%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO185+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO185+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:40:47 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(apart_point_and_line_type, type, (
% 0.18/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.18/0.37 tff(tptp_fun_U_1_type, type, (
% 0.18/0.37 tptp_fun_U_1: $i)).
% 0.18/0.37 tff(tptp_fun_X_3_type, type, (
% 0.18/0.37 tptp_fun_X_3: $i)).
% 0.18/0.37 tff(tptp_fun_V_0_type, type, (
% 0.18/0.37 tptp_fun_V_0: $i)).
% 0.18/0.37 tff(distinct_points_type, type, (
% 0.18/0.37 distinct_points: ( $i * $i ) > $o)).
% 0.18/0.37 tff(intersection_point_type, type, (
% 0.18/0.37 intersection_point: ( $i * $i ) > $i)).
% 0.18/0.37 tff(convergent_lines_type, type, (
% 0.18/0.37 convergent_lines: ( $i * $i ) > $o)).
% 0.18/0.37 tff(tptp_fun_Y_2_type, type, (
% 0.18/0.37 tptp_fun_Y_2: $i)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 ((~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_points(X, intersection_point(U, V))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_points(X, intersection_point(U, V))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V)))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 ((~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (~distinct_points(X, intersection_point(U, V)))) => ((~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V))))) <=> (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_points(X, intersection_point(U, V))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V)))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(3,axiom,(~![X: $i, Y: $i, U: $i, V: $i] : (((distinct_points(X, Y) & convergent_lines(U, V)) & (~distinct_points(X, intersection_point(U, V)))) => ((~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_points(X, intersection_point(U, V))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_points(X, intersection_point(U, V))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_points(X, intersection_point(U, V))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (~![X: $i, Y: $i, U: $i, V: $i] : ((~(distinct_points(X, Y) & convergent_lines(U, V) & (~distinct_points(X, intersection_point(U, V))))) | ((~apart_point_and_line(X, U)) & (~apart_point_and_line(X, V))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.18/0.37 tff(8,plain,(
% 0.18/0.37 ~((~(distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (~distinct_points(X!3, intersection_point(U!1, V!0))))) | ((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(X!3, V!0))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[7])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (distinct_points(X!3, Y!2) & convergent_lines(U!1, V!0) & (~distinct_points(X!3, intersection_point(U!1, V!0)))),
% 0.18/0.37 inference(or_elim,[status(thm)],[8])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (~distinct_points(X!3, intersection_point(U!1, V!0))),
% 0.18/0.37 inference(and_elim,[status(thm)],[9])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (convergent_lines(U!1, V!0)),
% 0.18/0.37 inference(and_elim,[status(thm)],[9])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (^[X: $i, Y: $i, Z: $i] : refl((distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.38 tff(14,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) <=> (apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))))), rewrite(((apart_point_and_line(Z, Y) | apart_point_and_line(Z, X)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))), (((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))) <=> ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))))), rewrite((convergent_lines(X, Y) => ((~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))) | distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))), ((convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y)))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.38 tff(17,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => ((apart_point_and_line(Z, X) | apart_point_and_line(Z, Y)) => distinct_points(Z, intersection_point(X, Y))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.18/0.38 tff(18,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.38 tff(20,plain,(
% 0.18/0.38 ![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[19])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(X!3, intersection_point(U!1, V!0)) | (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0))) | (~convergent_lines(U!1, V!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0))) | (~convergent_lines(U!1, V!0)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 ((distinct_points(X!3, intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0)))) <=> (distinct_points(X!3, intersection_point(U!1, V!0)) | (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0))) | (~convergent_lines(U!1, V!0)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 ((~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1))) <=> (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 ((distinct_points(X!3, intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1)))) <=> (distinct_points(X!3, intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 ((distinct_points(X!3, intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1)))) <=> (distinct_points(X!3, intersection_point(U!1, V!0)) | (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0))) | (~convergent_lines(U!1, V!0)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[25, 23])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(X!3, intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(X!3, intersection_point(U!1, V!0)) | (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0))) | (~convergent_lines(U!1, V!0))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[26])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(X!3, intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0))) | (~convergent_lines(U!1, V!0)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[27, 22])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (distinct_points(X!3, intersection_point(U!1, V!0)) | (~convergent_lines(U!1, V!0)) | (~(apart_point_and_line(X!3, V!0) | apart_point_and_line(X!3, U!1))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | distinct_points(X!3, intersection_point(U!1, V!0)) | (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0))) | (~convergent_lines(U!1, V!0))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[30, 21, 11, 10])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 ((apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0)) | (~apart_point_and_line(X!3, U!1))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 (~apart_point_and_line(X!3, U!1)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 ((apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0)) | (~apart_point_and_line(X!3, V!0))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 (~apart_point_and_line(X!3, V!0)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[34, 31])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 ((~(~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0)))) <=> (apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 (((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(X!3, V!0))) <=> (~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 ((~((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(X!3, V!0)))) <=> (~(~(apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[37])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 ((~((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(X!3, V!0)))) <=> (apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0))),
% 0.18/0.38 inference(transitivity,[status(thm)],[38, 36])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (~((~apart_point_and_line(X!3, U!1)) & (~apart_point_and_line(X!3, V!0)))),
% 0.18/0.38 inference(or_elim,[status(thm)],[8])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (apart_point_and_line(X!3, U!1) | apart_point_and_line(X!3, V!0)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[41, 35, 33])).
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------