%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO226+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:06:03 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO226+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:42:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(distinct_points_type, type, (
% 0.12/0.37 distinct_points: ( $i * $i ) > $o)).
% 0.12/0.37 tff(intersection_point_type, type, (
% 0.12/0.37 intersection_point: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_M_0_type, type, (
% 0.12/0.37 tptp_fun_M_0: $i)).
% 0.12/0.37 tff(tptp_fun_L_1_type, type, (
% 0.12/0.37 tptp_fun_L_1: $i)).
% 0.12/0.37 tff(apart_point_and_line_type, type, (
% 0.12/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.37 tff(point_type, type, (
% 0.12/0.37 point: $i > $o)).
% 0.12/0.37 tff(convergent_lines_type, type, (
% 0.12/0.37 convergent_lines: ( $i * $i ) > $o)).
% 0.12/0.37 tff(line_type, type, (
% 0.12/0.37 line: $i > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![X: $i] : (~distinct_points(X, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,(
% 0.12/0.37 ![X: $i] : (~distinct_points(X, X))),
% 0.12/0.37 inference(skolemize,[status(sab)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![X: $i] : (~distinct_points(X, X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (^[X: $i] : refl((~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0))))) <=> (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0))))) <=> ![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (^[X: $i] : rewrite((~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0))))) <=> (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0))))) <=> ![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (((line(L!1) & line(M!0) & convergent_lines(L!1, M!0)) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0)))))) <=> (line(L!1) & line(M!0) & convergent_lines(L!1, M!0) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 ((~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))) <=> (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 ((~![L: $i, M: $i] : (((line(L) & line(M)) & convergent_lines(L, M)) => ?[X: $i] : (point(X) => ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))) <=> (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(17,axiom,(~![L: $i, M: $i] : (((line(L) & line(M)) & convergent_lines(L, M)) => ?[X: $i] : (point(X) => ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (~![L: $i, M: $i] : ((~(line(L) & line(M) & convergent_lines(L, M))) | ?[X: $i] : ((~point(X)) | ((~apart_point_and_line(X, L)) & (~apart_point_and_line(X, M)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (line(L!1) & line(M!0) & convergent_lines(L!1, M!0) & ![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![X: $i] : (~((~point(X)) | ((~apart_point_and_line(X, L!1)) & (~apart_point_and_line(X, M!0)))))),
% 0.12/0.38 inference(and_elim,[status(thm)],[22])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 11])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 ((~![X: $i] : (~((~point(X)) | (~(apart_point_and_line(X, L!1) | apart_point_and_line(X, M!0)))))) | (~((~point(intersection_point(L!1, M!0))) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~((~point(intersection_point(L!1, M!0))) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (((~point(intersection_point(L!1, M!0))) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)))) | (apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (convergent_lines(L!1, M!0)),
% 0.12/0.38 inference(and_elim,[status(thm)],[22])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (^[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))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.38 tff(36,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/sandbox2/benchmark/Axioms/GEO008+0.ax','con2')).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.12/0.38 tff(39,plain,(
% 0.12/0.38 ![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))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (((~![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))))) | ((~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!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))))) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)))) <=> ((~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 ((~(apart_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), L!1))) <=> (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 ((distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), L!1)))) <=> (distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[43])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 ((distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), L!1)))) <=> ((~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[44, 42])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (((~![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(intersection_point(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), L!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))))) | ((~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[45])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (((~![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(intersection_point(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), L!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))))) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[46, 41])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((~![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(intersection_point(L!1, M!0), intersection_point(L!1, M!0)) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), M!0) | apart_point_and_line(intersection_point(L!1, M!0), L!1))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 ((~![X: $i, Y: $i, Z: $i] : (distinct_points(Z, intersection_point(X, Y)) | (~convergent_lines(X, Y)) | (~(apart_point_and_line(Z, Y) | apart_point_and_line(Z, X))))) | (~convergent_lines(L!1, M!0)) | (~(apart_point_and_line(intersection_point(L!1, M!0), L!1) | apart_point_and_line(intersection_point(L!1, M!0), M!0))) | distinct_points(intersection_point(L!1, M!0), intersection_point(L!1, M!0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[49, 40, 30, 29, 9])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------