distinct_points(Z, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','con1')).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.21/0.41 tff(37,plain,(
% 0.21/0.41 ![X: $i, Y: $i, Z: $i] : ((distinct_points(Z, X) & distinct_points(Z, Y)) | (~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[36])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(X!2, line_connecting(X!2, Y!1))) | (~((~distinct_points(X!2, X!2)) | (~distinct_points(X!2, Y!1))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[42, 39, 26, 16, 15])).
% 0.21/0.41 tff(44,plain,(~apart_point_and_line(X!2, line_connecting(X!2, Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (~apart_point_and_line(Y!1, Z!0)),
% 0.21/0.41 inference(and_elim,[status(thm)],[25])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (~apart_point_and_line(X!2, Z!0)),
% 0.21/0.41 inference(and_elim,[status(thm)],[25])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (distinct_lines(Z!0, line_connecting(X!2, Y!1))),
% 0.21/0.41 inference(or_elim,[status(thm)],[24])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (^[X: $i, Y: $i, U: $i, V: $i] : refl((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((distinct_points(X, Y) & distinct_lines(U, V)) <=> (~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> (~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))))), rewrite((~(~((~distinct_points(X, Y)) | (~distinct_lines(U, V))))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((~(distinct_points(X, Y) & distinct_lines(U, V))) <=> ((~distinct_points(X, Y)) | (~distinct_lines(U, V))))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))))), rewrite((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | ((~distinct_points(X, Y)) | (~distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))), ((apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V)))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (^[X: $i, Y: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(X, U) | apart_point_and_line(X, V)) <=> (apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> ((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)))), rewrite(((apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) <=> (apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> ((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)))), rewrite(((apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))), ((((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V)) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U)))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))))), rewrite(((distinct_points(X, Y) & distinct_lines(U, V)) => (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))), (((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : ((distinct_points(X, Y) & distinct_lines(U, V)) => (((apart_point_and_line(X, U) | apart_point_and_line(X, V)) | apart_point_and_line(Y, U)) | apart_point_and_line(Y, V))) <=> ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.41 tff(55,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')).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.21/0.41 tff(58,plain,(
% 0.21/0.41 ![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~(distinct_points(X, Y) & distinct_lines(U, V))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[57])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | ((~distinct_lines(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(Y!1, Z!0) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_lines(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(Y!1, Z!0) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 ((apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, Z!0) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, Z!0) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(Z!0, line_connecting(X!2, Y!1)))) <=> ((~distinct_lines(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(Y!1, Z!0) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, Z!0) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, Z!0) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | ((~distinct_lines(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(Y!1, Z!0) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[62])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, Z!0) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, Z!0) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(Z!0, line_connecting(X!2, Y!1))))) <=> ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_lines(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(Y!1, Z!0) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[63, 61])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(Y!1, Z!0) | apart_point_and_line(X!2, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, Z!0) | (~distinct_points(X!2, Y!1)) | (~distinct_lines(Z!0, line_connecting(X!2, Y!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, U: $i, V: $i] : (apart_point_and_line(Y, V) | apart_point_and_line(Y, U) | apart_point_and_line(X, V) | apart_point_and_line(X, U) | (~distinct_points(X, Y)) | (~distinct_lines(U, V)))) | (~distinct_lines(Z!0, line_connecting(X!2, Y!1))) | apart_point_and_line(X!2, Z!0) | apart_point_and_line(Y!1, Z!0) | (~distinct_points(X!2, Y!1)) | apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 (apart_point_and_line(Y!1, line_connecting(X!2, Y!1)) | apart_point_and_line(X!2, line_connecting(X!2, Y!1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[66, 60, 47, 26, 46, 45])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 (apart_point_and_line(Y!1, line_connecting(X!2, Y!1))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[67, 44])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))) | (~((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1)))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))) | (~((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | ((~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))) | (~((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1)))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 ((~![X: $i, Y: $i, Z: $i] : ((~distinct_points(X, Y)) | (~apart_point_and_line(Z, line_connecting(X, Y))) | (~((~distinct_points(Z, X)) | (~distinct_points(Z, Y)))))) | (~distinct_points(X!2, Y!1)) | (~apart_point_and_line(Y!1, line_connecting(X!2, Y!1))) | (~((~distinct_points(Y!1, X!2)) | (~distinct_points(Y!1, Y!1))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[71, 39, 26, 68, 11])).
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------