%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO215+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:05:59 AM UTC 2025
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO215+2 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.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 14:41:54 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(apart_point_and_line_type, type, (
% 0.20/0.43 apart_point_and_line: ( $i * $i ) > $o)).
% 0.20/0.43 tff(tptp_fun_L_2_type, type, (
% 0.20/0.43 tptp_fun_L_2: $i)).
% 0.20/0.43 tff(intersection_point_type, type, (
% 0.20/0.43 intersection_point: ( $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_M_1_type, type, (
% 0.20/0.43 tptp_fun_M_1: $i)).
% 0.20/0.43 tff(distinct_points_type, type, (
% 0.20/0.43 distinct_points: ( $i * $i ) > $o)).
% 0.20/0.43 tff(convergent_lines_type, type, (
% 0.20/0.43 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.43 tff(unorthogonal_lines_type, type, (
% 0.20/0.43 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.20/0.43 tff(tptp_fun_N_0_type, type, (
% 0.20/0.43 tptp_fun_N_0: $i)).
% 0.20/0.43 tff(distinct_lines_type, type, (
% 0.20/0.43 distinct_lines: ( $i * $i ) > $o)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 (^[X: $i] : refl((~distinct_points(X, X)) <=> (~distinct_points(X, X)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (![X: $i] : (~distinct_points(X, X)) <=> ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(4,axiom,(![X: $i] : (~distinct_points(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart1')).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.43 tff(6,plain,(
% 0.20/0.43 ![X: $i] : (~distinct_points(X, X))),
% 0.20/0.43 inference(skolemize,[status(sab)],[5])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (![X: $i] : (~distinct_points(X, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 ((~![X: $i] : (~distinct_points(X, X))) | (~distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (~distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 ((~(unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))) <=> (~(unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(L!2, M!1))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 ((~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))) <=> (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 ((~![L: $i, M: $i, N: $i] : (convergent_lines(L, M) => (unorthogonal_lines(L, N) | unorthogonal_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(13,axiom,(~![L: $i, M: $i, N: $i] : (convergent_lines(L, M) => (unorthogonal_lines(L, N) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (~![L: $i, M: $i, N: $i] : (unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | (~convergent_lines(L, M)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.20/0.43 tff(18,plain,(
% 0.20/0.43 ~(unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[17])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (~(unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~convergent_lines(L!2, M!1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (convergent_lines(L!2, M!1)),
% 0.20/0.43 inference(or_elim,[status(thm)],[19])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (^[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))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.43 tff(26,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')).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.43 tff(29,plain,(
% 0.20/0.43 ![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))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[28])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (((~![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!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))) <=> ((~![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!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 ((distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))) <=> ((~convergent_lines(L!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 ((~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))) <=> (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 ((distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))) <=> (distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 ((distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))) <=> ((~convergent_lines(L!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[34, 32])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (((~![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!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))) <=> ((~![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!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (((~![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!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))) <=> ((~![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!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[36, 31])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 ((~![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!2, M!1), intersection_point(L!2, M!1)) | (~convergent_lines(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 ((~![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!2, M!1)) | distinct_points(intersection_point(L!2, M!1), intersection_point(L!2, M!1)) | (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (~(apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[39, 30, 20, 9])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 ((apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)) | (~apart_point_and_line(intersection_point(L!2, M!1), L!2))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(42,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(L!2, M!1), L!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 ((apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)) | (~apart_point_and_line(intersection_point(L!2, M!1), M!1))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (~apart_point_and_line(intersection_point(L!2, M!1), M!1)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.20/0.43 tff(45,assumption,(~distinct_lines(M!1, L!2)), introduced(assumption)).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (^[X: $i] : refl((~distinct_lines(X, X)) <=> (~distinct_lines(X, X)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (![X: $i] : (~distinct_lines(X, X)) <=> ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(49,axiom,(![X: $i] : (~distinct_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart2')).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.43 tff(51,plain,(
% 0.20/0.43 ![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.43 inference(skolemize,[status(sab)],[50])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (![X: $i] : (~distinct_lines(X, X))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 ((~![X: $i] : (~distinct_lines(X, X))) | (~distinct_lines(L!2, L!2))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (~distinct_lines(L!2, L!2)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : refl(((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : rewrite((convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y)) <=> ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.44 tff(60,axiom,(![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','ceq3')).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.44 tff(63,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.44 inference(skolemize,[status(sab)],[62])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(L!2, M!1)) | distinct_lines(L!2, M!1))) <=> ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(L!2, M!1)) | distinct_lines(L!2, M!1))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | ((~convergent_lines(L!2, M!1)) | distinct_lines(L!2, M!1))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) | (~convergent_lines(L!2, M!1)) | distinct_lines(L!2, M!1)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 (distinct_lines(L!2, M!1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[67, 64, 20])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(X, Z) | distinct_lines(Y, Z)) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))))), rewrite((distinct_lines(X, Y) => (distinct_lines(Y, Z) | distinct_lines(X, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))), ((distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.44 tff(74,axiom,(![X: $i, Y: $i, Z: $i] : (distinct_lines(X, Y) => (distinct_lines(X, Z) | distinct_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax','apart5')).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.20/0.44 tff(77,plain,(
% 0.20/0.44 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[76])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(L!2, L!2) | distinct_lines(M!1, L!2) | (~distinct_lines(L!2, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(L!2, L!2) | distinct_lines(M!1, L!2) | (~distinct_lines(L!2, M!1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 ((distinct_lines(M!1, L!2) | distinct_lines(L!2, L!2) | (~distinct_lines(L!2, M!1))) <=> (distinct_lines(L!2, L!2) | distinct_lines(M!1, L!2) | (~distinct_lines(L!2, M!1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(M!1, L!2) | distinct_lines(L!2, L!2) | (~distinct_lines(L!2, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(L!2, L!2) | distinct_lines(M!1, L!2) | (~distinct_lines(L!2, M!1))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(M!1, L!2) | distinct_lines(L!2, L!2) | (~distinct_lines(L!2, M!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(L!2, L!2) | distinct_lines(M!1, L!2) | (~distinct_lines(L!2, M!1)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[81, 79])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | (distinct_lines(M!1, L!2) | distinct_lines(L!2, L!2) | (~distinct_lines(L!2, M!1)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | distinct_lines(X, Z) | (~distinct_lines(X, Y)))) | distinct_lines(L!2, L!2) | distinct_lines(M!1, L!2) | (~distinct_lines(L!2, M!1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[84, 78, 68, 54, 45])).
% 0.20/0.44 tff(86,plain,(distinct_lines(M!1, L!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (~unorthogonal_lines(L!2, N!0)),
% 0.20/0.44 inference(or_elim,[status(thm)],[19])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 (~unorthogonal_lines(M!1, N!0)),
% 0.20/0.44 inference(or_elim,[status(thm)],[19])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (^[A: $i, L: $i, M: $i, N: $i] : refl((apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (^[A: $i, L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((apart_point_and_line(A, L) | apart_point_and_line(A, M)) <=> (apart_point_and_line(A, M) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> ((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)))), rewrite(((apart_point_and_line(A, M) | apart_point_and_line(A, L)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> ((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)))), rewrite(((apart_point_and_line(A, M) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))), ((((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))))), rewrite((distinct_lines(L, M) => (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))), ((distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N))) <=> ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.44 tff(94,axiom,(![A: $i, L: $i, M: $i, N: $i] : (distinct_lines(L, M) => (((apart_point_and_line(A, L) | apart_point_and_line(A, M)) | unorthogonal_lines(L, N)) | unorthogonal_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax','ouo1')).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.44 tff(97,plain,(
% 0.20/0.44 ![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[96])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 (![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~distinct_lines(M!1, L!2)) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~distinct_lines(M!1, L!2)) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 ((apart_point_and_line(intersection_point(L!2, M!1), L!2) | unorthogonal_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | (~distinct_lines(M!1, L!2))) <=> (unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~distinct_lines(M!1, L!2)) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(L!2, M!1), L!2) | unorthogonal_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | (~distinct_lines(M!1, L!2)))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~distinct_lines(M!1, L!2)) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[100])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(L!2, M!1), L!2) | unorthogonal_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | (~distinct_lines(M!1, L!2)))) <=> ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~distinct_lines(M!1, L!2)) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2))),
% 0.20/0.44 inference(transitivity,[status(thm)],[101, 99])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | (apart_point_and_line(intersection_point(L!2, M!1), L!2) | unorthogonal_lines(L!2, N!0) | unorthogonal_lines(M!1, N!0) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | (~distinct_lines(M!1, L!2)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 ((~![A: $i, L: $i, M: $i, N: $i] : (apart_point_and_line(A, M) | unorthogonal_lines(M, N) | unorthogonal_lines(L, N) | apart_point_and_line(A, L) | (~distinct_lines(L, M)))) | unorthogonal_lines(M!1, N!0) | unorthogonal_lines(L!2, N!0) | (~distinct_lines(M!1, L!2)) | apart_point_and_line(intersection_point(L!2, M!1), M!1) | apart_point_and_line(intersection_point(L!2, M!1), L!2)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[104, 98, 88, 87, 86, 44, 42])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------